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arXiv:2005.10013 · Physical Review Letters

Dynamical Phase Transitions in Dissipative Quantum Dynamics with Quantum Optical Realization

Valentin Link, Walter T. Strunz

Published Sep 30, 2020• 33 citations
arXivHTMLPDF

Abstract

We study dynamical phase transitions (DPT) in the driven and damped Dicke model, realizable for example by a driven atomic ensemble collectively coupled to a damped cavity mode. These DPTs are characterized by nonanalyticities of certain observables, primarily the overlap of time evolved and initial state. Even though the dynamics is dissipative, this phenomenon occurs for a wide range of parameters and no fine-tuning is required. Focusing on the state of the "atoms" in the limit of a bad cavity, we are able to asymptotically evaluate an exact path integral representation of the relevant overlaps. The DPTs then arise by minimization of a certain action function, which is related to the large deviation theory of a classical stochastic process. Finally, we present a scheme which allows a measurement of the DPT in a cavity-QED setup.

DOI
10.1103/physrevlett.125.143602

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We study dynamical phase transitions (DPT) in the driven and damped Dicke model, realizable for example by a driven atomic ensemble collectively coupled to a damped cavity mode. These DPTs are characterized by nonanalyticities of certain observables, primarily the overlap of time evolved and initial state. Even though the dynamics is dissipative, this phenomenon occurs for a wide range of parameters and no fine-tuning is required. Focusing on the state of the "atoms" in the limit of a bad cavity, we are able to asymptotically evaluate an exact path integral representation of the relevant overlaps. The DPTs then arise by minimization of a certain action function, which is related to the large deviation theory of a classical stochastic process. Finally, we present a scheme which allows a measurement of the DPT in a cavity-QED setup.
We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number NNN of atoms. For finite NNN, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any NNN and correctly captures the atoms' depolarization due to dissipative dephasing.
We experimentally study the influence of dissipation on the driven Dicke quantum phase transition, realized by coupling external degrees of freedom of a Bose-Einstein condensate to the light field of a high-finesse optical cavity. The cavity provides a natural dissipation channel, which gives rise to vacuum-induced fluctuations and allows us to observe density fluctuations of the gas in real-time. We monitor the divergence of these fluctuations over two orders of magnitude while approaching the phase transition, and observe a behavior that deviates significantly from that expected for a closed system. A correlation analysis of the fluctuations reveals the diverging time scale of the atomic dynamics and allows us to extract a damping rate for the external degree of freedom of the atoms. We find good agreement with our theoretical model including dissipation via both the cavity field and the atomic field. Using a dissipation channel to nondestructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.
We investigate the quantum phase transitions (QPTs) of a four-level system in a noisy environment. The system is composed of a four-level atom which is driven by classical fields and simultaneously coupled with a quantum field mode. A second-order dissipative phase transition (DPT) is observed by combining unitary processes with dissipation dynamics. The analytical expression for the DPT in the anisotropic Rabi model is given. We demonstrate that the QPT in an open four-level system is characterized as several boundaries, which is completely different from that in a closed system. In addition, our model is robust against strong atomic spontaneous emission, providing a promising platform for observing DPT in an open system and studying the related dynamics associated with DPT.
The driven Dicke model, wherein an ensemble of atoms is driven by an external field and undergoes collective spontaneous emission due to coupling to a leaky cavity mode, is a paradigmatic example of a system exhibiting a driven-dissipative phase transition as a function of driving strength. Recently, a similar phenomenon was experimentally observed, not in a cavity setting, but rather in a free-space atomic ensemble. The reason why similar behavior should emerge in free space is not obvious, as the system interacts with a continuum of optical modes, which encodes light-propagation effects. Here, we present and solve a simple model to explain the behavior of the free-space system, based on the one-dimensional Maxwell-Bloch equations. On one hand, we show that a free-space ensemble at a low optical depth can exhibit similar behavior as the cavity system, as spatial propagation effects are negligible. On the other hand, in the thermodynamic limit of large atom number, we show that certain observables such as the transmittance or the atomic excited population exhibit nonanalytic behavior as a function of the driving intensity, reminiscent of a phase transition. However, a closer analysis reveals that the atomic properties are highly inhomogeneous in space, and based on this we argue that the free-space system does not undergo a phase transition but rather a “phase separation,” roughly speaking, between saturated and unsaturated regions.
Dissipative phase transitions (DPTs) are traditionally characterized through the spectrum of a time-independent Liouvillian superoperator. However, this definition does not apply to time-periodic (Floquet) systems that cannot be exactly recast as time-independent problems. Here, we develop a general framework to characterize DPTs in time-periodic open quantum systems through the spectrum of the Floquet propagator. We first study driven-dissipative Kerr resonators, known to display a DPT, showing that counter-rotating terms in the drive shift the critical point and significantly change the time scales associated with the transition. We then investigate DPTs in the driven quantum Rabi model and its time-independent approximation, the driven Jaynes-Cummings model, finding that the Rabi model exhibits distinct critical features as the ultrastrong coupling regime is approached. Moreover, our Floquet analysis unveils the disappearance of the DPT in the deep strong coupling regime, due to light-matter decoupling. Our approach sets the stage for the study of dissipative criticality in a broad class of time-dependent open quantum systems.
The interplay between many-body interactions and controlled dissipation provides a rich setting for nonequilibrium quantum phases. We explore the superradiant phase transitions in a Rydberg-interacting open Dicke model with cavity loss and local dissipation. We find that the nonlinear feedback from atomic interactions stabilizes the atomic collective excited state and induces resonant collective motion, which can be further converted into robust superradiant oscillations with the inclusion of local dissipation. Beyond the mean-field approximation, we prove this system can support the finite-size local dissipative temporal order, i.e., continuous time crystal, from evidences of the decreasing damping of a finite-frequency Liouvillian mode and the linear-size scaling of quantum fluctuations. The correlation between the atomic colletive dynamics and the cavity photon number makes our findings easy to detect from output optical signal. By bridging interacting atomic matter and driven-dissipative cavity QED, our Rydberg-interacting Dicke model provides a unique spin-1/2 platform for exploring dynamical phase transitions and macroscopic temporal order in open quantum matter.