Modeling quantum light-matter interactions in waveguide QED with retardation, nonlinear interactions, and a time-delayed feedback: Matrix product states versus a space-discretized waveguide model

Sofia Arranz Regidor, Gavin Crowder, Howard Carmichael +1 more

arXiv:2011.12205Physical Review ResearchApr 9, 202152 citations

Bulletin of the Korean Chemical Society

Discrete-time Quantum Dynamics for Non-perturbative Study of Matter-Light Interactions

Young Gie Ohr, Dae-Hyun Baik, Jongmin Lee, Byung Chan Eu

Published Jan 1, 1989• 0 citations

OpenAlex

Related papers

Quantum simulation of light-matter interaction

Jochen Braumüller, Michael Marthaler, Andre Schneider +4 more

Jan 1, 20180 citations

Observation of discrete time quasicrystal in Rydberg atomic gases

Dong-Yang Zhu, Zheng-Yuan Zhang, Qi-Feng Wang +17 more

Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry ${{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}$ . By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of ${{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}$ -symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry $${{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}$$. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of $${{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}$$-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.

arXiv:2509.21248Nature CommunicationsJul 29, 20261 citation

Time-dependent quantum dynamics

SC Althorpe, Pavel Soldán, Gabriel G. Balint‐Kurti

Jan 1, 20014 citations

Quasi-Discrete Time Crystals in the Quasiperiodically Driven Lipkin–Meshkov–Glick Model

Sk Anisur, W. Vincent Liu, Sayan Choudhury

A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasi-periodic Thue-Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host "quasi-discrete time crystal" (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of "all-to-all" interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasi-periodic Thue-Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host "quasi-discrete time crystal" (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of "all-to-all" interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.

arXiv:2109.05318EntropyJun 7, 20253 citations

Quantum Description of Light Interactions with Matter

Springer eBooksAug 11, 20050 citations

Modeling quantum light-matter interactions in waveguide QED with retardation, nonlinear interactions, and a time-delayed feedback: Matrix product states versus a space-discretized waveguide model

Sofia Arranz Regidor, Gavin Crowder, Howard Carmichael +1 more

We present two different methods for modeling non-Markovian quantum light-matter interactions in waveguide QED systems, using matrix product states (MPSs) and a space-discretized waveguide (SDW) model.After describing the general theory and implementation of both approaches, we compare and contrast these methods directly on three topical problems of interest in waveguide-QED, including (i) a two-level system (TLS) coupled to an infinite (one-dimensional) waveguide, (ii) a TLS coupled to a terminated waveguide with a time-delayed coherent feedback, and (iii) two spatially separated TLSs coupled within an infinite waveguide.Both approaches are shown to efficiently describe multiphoton nonlinear dynamics in highly non-Markovian regimes, and we highlight the advantages and disadvantages of these methods for modeling waveguide QED interactions, including their implementation in PYTHON, computational run times, and ease of conceptual understanding.We explore both vacuum dynamics as well as regimes of strong optical pumping, where a weak excitation approximation cannot be applied.The MPS approach scales better when modeling multiphoton dynamics and long delay times and explicitly includes non-Markovian memory effects.In contrast, the SDW model accounts for non-Markovian effects through space discretization and solves Markovian equations of motion, yet rigorously includes the effects of retardation.The SDW model, based on an extension of recent collisional pictures in quantum optics, is solved through quantum trajectory techniques and can more easily add in additional dissipation processes, including off-chip decay and TLS pure dephasing.The impact of these processes is shown directly on feedback-induced population trapping and TLS entanglement between spatially separated TLSs.We present two different methods for modeling non-Markovian quantum light-matter interactions in waveguide QED systems, using matrix product states (MPSs) and a space-discretized waveguide (SDW) model.After describing the general theory and implementation of both approaches, we compare and contrast these methods directly on three topical problems of interest in waveguide-QED, including (i) a two-level system (TLS) coupled to an infinite (one-dimensional) waveguide, (ii) a TLS coupled to a terminated waveguide with a time-delayed coherent feedback, and (iii) two spatially separated TLSs coupled within an infinite waveguide.Both approaches are shown to efficiently describe multiphoton nonlinear dynamics in highly non-Markovian regimes, and we highlight the advantages and disadvantages of these methods for modeling waveguide QED interactions, including their implementation in PYTHON, computational run times, and ease of conceptual understanding.We explore both vacuum dynamics as well as regimes of strong optical pumping, where a weak excitation approximation cannot be applied.The MPS approach scales better when modeling multiphoton dynamics and long delay times and explicitly includes non-Markovian memory effects.In contrast, the SDW model accounts for non-Markovian effects through space discretization and solves Markovian equations of motion, yet rigorously includes the effects of retardation.The SDW model, based on an extension of recent collisional pictures in quantum optics, is solved through quantum trajectory techniques and can more easily add in additional dissipation processes, including off-chip decay and TLS pure dephasing.The impact of these processes is shown directly on feedback-induced population trapping and TLS entanglement between spatially separated TLSs.

arXiv:2011.12205Physical Review ResearchApr 9, 202152 citations

{{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}

. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of

{{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}

-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.