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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.13777">arXiv:2412.13777</a> <span> [<a href="https://arxiv.org/pdf/2412.13777">pdf</a>, <a href="https://arxiv.org/format/2412.13777">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Reduced density matrix and entanglement Hamiltonian for a free real scalar field on an interval </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.13777v1-abstract-short" style="display: inline;"> An exact result for the reduced density matrix on a finite interval for a $1+1$ dimensional free real scalar field in the ground state is presented. In the massless case, the Williamson decomposition of the appearing kernels is explicitly performed, which allows to reproduce the known result for the entanglement (modular) Hamiltonian and, for a small mass $M$ of the field, find the leading… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.13777v1-abstract-full').style.display = 'inline'; document.getElementById('2412.13777v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.13777v1-abstract-full" style="display: none;"> An exact result for the reduced density matrix on a finite interval for a $1+1$ dimensional free real scalar field in the ground state is presented. In the massless case, the Williamson decomposition of the appearing kernels is explicitly performed, which allows to reproduce the known result for the entanglement (modular) Hamiltonian and, for a small mass $M$ of the field, find the leading $\sim1/\ln M$ non-local corrections. In the opposite $M\to\infty$ case, it is argued that, up to terms $O(M^{-1/2})$, the entanglement Hamiltonian is local with the density being the Hamiltonian density spatially modulated by a triangular-shape function. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.13777v1-abstract-full').style.display = 'none'; document.getElementById('2412.13777v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.11856">arXiv:2108.11856</a> <span> [<a href="https://arxiv.org/pdf/2108.11856">pdf</a>, <a href="https://arxiv.org/format/2108.11856">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.22331/q-2022-06-07-731">10.22331/q-2022-06-07-731 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Topological phonons in arrays of ultracold dipolar particles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Di+Liberto%2C+M">Marco Di Liberto</a>, <a href="/search/quant-ph?searchtype=author&query=Kruckenhauser%2C+A">Andreas Kruckenhauser</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2108.11856v2-abstract-short" style="display: inline;"> The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for developing new fault-tolerant applications. We discuss how to design and study a large variety of topology-related phenomena for phonon-like collective modes in a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.11856v2-abstract-full').style.display = 'inline'; document.getElementById('2108.11856v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.11856v2-abstract-full" style="display: none;"> The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for developing new fault-tolerant applications. We discuss how to design and study a large variety of topology-related phenomena for phonon-like collective modes in arrays of ultracold polarized dipolar particles. These modes are coherently propagating vibrational excitations, corresponding to oscillations of particles around their equilibrium positions, which exist in the regime where long-range interactions dominate over single-particle motion. We demonstrate that such systems offer a distinct and versatile tool to investigate a wide range of topological effects in a single experimental setup with a chosen underlying crystal structure by simply controlling the anisotropy of the interactions via the orientation of the external polarizing field. Our results show that arrays of dipolar particles provide a promising unifying platform to investigate topological phenomena with phononic modes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.11856v2-abstract-full').style.display = 'none'; document.getElementById('2108.11856v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages + 9 figures and 1 table</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Quantum 6, 731 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.00214">arXiv:2006.00214</a> <span> [<a href="https://arxiv.org/pdf/2006.00214">pdf</a>, <a href="https://arxiv.org/format/2006.00214">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PRXQuantum.1.020302">10.1103/PRXQuantum.1.020302 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Monitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Vasilyev%2C+D+V">Denis V. Vasilyev</a>, <a href="/search/quant-ph?searchtype=author&query=Grankin%2C+A">Andrey Grankin</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Sieberer%2C+L+M">Lukas M. Sieberer</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2006.00214v2-abstract-short" style="display: inline;"> We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays us… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.00214v2-abstract-full').style.display = 'inline'; document.getElementById('2006.00214v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.00214v2-abstract-full" style="display: none;"> We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to identify signatures of ergodic vs. non-ergodic dynamics, which we illustrate for disordered 1D Heisenberg and Floquet spin models on Rydberg platforms. Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies, and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.00214v2-abstract-full').style.display = 'none'; document.getElementById('2006.00214v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 11 figures, accepted for publication in PRX Quantum</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PRX Quantum 1, 020302 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2005.02213">arXiv:2005.02213</a> <span> [<a href="https://arxiv.org/pdf/2005.02213">pdf</a>, <a href="https://arxiv.org/format/2005.02213">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.104.L011302">10.1103/PhysRevA.104.L011302 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> High-energy Bragg scattering measurements of a dipolar supersolid </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Petter%2C+D">D. Petter</a>, <a href="/search/quant-ph?searchtype=author&query=Patscheider%2C+A">A. Patscheider</a>, <a href="/search/quant-ph?searchtype=author&query=Natale%2C+G">G. Natale</a>, <a href="/search/quant-ph?searchtype=author&query=Mark%2C+M+J">M. J. Mark</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Bijnen%2C+R+v">R. v. Bijnen</a>, <a href="/search/quant-ph?searchtype=author&query=Roccuzzo%2C+S+M">S. M. Roccuzzo</a>, <a href="/search/quant-ph?searchtype=author&query=Recati%2C+A">A. Recati</a>, <a href="/search/quant-ph?searchtype=author&query=Blakie%2C+B">B. Blakie</a>, <a href="/search/quant-ph?searchtype=author&query=Baillie%2C+D">D. Baillie</a>, <a href="/search/quant-ph?searchtype=author&query=Chomaz%2C+L">L. Chomaz</a>, <a href="/search/quant-ph?searchtype=author&query=Ferlaino%2C+F">F. Ferlaino</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2005.02213v2-abstract-short" style="display: inline;"> We present an experimental and theoretical study of the high-energy excitation spectra of a dipolar supersolid. Using Bragg spectroscopy, we study the scattering response of the system to a high-energy probe, enabling measurements of the dynamic structure factor. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary Bose-Einstein cond… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.02213v2-abstract-full').style.display = 'inline'; document.getElementById('2005.02213v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2005.02213v2-abstract-full" style="display: none;"> We present an experimental and theoretical study of the high-energy excitation spectra of a dipolar supersolid. Using Bragg spectroscopy, we study the scattering response of the system to a high-energy probe, enabling measurements of the dynamic structure factor. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary Bose-Einstein condensate to a supersolid state. Yet the observed reduction is faster than the one theoretically predicted by the Bogoliubov-de-Gennes theory. Based on an intuitive semi-analytic model and real-time simulations, we primarily attribute such a discrepancy to the out-of-equilibrium phase dynamics, which although not affecting the system global coherence, reduces its response. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.02213v2-abstract-full').style.display = 'none'; document.getElementById('2005.02213v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, 4+10 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 104, 011302 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.11792">arXiv:2001.11792</a> <span> [<a href="https://arxiv.org/pdf/2001.11792">pdf</a>, <a href="https://arxiv.org/format/2001.11792">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.102.023320">10.1103/PhysRevA.102.023320 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Many-Body Physics with Ultracold Polar Molecules: Nanostructured Potential Barriers and Interactions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Kruckenhauser%2C+A">Andreas Kruckenhauser</a>, <a href="/search/quant-ph?searchtype=author&query=Sieberer%2C+L+M">Lukas M. Sieberer</a>, <a href="/search/quant-ph?searchtype=author&query=Tobias%2C+W+G">William G. Tobias</a>, <a href="/search/quant-ph?searchtype=author&query=Matsuda%2C+K">Kyle Matsuda</a>, <a href="/search/quant-ph?searchtype=author&query=De+Marco%2C+L">Luigi De Marco</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+J">Jun-Ru Li</a>, <a href="/search/quant-ph?searchtype=author&query=Valtolina%2C+G">Giacomo Valtolina</a>, <a href="/search/quant-ph?searchtype=author&query=Rey%2C+A+M">Ana Maria Rey</a>, <a href="/search/quant-ph?searchtype=author&query=Ye%2C+J">Jun Ye</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.11792v2-abstract-short" style="display: inline;"> We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential barriers and two-body dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.11792v2-abstract-full').style.display = 'inline'; document.getElementById('2001.11792v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.11792v2-abstract-full" style="display: none;"> We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential barriers and two-body dipolar interactions on a spatial scale of tens of nanometers to strongly enhance energy scales and, therefore, relax temperature requirements for observing new quantum phases of engineered many-body systems. We consider and compare two approaches. In the first, nanoscale barriers are generated with standing wave optical light fields exploiting optical nonlinearities. In the second, static electric field gradients in combination with microwave dressing are used to write nanostructured spatial patterns on the induced electric dipole moments, and thus dipolar interactions. We study the formation of inter-layer and interface bound states of molecules in these configurations, and provide detailed estimates for binding energies and expected losses for present experimental setups. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.11792v2-abstract-full').style.display = 'none'; document.getElementById('2001.11792v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 102, 023320 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1906.07649">arXiv:1906.07649</a> <span> [<a href="https://arxiv.org/pdf/1906.07649">pdf</a>, <a href="https://arxiv.org/format/1906.07649">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.100.033610">10.1103/PhysRevA.100.033610 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Stroboscopic painting of optical potentials for atoms with subwavelength resolution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lacki%2C+M">M. Lacki</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A Baranov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1906.07649v1-abstract-short" style="display: inline;"> We propose and discuss a method to engineer stroboscopically arbitrary one-dimensional optical potentials with subwavelength resolution. Our approach is based on subwavelength optical potential barriers for atoms in the dark state in an optical 螞system, which we use as a stroboscopic drawing tool by controlling their amplitude and position by changing the amplitude and the phase of the control Rab… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.07649v1-abstract-full').style.display = 'inline'; document.getElementById('1906.07649v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1906.07649v1-abstract-full" style="display: none;"> We propose and discuss a method to engineer stroboscopically arbitrary one-dimensional optical potentials with subwavelength resolution. Our approach is based on subwavelength optical potential barriers for atoms in the dark state in an optical 螞system, which we use as a stroboscopic drawing tool by controlling their amplitude and position by changing the amplitude and the phase of the control Rabi frequency in the 螞system. We demonstrate the ability of the method to engineer both smooth and comb-like periodic potentials for atoms in the dark state, and establish the range of stroboscopic frequencies when the quasienergies of the stroboscopic Floquet system reproduce the band structure of the time-averaged potentials. In contrast to usual stroboscopic engineering which becomes increasingly accurate with increasing the stroboscopic frequency, the presence of the bright states of the 螞-system results in the upper bound on the frequency, above which the dynamics strongly mixes the dark and the bright channels, and the description in terms of a time-averaged potential fails. For frequencies below this bound, the lowest Bloch band of quasienergies contains several avoided-crossing coming from the coupling to high energy states, with widths decreasing with increasing stroboscopic frequency. We analyze the influence of these avoided crossings on the dynamics in the lowest band using Bloch oscillations as an example, and establish the parameter regimes when the population transfer from the lowest band into high bands is negligible. We also present protocols for loading atoms into the lowest band of the painted potentials starting from atoms in the lowest band of a standard optical lattice. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.07649v1-abstract-full').style.display = 'none'; document.getElementById('1906.07649v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 9 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 100, 033610 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1805.09220">arXiv:1805.09220</a> <span> [<a href="https://arxiv.org/pdf/1805.09220">pdf</a>, <a href="https://arxiv.org/format/1805.09220">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.98.023852">10.1103/PhysRevA.98.023852 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Scanning Microscope for Cold Atoms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Yang%2C+D">Dayou Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Vasilyev%2C+D+V">Denis V. Vasilyev</a>, <a href="/search/quant-ph?searchtype=author&query=Laflamme%2C+C">Catherine Laflamme</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1805.09220v2-abstract-short" style="display: inline;"> We present a detailed theoretical description of an atomic scanning microscope in a cavity QED setup proposed in Phys. Rev. Lett. 120, 133601 (2018). The microscope continuously observes atomic densities with optical subwavelength resolution in a nondestructive way. The super-resolution is achieved by engineering an internal atomic dark state with a sharp spatial variation of population of a groun… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.09220v2-abstract-full').style.display = 'inline'; document.getElementById('1805.09220v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1805.09220v2-abstract-full" style="display: none;"> We present a detailed theoretical description of an atomic scanning microscope in a cavity QED setup proposed in Phys. Rev. Lett. 120, 133601 (2018). The microscope continuously observes atomic densities with optical subwavelength resolution in a nondestructive way. The super-resolution is achieved by engineering an internal atomic dark state with a sharp spatial variation of population of a ground level dispersively coupled to the cavity field. Thus, the atomic position encoded in the internal state is revealed as a phase shift of the light reflected from the cavity in a homodyne experiment. Our theoretical description of the microscope operation is based on the stochastic master equation describing the conditional time evolution of the atomic system under continuous observation as a competition between dynamics induced by the Hamiltonian of the system, decoherence effects due to atomic spontaneous decay, and the measurement backaction. Within our approach we relate the observed homodyne current with a local atomic density, and discuss the emergence of a quantum nondemolition measurement regime allowing continuous observation of spatial densities of quantum motional eigenstates without measurement backaction in a single experimental run. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.09220v2-abstract-full').style.display = 'none'; document.getElementById('1805.09220v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 August, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 May, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16+6 pages, 10+1 figures; published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 98, 023852 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1702.04662">arXiv:1702.04662</a> <span> [<a href="https://arxiv.org/pdf/1702.04662">pdf</a>, <a href="https://arxiv.org/format/1702.04662">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.96.033602">10.1103/PhysRevA.96.033602 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Adiabatic state preparation of stripe phases with strongly magnetic atoms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Mazloom%2C+A">Azadeh Mazloom</a>, <a href="/search/quant-ph?searchtype=author&query=Vermersch%2C+B">Beno卯t Vermersch</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Dalmonte%2C+M">Marcello Dalmonte</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1702.04662v1-abstract-short" style="display: inline;"> We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground state manifold. The protocol is tested with cluster-mean-field time-dependent variational ans盲tze, validated by comparison with exact resu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.04662v1-abstract-full').style.display = 'inline'; document.getElementById('1702.04662v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1702.04662v1-abstract-full" style="display: none;"> We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground state manifold. The protocol is tested with cluster-mean-field time-dependent variational ans盲tze, validated by comparison with exact results for small systems, which enable us to simulate the dynamics of systems with up to 64 sites during the state-preparation protocol. This allows, in particular, to estimate the time required for preparation of the stripe phase with high fidelity under real experimental conditions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.04662v1-abstract-full').style.display = 'none'; document.getElementById('1702.04662v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 February, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 96, 033602 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1702.02651">arXiv:1702.02651</a> <span> [<a href="https://arxiv.org/pdf/1702.02651">pdf</a>, <a href="https://arxiv.org/format/1702.02651">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.95.043632">10.1103/PhysRevA.95.043632 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Coupled Atomic Wires in a Synthetic Magnetic Field </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Budich%2C+J+C">J. C. Budich</a>, <a href="/search/quant-ph?searchtype=author&query=Elben%2C+A">A. Elben</a>, <a href="/search/quant-ph?searchtype=author&query=%C5%81%C4%85cki%2C+M">M. 艁膮cki</a>, <a href="/search/quant-ph?searchtype=author&query=Sterdyniak%2C+A">A. Sterdyniak</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1702.02651v2-abstract-short" style="display: inline;"> We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as well as Meissner phases and Vortex phases in double-wires. With one continuous and one discrete… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.02651v2-abstract-full').style.display = 'inline'; document.getElementById('1702.02651v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1702.02651v2-abstract-full" style="display: none;"> We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [Kane et al. PRL {\bf{88}}, 036401 (2002)], as well as Meissner phases and Vortex phases in double-wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e. the Harper-Hofstadter model and the two leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semi-continuous Harper-Hofstadter model accessible with cold atom experiments. For the minimal setup of a double-wire, we explore how a sub-wavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in non-planar geometries such as cylinders, discs, and tori. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1702.02651v2-abstract-full').style.display = 'none'; document.getElementById('1702.02651v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 April, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 February, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 95, 043632 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1506.06977">arXiv:1506.06977</a> <span> [<a href="https://arxiv.org/pdf/1506.06977">pdf</a>, <a href="https://arxiv.org/format/1506.06977">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mesoscale and Nanoscale Physics">cond-mat.mes-hall</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.92.165118">10.1103/PhysRevB.92.165118 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Majoranas in Noisy Kitaev Wires </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Hu%2C+Y">Ying Hu</a>, <a href="/search/quant-ph?searchtype=author&query=Cai%2C+Z">Zi Cai</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1506.06977v1-abstract-short" style="display: inline;"> Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which is naturally immune against microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum system from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1506.06977v1-abstract-full').style.display = 'inline'; document.getElementById('1506.06977v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1506.06977v1-abstract-full" style="display: none;"> Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which is naturally immune against microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum system from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana edge modes storing qubits to investigate the effects of classical noise in the crossover from the quasi-static to the fast fluctuation regime. We present detailed results for the Majorana edge correlations, and fidelity of braiding operations for both global and local noise sources preserving parity symmetry, such as random chemical potentials and phase fluctuations. While in general noise will induce heating and dephasing, we identify examples of long-lived quantum correlations in presence of fast noise due to motional narrowing, where external noise drives the system rapidly between the topological and non-topological phases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1506.06977v1-abstract-full').style.display = 'none'; document.getElementById('1506.06977v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. B 92, 165118 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1312.6583">arXiv:1312.6583</a> <span> [<a href="https://arxiv.org/pdf/1312.6583">pdf</a>, <a href="https://arxiv.org/format/1312.6583">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.89.022319">10.1103/PhysRevA.89.022319 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hybrid Topological Quantum Computation with Majorana Fermions: A Cold Atom Setup </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Laflamme%2C+C">C. Laflamme</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Kraus%2C+C+V">C. V. Kraus</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1312.6583v2-abstract-short" style="display: inline;"> In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Major… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.6583v2-abstract-full').style.display = 'inline'; document.getElementById('1312.6583v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1312.6583v2-abstract-full" style="display: none;"> In this paper we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Majorana fermions via a single parity measurement. We then introduce a proposal for the efficient, robust and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. There, well-controlled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient non-destructive protocol to check for errors in the mapping. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.6583v2-abstract-full').style.display = 'none'; document.getElementById('1312.6583v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 December, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 18 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 89, 022319 (2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.5135">arXiv:1302.5135</a> <span> [<a href="https://arxiv.org/pdf/1302.5135">pdf</a>, <a href="https://arxiv.org/format/1302.5135">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1367-2630/15/8/085001">10.1088/1367-2630/15/8/085001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Topology by dissipation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Bardyn%2C+C+-">C. -E. Bardyn</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Kraus%2C+C+V">C. V. Kraus</a>, <a href="/search/quant-ph?searchtype=author&query=Rico%2C+E">E. Rico</a>, <a href="/search/quant-ph?searchtype=author&query=Imamoglu%2C+A">A. Imamoglu</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Diehl%2C+S">S. Diehl</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.5135v1-abstract-short" style="display: inline;"> Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.5135v1-abstract-full').style.display = 'inline'; document.getElementById('1302.5135v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.5135v1-abstract-full" style="display: none;"> Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix which replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences mainly arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in a Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.5135v1-abstract-full').style.display = 'none'; document.getElementById('1302.5135v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">61 pages, 8 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.1824">arXiv:1302.1824</a> <span> [<a href="https://arxiv.org/pdf/1302.1824">pdf</a>, <a href="https://arxiv.org/format/1302.1824">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.111.203001">10.1103/PhysRevLett.111.203001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Braiding of Atomic Majorana Fermions in Wire Networks and Implementation of the Deutsch-Josza Algorithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Kraus%2C+C+V">Christina V. Kraus</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.1824v1-abstract-short" style="display: inline;"> We propose an efficient protocol for braiding atomic Majorana fermions in wire networks with AMO techniques and demonstrate its robustness against experimentally relevant errors. Based on this protocol we provide a topologically protected implementation of the Deutsch-Josza algorithm. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.1824v1-abstract-full" style="display: none;"> We propose an efficient protocol for braiding atomic Majorana fermions in wire networks with AMO techniques and demonstrate its robustness against experimentally relevant errors. Based on this protocol we provide a topologically protected implementation of the Deutsch-Josza algorithm. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.1824v1-abstract-full').style.display = 'none'; document.getElementById('1302.1824v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 111, 203001 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.0701">arXiv:1302.0701</a> <span> [<a href="https://arxiv.org/pdf/1302.0701">pdf</a>, <a href="https://arxiv.org/format/1302.0701">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.111.173004">10.1103/PhysRevLett.111.173004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Majorana edge states in two atomic wires coupled by pair-hopping </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Kraus%2C+C+V">Christina V. Kraus</a>, <a href="/search/quant-ph?searchtype=author&query=Dalmonte%2C+M">Marcello Dalmonte</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Laeuchli%2C+A+M">Andreas M. Laeuchli</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.0701v1-abstract-short" style="display: inline;"> We present evidence for the existence of Majorana edge states in a number conserving theory describing a system of spinless fermions on two wires that are coupled by a pair hopping. Our analysis is based on the combination of a qualitative low energy approach and numerical techniques using the Density Matrix Renormalization Group. We also discuss an experimental realization of pair-hopping interac… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.0701v1-abstract-full').style.display = 'inline'; document.getElementById('1302.0701v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.0701v1-abstract-full" style="display: none;"> We present evidence for the existence of Majorana edge states in a number conserving theory describing a system of spinless fermions on two wires that are coupled by a pair hopping. Our analysis is based on the combination of a qualitative low energy approach and numerical techniques using the Density Matrix Renormalization Group. We also discuss an experimental realization of pair-hopping interactions in cold atom gases confined in optical lattices, and its possible alternative applications to quantum simulation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.0701v1-abstract-full').style.display = 'none'; document.getElementById('1302.0701v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 111, 173004 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1201.3253">arXiv:1201.3253</a> <span> [<a href="https://arxiv.org/pdf/1201.3253">pdf</a>, <a href="https://arxiv.org/format/1201.3253">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1367-2630/14/11/113036">10.1088/1367-2630/14/11/113036 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Probing Atomic Majorana Fermions in Optical Lattices </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Kraus%2C+C+V">Christina V. Kraus</a>, <a href="/search/quant-ph?searchtype=author&query=Diehl%2C+S">Sebastian Diehl</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1201.3253v2-abstract-short" style="display: inline;"> We introduce a one-dimensional system of fermionic atoms in an optical lattice whose phase diagram includes topological states of different symmetry classes. These states can be identified by their zero-energy edge modes which are Majorana fermions. We propose several universal methods of detecting the Majorana edge states, based on their genuine features: zero-energy, localized character of the w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.3253v2-abstract-full').style.display = 'inline'; document.getElementById('1201.3253v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1201.3253v2-abstract-full" style="display: none;"> We introduce a one-dimensional system of fermionic atoms in an optical lattice whose phase diagram includes topological states of different symmetry classes. These states can be identified by their zero-energy edge modes which are Majorana fermions. We propose several universal methods of detecting the Majorana edge states, based on their genuine features: zero-energy, localized character of the wave functions, and induced non-local fermionic correlations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.3253v2-abstract-full').style.display = 'none'; document.getElementById('1201.3253v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 April, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 January, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> New J. Phys. 14 (2012) 113036 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1201.2112">arXiv:1201.2112</a> <span> [<a href="https://arxiv.org/pdf/1201.2112">pdf</a>, <a href="https://arxiv.org/format/1201.2112">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.109.130402">10.1103/PhysRevLett.109.130402 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Bardyn%2C+C+-">C. -E. Bardyn</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Rico%2C+E">E. Rico</a>, <a href="/search/quant-ph?searchtype=author&query=Imamoglu%2C+A">A. Imamoglu</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Diehl%2C+S">S. Diehl</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1201.2112v3-abstract-short" style="display: inline;"> We investigate dissipation-induced p-wave paired states of fermions in two dimensions and show the existence of spatially separated Majorana zero modes in a phase with vanishing Chern number. We construct an explicit and natural model of a dissipative vortex that traps a single of these modes, and establish its topological origin by mapping the problem to a chiral one-dimensional wire where we obs… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.2112v3-abstract-full').style.display = 'inline'; document.getElementById('1201.2112v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1201.2112v3-abstract-full" style="display: none;"> We investigate dissipation-induced p-wave paired states of fermions in two dimensions and show the existence of spatially separated Majorana zero modes in a phase with vanishing Chern number. We construct an explicit and natural model of a dissipative vortex that traps a single of these modes, and establish its topological origin by mapping the problem to a chiral one-dimensional wire where we observe a non-equilibrium topological phase transition characterized by an abrupt change of a topological invariant (winding number). We show that the existence of a single Majorana zero mode in the vortex core is intimately tied to the dissipative nature of our model. Engineered dissipation opens up possibilities for experimentally realizing such states with no Hamiltonian counterpart. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1201.2112v3-abstract-full').style.display = 'none'; document.getElementById('1201.2112v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 August, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 January, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 2 figures; with supplementary material (11 pages); to appear in PRL</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 109, 130402 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1105.5947">arXiv:1105.5947</a> <span> [<a href="https://arxiv.org/pdf/1105.5947">pdf</a>, <a href="https://arxiv.org/format/1105.5947">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/nphys2106">10.1038/nphys2106 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Topology by Dissipation in Atomic Quantum Wires </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Diehl%2C+S">S. Diehl</a>, <a href="/search/quant-ph?searchtype=author&query=Rico%2C+E">E. Rico</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">M. A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">P. Zoller</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1105.5947v1-abstract-short" style="display: inline;"> Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been exclusively discussed in a Hamiltonian context, we show that such phases and the associated topological protection and phenomena also emerge in open quantum systems wit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1105.5947v1-abstract-full').style.display = 'inline'; document.getElementById('1105.5947v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1105.5947v1-abstract-full" style="display: none;"> Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been exclusively discussed in a Hamiltonian context, we show that such phases and the associated topological protection and phenomena also emerge in open quantum systems with engineered dissipation. The specific system studied here is a quantum wire of spinless atomic fermions in an optical lattice coupled to a bath. The key feature of the dissipative dynamics described by a Lindblad master equation is the existence of Majorana edge modes, representing a non-local decoherence free subspace. The isolation of the edge states is enforced by a dissipative gap in the p-wave paired bulk of the wire. We describe dissipative non-Abelian braiding operations within the Majorana subspace, and we illustrate the insensitivity to imperfections. Topological protection is granted by a nontrivial winding number of the system density matrix. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1105.5947v1-abstract-full').style.display = 'none'; document.getElementById('1105.5947v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 May, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature Physics 7, 971 (2011) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1004.5420">arXiv:1004.5420</a> <span> [<a href="https://arxiv.org/pdf/1004.5420">pdf</a>, <a href="https://arxiv.org/format/1004.5420">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.105.073202">10.1103/PhysRevLett.105.073202 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Universal rates for reactive ultracold polar molecules in reduced dimensions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Micheli%2C+A">Andrea Micheli</a>, <a href="/search/quant-ph?searchtype=author&query=Idziaszek%2C+Z">Zbigniew Idziaszek</a>, <a href="/search/quant-ph?searchtype=author&query=Pupillo%2C+G">Guido Pupillo</a>, <a href="/search/quant-ph?searchtype=author&query=Baranov%2C+M+A">Mikhail A. Baranov</a>, <a href="/search/quant-ph?searchtype=author&query=Zoller%2C+P">Peter Zoller</a>, <a href="/search/quant-ph?searchtype=author&query=Julienne%2C+P+S">Paul S. Julienne</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1004.5420v1-abstract-short" style="display: inline;"> Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping str… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1004.5420v1-abstract-full').style.display = 'inline'; document.getElementById('1004.5420v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1004.5420v1-abstract-full" style="display: none;"> Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1004.5420v1-abstract-full').style.display = 'none'; document.getElementById('1004.5420v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 April, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 105, 073202 (2010) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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