Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1909.00266 · Physical Review A

Time crystals in a shaken atom-cavity system

Jayson G. Cosme, Jim Skulte, Ludwig Mathey

Published Nov 19, 2019• 56 citations
arXivHTMLPDF

Abstract

We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of cavity photons and order parameters at noninteger multiples of the driving period, which signals the appearance of an incommensurate time crystal. The subharmonic oscillatory motion corresponds to dynamical switching between symmetry-broken states, which are nonequilibrium bond ordered density wave states. Employing a semiclassical phase-space representation for the driven-dissipative quantum dynamics, we confirm the rigidity and persistence of the time crystalline phase. We identify experimentally relevant parameter regimes for which the time crystal phase is long lived, and map out the dynamical phase diagram. We compare and contrast the incommensurate time crystal with the commensurate Dicke time crystal in the amplitude-modulated case.

DOI
10.1103/physreva.100.053615

Related papers

Dynamical control of phases and time crystals in an atom-cavity system

Jayson G. Cosme

Periodic driving of strongly correlated systems has led to outstanding discoveries from light-induced superconductivity to time crystals. To gain insights into the fundamental nature of these phenomena, we have recently studied the effects of an external periodic driving in a well-controlled yet simple many-body platform consisting of a Bose-Einstein condensate inside a high-finesse optical cavity. This system hosts a competition between a homogeneous condensate phase and a self-organized density wave phase, which manifests in a superradiant phase transition as the intensity of a transverse pump beam is increased. We demonstrate dynamical control of this phase transition by periodic driving of the pump laser. Furthermore, we discover the emergence of genuine dynamical phases, namely a discrete time crystalline phase and nonequilibrium density wave orders. Accompanying experimental results confirm our theoretical predictions about light-induced control in the atom-cavity system.

Proceedings of the Samahang Pisika ng Pilipinas•Feb 9, 2020•0 citations

From a continuous to a discrete time crystal in a dissipative atom-cavity system

Hans Keßler, Jayson G. Cosme, Christoph Georges +2 more

Abstract We propose the dynamical stabilization of a nonequilibrium order in a driven dissipative system comprised an atomic Bose–Einstein condensate inside a high finesse optical cavity, pumped with an optical standing wave operating in the regime of anomalous dispersion. When the amplitude of the pump field is modulated close to twice the characteristic limit-cycle frequency of the unmodulated system, a stable subharmonic response is found. The dynamical phase diagram shows that this subharmonic response occurs in a region expanded with respect to that where stable limit-cycle dynamics occurs for the unmodulated system. In turning on the modulation we tune the atom-cavity system from a continuous to a discrete time crystal.

arXiv:2004.14633•New Journal of Physics•Jul 31, 2020•77 citations

Emergent limit cycles and time crystal dynamics in an atom-cavity system

Hans Keßler, Jayson G. Cosme, M. Hemmerling +2 more

We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant atomic resonance. By mapping out the dynamical phase diagram, we identify regions in parameter space showing stable limit cycle dynamics. Since the model describing the system is time independent, the emergence of a limit cycle phase indicates the breaking of continuous time translation symmetry. Employing a semiclassical analysis to demonstrate the robustness of the limit cycles against perturbations and quantum fluctuations, we establish the emergence of a time crystal.

arXiv:1905.02751•Physical Review A•May 9, 2019•100 citations

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

Zongping Gong, Ryusuke Hamazaki, Masahito Ueda

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.

arXiv:1708.01472•Physical Review Letters•Jan 25, 2018•240 citations

Shattered time: can a dissipative time crystal survive many-body correlations?

Tucker, K., Zhu, B., Lewis-Swan, R.J. +4 more

We investigate the emergence of a time crystal in a driven-dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the time crystal formation and establish a connection between the regime where it is stable and a slow growth rate of the mutual information, signalling that the time crystal studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the time crystal to single-particle dephasing. Finally, we discuss an experimental implementation using long-lived dipoles in an optical cavity

•Jan 1, 2018•75 citations

Realization of a Periodically Driven Open Three-Level Dicke Model

Phatthamon Kongkhambut, Hans Keßler, Jim Skulte +3 more

A periodically driven open three-level Dicke model is realized by resonantly shaking the pump field in an atom-cavity system. As an unambiguous signature, we demonstrate the emergence of a dynamical phase, in which the atoms periodically localize between the antinodes of the pump lattice, associated with an oscillating net momentum along the pump axis. We observe this dynamical phase through the periodic switching of the relative phase between the pump and cavity fields at a small fraction of the driving frequency, suggesting that it exhibits a time crystalline character.

arXiv:2108.11113•Physical Review Letters•Dec 13, 2021•42 citations
We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of cavity photons and order parameters at noninteger multiples of the driving period, which signals the appearance of an incommensurate time crystal. The subharmonic oscillatory motion corresponds to dynamical switching between symmetry-broken states, which are nonequilibrium bond ordered density wave states. Employing a semiclassical phase-space representation for the driven-dissipative quantum dynamics, we confirm the rigidity and persistence of the time crystalline phase. We identify experimentally relevant parameter regimes for which the time crystal phase is long lived, and map out the dynamical phase diagram. We compare and contrast the incommensurate time crystal with the commensurate Dicke time crystal in the amplitude-modulated case.
Periodic driving of strongly correlated systems has led to outstanding discoveries from light-induced superconductivity to time crystals. To gain insights into the fundamental nature of these phenomena, we have recently studied the effects of an external periodic driving in a well-controlled yet simple many-body platform consisting of a Bose-Einstein condensate inside a high-finesse optical cavity. This system hosts a competition between a homogeneous condensate phase and a self-organized density wave phase, which manifests in a superradiant phase transition as the intensity of a transverse pump beam is increased. We demonstrate dynamical control of this phase transition by periodic driving of the pump laser. Furthermore, we discover the emergence of genuine dynamical phases, namely a discrete time crystalline phase and nonequilibrium density wave orders. Accompanying experimental results confirm our theoretical predictions about light-induced control in the atom-cavity system.
Abstract We propose the dynamical stabilization of a nonequilibrium order in a driven dissipative system comprised an atomic Bose–Einstein condensate inside a high finesse optical cavity, pumped with an optical standing wave operating in the regime of anomalous dispersion. When the amplitude of the pump field is modulated close to twice the characteristic limit-cycle frequency of the unmodulated system, a stable subharmonic response is found. The dynamical phase diagram shows that this subharmonic response occurs in a region expanded with respect to that where stable limit-cycle dynamics occurs for the unmodulated system. In turning on the modulation we tune the atom-cavity system from a continuous to a discrete time crystal.
We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant atomic resonance. By mapping out the dynamical phase diagram, we identify regions in parameter space showing stable limit cycle dynamics. Since the model describing the system is time independent, the emergence of a limit cycle phase indicates the breaking of continuous time translation symmetry. Employing a semiclassical analysis to demonstrate the robustness of the limit cycles against perturbations and quantum fluctuations, we establish the emergence of a time crystal.
Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic dynamics of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.
We investigate the emergence of a time crystal in a driven-dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which in the thermodynamic limit features a self-generated time-periodic pattern imposed by collective elastic interactions. In contrast to prior realizations where the time symmetry is already broken by an external drive, here it is only spontaneously broken by the elastic exchange interactions and manifest in the two-time correlation spectrum. Employing a combination of exact numerical calculations and a second-order cumulant expansion, we investigate the impact of many-body correlations on the time crystal formation and establish a connection between the regime where it is stable and a slow growth rate of the mutual information, signalling that the time crystal studied here is an emergent semi-classical out-of-equilibrium state of matter. We also confirm the rigidity of the time crystal to single-particle dephasing. Finally, we discuss an experimental implementation using long-lived dipoles in an optical cavity
A periodically driven open three-level Dicke model is realized by resonantly shaking the pump field in an atom-cavity system. As an unambiguous signature, we demonstrate the emergence of a dynamical phase, in which the atoms periodically localize between the antinodes of the pump lattice, associated with an oscillating net momentum along the pump axis. We observe this dynamical phase through the periodic switching of the relative phase between the pump and cavity fields at a small fraction of the driving frequency, suggesting that it exhibits a time crystalline character.