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<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/2409.07731">arXiv:2409.07731</a> <span> [<a href="https://arxiv.org/pdf/2409.07731">pdf</a>, <a href="https://arxiv.org/format/2409.07731">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"> Group delay controlled by the decoherence of a single artificial atom </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cheng%2C+Y+-">Y. -T. Cheng</a>, <a href="/search/quant-ph?searchtype=author&query=Hsieh%2C+K+-">K. -M. Hsieh</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+B+-">B. -Y. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Niu%2C+Z+Q">Z. Q. Niu</a>, <a href="/search/quant-ph?searchtype=author&query=Aziz%2C+F">F. Aziz</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -H. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Wen%2C+P+Y">P. Y. Wen</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+K+-">K. -T. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+Y+-">Y. -H. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+J+C">J. C. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Kockum%2C+A+F">A. F. Kockum</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+Z+-">Z. -R. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Lu%2C+Y">Y. Lu</a>, <a href="/search/quant-ph?searchtype=author&query=Hoi%2C+I+-">I. -C. Hoi</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="2409.07731v1-abstract-short" style="display: inline;"> The ability to slow down light at the single-photon level has applications in quantum information processing and other quantum technologies. We demonstrate two methods, both using just a single artificial atom, enabling dynamic control over microwave light velocities in waveguide quantum electrodynamics (waveguide QED). Our methods are based on two distinct mechanisms harnessing the balance betwee… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.07731v1-abstract-full').style.display = 'inline'; document.getElementById('2409.07731v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.07731v1-abstract-full" style="display: none;"> The ability to slow down light at the single-photon level has applications in quantum information processing and other quantum technologies. We demonstrate two methods, both using just a single artificial atom, enabling dynamic control over microwave light velocities in waveguide quantum electrodynamics (waveguide QED). Our methods are based on two distinct mechanisms harnessing the balance between radiative and non-radiative decay rates of a superconducting artificial atom in front of a mirror. In the first method, we tune the radiative decay of the atom using interference effects due to the mirror; in the second method, we pump the atom to control its non-radiative decay through the Autler--Townes effect. When the half the radiative decay rate exceeds the non-radiative decay rate, we observe positive group delay; conversely, dominance of the non-radiative decay rate results in negative group delay. Our results advance signal-processing capabilities in waveguide QED. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.07731v1-abstract-full').style.display = 'none'; document.getElementById('2409.07731v1-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> 11 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.14562">arXiv:2311.14562</a> <span> [<a href="https://arxiv.org/pdf/2311.14562">pdf</a>, <a href="https://arxiv.org/ps/2311.14562">ps</a>, <a href="https://arxiv.org/format/2311.14562">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"> Steady-state phases and interaction-induced depletion in a driven-dissipative chirally-coupled dissimilar atomic array </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Chung%2C+S">Shao-Hung Chung</a>, <a href="/search/quant-ph?searchtype=author&query=Handayana%2C+I+G+N+Y">I Gusti Ngurah Yudi Handayana</a>, <a href="/search/quant-ph?searchtype=author&query=Tsao%2C+Y">Yi-Lin Tsao</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+C">Chun-Chi Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Jen%2C+H+H">H. H. Jen</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="2311.14562v1-abstract-short" style="display: inline;"> A nanophotonic waveguide coupled with an atomic array forms one of the strongly-coupled quantum interfaces to showcase many fascinating collective features of quantum dynamics. In particular for a dissimilar array of two different interparticle spacings with competing photon-mediated dipole-dipole interactions and directionality of couplings, we study the steady-state phases of atomic excitations… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.14562v1-abstract-full').style.display = 'inline'; document.getElementById('2311.14562v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.14562v1-abstract-full" style="display: none;"> A nanophotonic waveguide coupled with an atomic array forms one of the strongly-coupled quantum interfaces to showcase many fascinating collective features of quantum dynamics. In particular for a dissimilar array of two different interparticle spacings with competing photon-mediated dipole-dipole interactions and directionality of couplings, we study the steady-state phases of atomic excitations under a weakly-driven condition of laser field. We identify a partial set of steady-state phases of the driven system composed of combinations of steady-state solutions in a homogeneous array. We also reveal an intricate role of the atom at the interface of the dissimilar array in determining the steady-state phases and find an alteration in the dichotomy of the phases strongly associated with steady-state distributions with crystalline orders. We further investigate in detail the interaction-induced depletion in half of the dissimilar array. This blockaded region results from two contrasting interparticle spacings near the reciprocal coupling regime, which is evidenced from the analytical solutions under the reciprocal coupling. Our results can provide insights in the driven-dissipative quantum phases of atomic excitations with nonreciprocal couplings and pave the avenues toward quantum simulations of exotic many-body states essential for quantum information applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.14562v1-abstract-full').style.display = 'none'; document.getElementById('2311.14562v1-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> 24 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </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">6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Research 6, 023232 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.15361">arXiv:2309.15361</a> <span> [<a href="https://arxiv.org/pdf/2309.15361">pdf</a>, <a href="https://arxiv.org/format/2309.15361">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="Atomic Physics">physics.atom-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/PhysRevResearch.6.013159">10.1103/PhysRevResearch.6.013159 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Atomic excitation delocalization at the clean to disordered interface in a chirally-coupled atomic array </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Wu%2C+C+-">C. -C. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+K+-">K. -T. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Handayana%2C+I+G+N+Y">I G. N. Y. Handayana</a>, <a href="/search/quant-ph?searchtype=author&query=Chien%2C+C+-">C. -H. Chien</a>, <a href="/search/quant-ph?searchtype=author&query=Goswami%2C+S">S. Goswami</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Y+-">Y. -C. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Jen%2C+H+H">H. H. Jen</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="2309.15361v3-abstract-short" style="display: inline;"> In one-dimensional quantum emitter systems, the dynamics of atomic excitations are influenced by the collective coupling between emitters through photon-mediated dipole-dipole interactions. By introducing positional disorders in a portion of the atomic array, we investigate the delocalization phenomena at the interface between disordered zone and clean zone. The excitation is initialized as symmet… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.15361v3-abstract-full').style.display = 'inline'; document.getElementById('2309.15361v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.15361v3-abstract-full" style="display: none;"> In one-dimensional quantum emitter systems, the dynamics of atomic excitations are influenced by the collective coupling between emitters through photon-mediated dipole-dipole interactions. By introducing positional disorders in a portion of the atomic array, we investigate the delocalization phenomena at the interface between disordered zone and clean zone. The excitation is initialized as symmetric Dicke states in the disordered zone, and several measures are used to quantify the excitation localization. We first use population imbalance and half-chain entropy to investigate the excitation dynamics under time evolutions, and further investigate the crossover of excitation localization to delocalization via the gap ratio from the eigenspectrum in the reciprocal coupling case. In particular, we study the participation ratio of the whole chain and the photon loss ratio between both ends of the atomic chain, which can be used to quantify the delocalization crossover in the non-reciprocal coupling cases. Furthermore, by increasing the overall size or the ratio of the disordered zone under a fixed number of the whole chain, we observe that excitation localization occurs at a smaller disorder strength in the former case, while in the latter, a facilitation of the delocalization appears when a significant ratio of clean zone to disordered zone is applied. Our results can reveal the competition between the clean zone and the disordered zone sizes on localization phenomenon, give insights to non-equilibrium dynamics in the emitter-waveguide interface, and provide potential applications in quantum information processing. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.15361v3-abstract-full').style.display = 'none'; document.getElementById('2309.15361v3-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 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.13750">arXiv:2305.13750</a> <span> [<a href="https://arxiv.org/pdf/2305.13750">pdf</a>, <a href="https://arxiv.org/format/2305.13750">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.109.023705">10.1103/PhysRevA.109.023705 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Tuning atom-field interaction via phase shaping </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Cheng%2C+Y+-">Y. -T. Cheng</a>, <a href="/search/quant-ph?searchtype=author&query=Chien%2C+C+-">C. -H. Chien</a>, <a href="/search/quant-ph?searchtype=author&query=Hsieh%2C+K+-">K. -M. Hsieh</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -H. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Wen%2C+P+Y">P. Y. Wen</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+W+-">W. -J. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Lu%2C+Y">Y. Lu</a>, <a href="/search/quant-ph?searchtype=author&query=Aziz%2C+F">F. Aziz</a>, <a href="/search/quant-ph?searchtype=author&query=Lee%2C+C+-">C. -P. Lee</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+K+-">K. -T. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+C+-">C. -Y. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+J+C">J. C. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Chuu%2C+C+-">C. -S. Chuu</a>, <a href="/search/quant-ph?searchtype=author&query=Kockum%2C+A+F">A. F. Kockum</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+Y+-">Y. -H. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Hoi%2C+I+-">I. -C. Hoi</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="2305.13750v2-abstract-short" style="display: inline;"> A coherent electromagnetic field can be described by its amplitude, frequency, and phase. All these properties can influence the interaction between the field and an atom. Here we demonstrate the phase shaping of microwaves that are scattered by a superconducting artificial atom coupled to the end of a semi-infinite 1D transmission line. In particular, we input a weak exponentially rising pulse wi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.13750v2-abstract-full').style.display = 'inline'; document.getElementById('2305.13750v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.13750v2-abstract-full" style="display: none;"> A coherent electromagnetic field can be described by its amplitude, frequency, and phase. All these properties can influence the interaction between the field and an atom. Here we demonstrate the phase shaping of microwaves that are scattered by a superconducting artificial atom coupled to the end of a semi-infinite 1D transmission line. In particular, we input a weak exponentially rising pulse with phase modulation to a transmon qubit. We observe that field-atom interaction can be tuned from nearly full interaction (interaction efficiency, i.e., amount of the field energy interacting with the atom, of 94.5%) to effectively no interaction (interaction efficiency 3.5%). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.13750v2-abstract-full').style.display = 'none'; document.getElementById('2305.13750v2-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> 26 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review A 109, 023705 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.02790">arXiv:2112.02790</a> <span> [<a href="https://arxiv.org/pdf/2112.02790">pdf</a>, <a href="https://arxiv.org/ps/2112.02790">ps</a>, <a href="https://arxiv.org/format/2112.02790">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.105.063711">10.1103/PhysRevA.105.063711 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Resonant Dipole-Dipole Interactions in Electromagnetically Induced Transparency </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Jen%2C+H+H">H. H. Jen</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Y+-">Y. -C. Chen</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="2112.02790v4-abstract-short" style="display: inline;"> Resonant dipole-dipole interaction (RDDI) is ubiquitous in light-matter interacting systems and is responsible for many fascinating properties of collective radiations. Here we theoretically investigate the role of RDDI in electromagnetically induced transparency (EIT). The resonant dipole-dipole interactions manifest in the cooperative spontaneous emission of the probe light transition, which giv… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.02790v4-abstract-full').style.display = 'inline'; document.getElementById('2112.02790v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.02790v4-abstract-full" style="display: none;"> Resonant dipole-dipole interaction (RDDI) is ubiquitous in light-matter interacting systems and is responsible for many fascinating properties of collective radiations. Here we theoretically investigate the role of RDDI in electromagnetically induced transparency (EIT). The resonant dipole-dipole interactions manifest in the cooperative spontaneous emission of the probe light transition, which give rise a broadened linewidth and associated collective frequency shift. This cooperative linewidth originates from the nonlocal and long-range RDDI, which can be determined by the atomic density, optical depth, and macroscopic length scales of the atomic ensemble. We present that EIT spectroscopy essentially demonstrates all-order multiple scattering of RDDI. Furthermore, we find that EIT transparency window becomes narrower as the cooperative linewidth increases, which essentially reduces the storage efficiency of slow light as EIT-based quantum memory application. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.02790v4-abstract-full').style.display = 'none'; document.getElementById('2112.02790v4-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> 25 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">4 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 105, 063711 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2012.15084">arXiv:2012.15084</a> <span> [<a href="https://arxiv.org/pdf/2012.15084">pdf</a>, <a href="https://arxiv.org/format/2012.15084">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/10.1021/acs.nanolett.2c02578">10.1021/acs.nanolett.2c02578 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Deterministic loading and phase shaping of microwaves onto a single artificial atom </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lin%2C+W+-">W. -J. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Lu%2C+Y">Y. Lu</a>, <a href="/search/quant-ph?searchtype=author&query=Wen%2C+P+Y">P. Y. Wen</a>, <a href="/search/quant-ph?searchtype=author&query=Cheng%2C+Y+-">Y. -T. Cheng</a>, <a href="/search/quant-ph?searchtype=author&query=Lee%2C+C+-">C. -P. Lee</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+K+-">K. -T. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Chiang%2C+K+-">K. -H. Chiang</a>, <a href="/search/quant-ph?searchtype=author&query=Hsieh%2C+M+C">M. C. Hsieh</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+J+C">J. C. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Chuu%2C+C+-">C. -S. Chuu</a>, <a href="/search/quant-ph?searchtype=author&query=Nori%2C+F">F. Nori</a>, <a href="/search/quant-ph?searchtype=author&query=Kockum%2C+A+F">A. F. Kockum</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Delsing%2C+P">P. Delsing</a>, <a href="/search/quant-ph?searchtype=author&query=Hoi%2C+I+-">I. -C. Hoi</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="2012.15084v1-abstract-short" style="display: inline;"> Loading quantum information deterministically onto a quantum node is an important step towards a quantum network. Here, we demonstrate that coherent-state microwave photons, with an optimal temporal waveform, can be efficiently loaded onto a single superconducting artificial atom in a semi-infinite one-dimensional (1D) transmission-line waveguide. Using a weak coherent state (average photon number… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.15084v1-abstract-full').style.display = 'inline'; document.getElementById('2012.15084v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2012.15084v1-abstract-full" style="display: none;"> Loading quantum information deterministically onto a quantum node is an important step towards a quantum network. Here, we demonstrate that coherent-state microwave photons, with an optimal temporal waveform, can be efficiently loaded onto a single superconducting artificial atom in a semi-infinite one-dimensional (1D) transmission-line waveguide. Using a weak coherent state (average photon number N<<1 with an exponentially rising waveform, whose time constant matches the decoherence time of the artificial atom, we demonstrate a loading efficiency of above 94% from 1D semi-free space to the artificial atom. We also show that Fock-state microwave photons can be deterministically loaded with an efficiency of 98.5%. We further manipulate the phase of the coherent state exciting the atom, enabling coherent control of the loading process. Our results open up promising applications in realizing quantum networks based on waveguide quantum electrodynamics (QED). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.15084v1-abstract-full').style.display = 'none'; document.getElementById('2012.15084v1-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 December, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nano Letters 2022 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.09482">arXiv:1905.09482</a> <span> [<a href="https://arxiv.org/pdf/1905.09482">pdf</a>, <a href="https://arxiv.org/ps/1905.09482">ps</a>, <a href="https://arxiv.org/format/1905.09482">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/10.1088/1361-6455/ab7556">10.1088/1361-6455/ab7556 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spectral shaping of the biphoton state from multiplexed thermal atomic ensembles </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Chang%2C+T+H">T. H. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Jen%2C+H+H">H. H. Jen</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="1905.09482v1-abstract-short" style="display: inline;"> We theoretically investigate the spectral property of a biphoton state from multiplexed thermal atomic ensembles. This biphoton state originates from the cascade emissions, which can be generated by two weak pump fields under four-wave mixing condition. Under this condition, a signal photon from the upper transition, chosen in a telecommunication bandwidth, can be generated along with a correlated… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.09482v1-abstract-full').style.display = 'inline'; document.getElementById('1905.09482v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.09482v1-abstract-full" style="display: none;"> We theoretically investigate the spectral property of a biphoton state from multiplexed thermal atomic ensembles. This biphoton state originates from the cascade emissions, which can be generated by two weak pump fields under four-wave mixing condition. Under this condition, a signal photon from the upper transition, chosen in a telecommunication bandwidth, can be generated along with a correlated idler photon from the lower infrared transition. We can spectrally shape the biphoton state by multiplexing the atomic ensembles with frequency-shifted emissions, where the entropy of entanglement can be analyzed via Schmidt decompositions. We find that this spectral entanglement increases when more vapor cells are multiplexed with correlated or anti-correlated signal and idler fields. The eigenvalues in Schmidt bases approach degenerate under this multiplexing scheme, and corresponding Schmidt numbers can be larger than the number of the multiplexed vapor cells, showing the enlarged entropy of entanglement and excess correlated modes in continuous frequency spaces. We also investigate the lowest entropy of entanglement allowed in the multiplexing scheme, which is preferential for generating a pure single photon source. This shows the potentiality to spectrally shape the biphoton source, where high-capacity spectral modes can be applied in long-distance quantum communication and multimode quantum information processing. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.09482v1-abstract-full').style.display = 'none'; document.getElementById('1905.09482v1-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 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. B: At. Mol. Opt. Phys. 53, 085403 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.00558">arXiv:1905.00558</a> <span> [<a href="https://arxiv.org/pdf/1905.00558">pdf</a>, <a href="https://arxiv.org/ps/1905.00558">ps</a>, <a href="https://arxiv.org/format/1905.00558">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> </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.101.023830">10.1103/PhysRevA.101.023830 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Subradiance dynamics in a singly-excited chiral-coupled atomic chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Jen%2C+H+H">H. H. Jen</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+M+-">M. -S. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+Y+-">Y. -C. Chen</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="1905.00558v2-abstract-short" style="display: inline;"> We theoretically investigate the subradiance dynamics in a nonreciprocal chiral-coupled atomic chain, in which infinite-range dipole-dipole interaction emerges in the dissipation. We find that super- and subradiance are both present in the dissipation process following single photon excitation, and the decay dynamics shows burst emissions from uniform initial excitations, which reflects the influe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.00558v2-abstract-full').style.display = 'inline'; document.getElementById('1905.00558v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.00558v2-abstract-full" style="display: none;"> We theoretically investigate the subradiance dynamics in a nonreciprocal chiral-coupled atomic chain, in which infinite-range dipole-dipole interaction emerges in the dissipation. We find that super- and subradiance are both present in the dissipation process following single photon excitation, and the decay dynamics shows burst emissions from uniform initial excitations, which reflects the influence of atomic ordering on the propagation of light-induced atom-atom correlations. By tuning the nonreciprocal couplings in the chiral-coupled atomic system, we show that the subradiance dynamics can be greatly modified. We further study the effect of atomic local disorder, and find occurrence of plateaus on the decay curve dependent on the defect locations, as well as persistent localized excitations induced by disorders. We also discuss the effect of imperfections of systems on the subradiance dynamics. Our results show rich opportunities in the chiral-coupled system toward photon storage and routing. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.00558v2-abstract-full').style.display = 'none'; document.getElementById('1905.00558v2-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 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">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 101, 023830 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.12473">arXiv:1904.12473</a> <span> [<a href="https://arxiv.org/pdf/1904.12473">pdf</a>, <a href="https://arxiv.org/format/1904.12473">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> </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.123.233602">10.1103/PhysRevLett.123.233602 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Large collective Lamb shift of two distant superconducting artificial atoms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Wen%2C+P+Y">P. Y. Wen</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+K+-">K. -T. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Kockum%2C+A+F">A. F. Kockum</a>, <a href="/search/quant-ph?searchtype=author&query=Suri%2C+B">B. Suri</a>, <a href="/search/quant-ph?searchtype=author&query=Ian%2C+H">H. Ian</a>, <a href="/search/quant-ph?searchtype=author&query=Chen%2C+J+C">J. C. Chen</a>, <a href="/search/quant-ph?searchtype=author&query=Mao%2C+S+Y">S. Y. Mao</a>, <a href="/search/quant-ph?searchtype=author&query=Chiu%2C+C+C">C. C. Chiu</a>, <a href="/search/quant-ph?searchtype=author&query=Delsing%2C+P">P. Delsing</a>, <a href="/search/quant-ph?searchtype=author&query=Nori%2C+F">F. Nori</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Hoi%2C+I+-">I. -C. Hoi</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="1904.12473v1-abstract-short" style="display: inline;"> Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift rea… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.12473v1-abstract-full').style.display = 'inline'; document.getElementById('1904.12473v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.12473v1-abstract-full" style="display: none;"> Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.12473v1-abstract-full').style.display = 'none'; document.getElementById('1904.12473v1-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, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">7+5 pages, 4+2 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. 123, 233602 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1807.06817">arXiv:1807.06817</a> <span> [<a href="https://arxiv.org/pdf/1807.06817">pdf</a>, <a href="https://arxiv.org/ps/1807.06817">ps</a>, <a href="https://arxiv.org/format/1807.06817">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/10.1088/1361-6455/ab1303">10.1088/1361-6455/ab1303 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spectrally entangled biphoton state of cascade emissions from a Doppler-broadened atomic ensemble </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Chang%2C+T+H">T. H. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Jen%2C+H+H">H. H. Jen</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="1807.06817v1-abstract-short" style="display: inline;"> We theoretically investigate the spectral property of biphoton state from the cascade emissions from a Doppler-broadened atomic ensemble. This biphoton state is spontaneously created in the four-wave-mixing process. The upper transition of the emissions lies in telecom bandwidth, which prevails in fiber-based quantum communication for low-loss transmission. We obtain the spectral property in terms… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.06817v1-abstract-full').style.display = 'inline'; document.getElementById('1807.06817v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1807.06817v1-abstract-full" style="display: none;"> We theoretically investigate the spectral property of biphoton state from the cascade emissions from a Doppler-broadened atomic ensemble. This biphoton state is spontaneously created in the four-wave-mixing process. The upper transition of the emissions lies in telecom bandwidth, which prevails in fiber-based quantum communication for low-loss transmission. We obtain the spectral property in terms of superradiant decay rates of the lower transition, excitation pulse durations, and temperature of the medium. We quantify their frequency entanglement by Schmidt decomposition and find that more entangled source can be generated with longer excitation pulses, enhanced decay rates, and significant Doppler broadening. A minimally entangled biphoton source can also be located at some optimal temperature of the atoms. This allows spectral shaping of continuous frequency entanglement, which is useful in multimode long-distance quantum communication. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.06817v1-abstract-full').style.display = 'none'; document.getElementById('1807.06817v1-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 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 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">4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Phys. B: At. Mol. Opt. Phys. 52, 135501 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1112.1975">arXiv:1112.1975</a> <span> [<a href="https://arxiv.org/pdf/1112.1975">pdf</a>, <a href="https://arxiv.org/ps/1112.1975">ps</a>, <a href="https://arxiv.org/format/1112.1975">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.85.033831">10.1103/PhysRevA.85.033831 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Superradiance in spin-$J$ particles: Effects of multiple levels </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Yelin%2C+S+F">S. F. Yelin</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="1112.1975v1-abstract-short" style="display: inline;"> We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems, and compare the results based on a novel approach we have developed in {[}Yelin \textit{et al.}, arXiv:quant-ph/0509184{]}. Using this formalism we derive an effective two-b… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1112.1975v1-abstract-full').style.display = 'inline'; document.getElementById('1112.1975v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1112.1975v1-abstract-full" style="display: none;"> We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems, and compare the results based on a novel approach we have developed in {[}Yelin \textit{et al.}, arXiv:quant-ph/0509184{]}. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-$j$ particles, taking into account the coherence of transitions between different atomic levels. We find that the superradiance, which is well-known as a many-body phenomenon, can also be modified by multiple level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have multi-level structure which is partially harmonic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1112.1975v1-abstract-full').style.display = 'none'; document.getElementById('1112.1975v1-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 December, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 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">11 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 85, 033831 (2012) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1103.2400">arXiv:1103.2400</a> <span> [<a href="https://arxiv.org/pdf/1103.2400">pdf</a>, <a href="https://arxiv.org/ps/1103.2400">ps</a>, <a href="https://arxiv.org/format/1103.2400">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="Atomic Physics">physics.atom-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/10.1038/ncomms1374">10.1038/ncomms1374 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Islam%2C+R">R. Islam</a>, <a href="/search/quant-ph?searchtype=author&query=Edwards%2C+E+E">E. E. Edwards</a>, <a href="/search/quant-ph?searchtype=author&query=Kim%2C+K">K. Kim</a>, <a href="/search/quant-ph?searchtype=author&query=Korenblit%2C+S">S. Korenblit</a>, <a href="/search/quant-ph?searchtype=author&query=Noh%2C+C">C. Noh</a>, <a href="/search/quant-ph?searchtype=author&query=Carmichael%2C+H">H. Carmichael</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+C+-+J">C. -C. Joseph Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Freericks%2C+J+K">J. K. Freericks</a>, <a href="/search/quant-ph?searchtype=author&query=Monroe%2C+C">C. Monroe</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="1103.2400v1-abstract-short" style="display: inline;"> A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the use of quantum logic gates on a standard controllable quantum system to efficiently simulate the behavior of a model Hamiltonian. Recent experiments using trap… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.2400v1-abstract-full').style.display = 'inline'; document.getElementById('1103.2400v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1103.2400v1-abstract-full" style="display: none;"> A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the use of quantum logic gates on a standard controllable quantum system to efficiently simulate the behavior of a model Hamiltonian. Recent experiments using trapped ions and neutral atoms have realized quantum simulation of Ising model in presence of external magnetic fields, and showed almost arbitrary control in generating non-trivial Ising coupling patterns. Here we use laser-cooled trapped 171-Yb+ ions to simulate the emergence of magnetism in a system of interacting spins by implementing a fully-connected non-uniform ferromagnetic Ising model in a transverse magnetic field. To link this quantum simulation to condensed matter physics, we measure scalable correlation functions and order parameters appropriate for the description of larger systems, such as various moments of the magnetization. By increasing the Ising coupling strengths compared with the external field, the crossover from paramagnetism to ferromagnetic order sharpens as the system is scaled up from N = 2 to 9 trapped ion spins. This points toward the onset of a quantum phase transition that should become infinitely sharp as the system approaches the macroscopic scale. We compare the measured ground state order to theory, which may become intractable for non-uniform Ising couplings as the number of spins grows beyond 20- 30 and even NP complete for a fully-connected frustrated Ising model, making this experiment an important benchmark for large-scale quantum simulation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1103.2400v1-abstract-full').style.display = 'none'; document.getElementById('1103.2400v1-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> 11 March, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 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">7 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nature Commun. 2, 377 (2011) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1011.5885">arXiv:1011.5885</a> <span> [<a href="https://arxiv.org/pdf/1011.5885">pdf</a>, <a href="https://arxiv.org/ps/1011.5885">ps</a>, <a href="https://arxiv.org/format/1011.5885">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="Statistical Mechanics">cond-mat.stat-mech</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.106.230402">10.1103/PhysRevLett.106.230402 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Sharp phase transitions in a small frustrated network of trapped ion spins </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Monroe%2C+C">C. Monroe</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="1011.5885v1-abstract-short" style="display: inline;"> Sharp quantum phase transitions typically require a large system with many particles. Here we show that for a frustrated fully-connected Ising spin network represented by trapped atomic ions, the competition between different spin orders leads to rich phase transitions whose sharpness scales exponentially with the number of spins. This unusual finite-size scaling behavior opens up the possibility… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1011.5885v1-abstract-full').style.display = 'inline'; document.getElementById('1011.5885v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1011.5885v1-abstract-full" style="display: none;"> Sharp quantum phase transitions typically require a large system with many particles. Here we show that for a frustrated fully-connected Ising spin network represented by trapped atomic ions, the competition between different spin orders leads to rich phase transitions whose sharpness scales exponentially with the number of spins. This unusual finite-size scaling behavior opens up the possibility of observing sharp quantum phase transitions in a system of just a few trapped ion spins. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1011.5885v1-abstract-full').style.display = 'none'; document.getElementById('1011.5885v1-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> 25 November, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">5 pages, 4 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. 106, 230402 (2011) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1009.0089">arXiv:1009.0089</a> <span> [<a href="https://arxiv.org/pdf/1009.0089">pdf</a>, <a href="https://arxiv.org/format/1009.0089">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Strongly Correlated Electrons">cond-mat.str-el</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.105.265703">10.1103/PhysRevLett.105.265703 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Temperature driven structural phase transition for trapped ions and its experimental detection </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Gong%2C+Z">Zhe-Xuan Gong</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="1009.0089v1-abstract-short" style="display: inline;"> A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1009.0089v1-abstract-full').style.display = 'inline'; document.getElementById('1009.0089v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1009.0089v1-abstract-full" style="display: none;"> A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1009.0089v1-abstract-full').style.display = 'none'; document.getElementById('1009.0089v1-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> 1 September, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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, 5 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, 265703 (2010) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1005.4160">arXiv:1005.4160</a> <span> [<a href="https://arxiv.org/pdf/1005.4160">pdf</a>, <a href="https://arxiv.org/format/1005.4160">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/PhysRevB.82.060412">10.1103/PhysRevB.82.060412 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Simulation and Phase Diagram of the Transverse Field Ising Model with Three Atomic Spins </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Edwards%2C+E+E">E. E. Edwards</a>, <a href="/search/quant-ph?searchtype=author&query=Korenblit%2C+S">S. Korenblit</a>, <a href="/search/quant-ph?searchtype=author&query=Kim%2C+K">K. Kim</a>, <a href="/search/quant-ph?searchtype=author&query=Islam%2C+R">R. Islam</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+M+-">M. -S. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Freericks%2C+J+K">J. K. Freericks</a>, <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a>, <a href="/search/quant-ph?searchtype=author&query=Monroe%2C+C">C. Monroe</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="1005.4160v1-abstract-short" style="display: inline;"> We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields and form of the Ising couplings, leading to a phase diagram of magnetic order in this microscopic system. The technique is scalable to much larger numbers of trap… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.4160v1-abstract-full').style.display = 'inline'; document.getElementById('1005.4160v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1005.4160v1-abstract-full" style="display: none;"> We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields and form of the Ising couplings, leading to a phase diagram of magnetic order in this microscopic system. The technique is scalable to much larger numbers of trapped ion spins, where phase transitions approaching the thermodynamic limit can be studied in cases where theory becomes intractable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.4160v1-abstract-full').style.display = 'none'; document.getElementById('1005.4160v1-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> 22 May, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">5 pages, 4 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. B 82, 060412(R) (2010) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1001.4559">arXiv:1001.4559</a> <span> [<a href="https://arxiv.org/pdf/1001.4559">pdf</a>, <a href="https://arxiv.org/ps/1001.4559">ps</a>, <a href="https://arxiv.org/format/1001.4559">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/10.1088/1367-2630/13/7/075015">10.1088/1367-2630/13/7/075015 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Thermalization and temperature distribution in a driven ion chain </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="1001.4559v1-abstract-short" style="display: inline;"> We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1001.4559v1-abstract-full').style.display = 'inline'; document.getElementById('1001.4559v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1001.4559v1-abstract-full" style="display: none;"> We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the ion coupling rate to the bath, the location of the driven ions, and the dissipation rates of the other ions in the chain. Through simulation of the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1001.4559v1-abstract-full').style.display = 'none'; document.getElementById('1001.4559v1-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> 25 January, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">5 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> New J. Phys. 13 075015 (2011) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0901.0579">arXiv:0901.0579</a> <span> [<a href="https://arxiv.org/pdf/0901.0579">pdf</a>, <a href="https://arxiv.org/ps/0901.0579">ps</a>, <a href="https://arxiv.org/format/0901.0579">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/10.1209/0295-5075/86/60004">10.1209/0295-5075/86/60004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Large Scale Quantum Computation in an Anharmonic Linear Ion Trap </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lin%2C+G+-">G. -D. Lin</a>, <a href="/search/quant-ph?searchtype=author&query=Zhu%2C+S+-">S. -L. Zhu</a>, <a href="/search/quant-ph?searchtype=author&query=Islam%2C+R">R. Islam</a>, <a href="/search/quant-ph?searchtype=author&query=Kim%2C+K">K. Kim</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+M+-">M. -S. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Korenblit%2C+S">S. Korenblit</a>, <a href="/search/quant-ph?searchtype=author&query=Monroe%2C+C">C. Monroe</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</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="0901.0579v2-abstract-short" style="display: inline;"> We propose a large-scale quantum computer architecture by stabilizing a single large linear ion chain in a very simple trap geometry. By confining ions in an anharmonic linear trap with nearly uniform spacing between ions, we show that high-fidelity quantum gates can be realized in large linear ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motiona… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0901.0579v2-abstract-full').style.display = 'inline'; document.getElementById('0901.0579v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0901.0579v2-abstract-full" style="display: none;"> We propose a large-scale quantum computer architecture by stabilizing a single large linear ion chain in a very simple trap geometry. By confining ions in an anharmonic linear trap with nearly uniform spacing between ions, we show that high-fidelity quantum gates can be realized in large linear ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0901.0579v2-abstract-full').style.display = 'none'; document.getElementById('0901.0579v2-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 January, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 January, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2009. </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, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Europhys. Lett. 86 (2009) 60004 </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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