Nonequilibrium Quantum Criticality and Non-Markovian Environment: Critical Exponent of a Quantum Phase Transition

We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a singlemode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems. The quest for a systematic understanding of nonequilibrium phenomena is an open problem in theoretical physics for its importance in the description of dynamics from the microscopic up to astrophysical scales [1-3]. Aspects of these dynamics are studied in the relaxation of systems undergoing temporal changes (quenches) of the control field across a critical point [4][5][6]. Quenches across a non-equilibrium phase transition provide further insight into the interplay between noise and external drives on criticality and thermalization [7,8]. In this context photonic systems play a prominent role, thanks to their versatility [9][10][11][12][13][14][15].Polarizable particles in a high-finesse cavity, like in the setup illustrated in Fig. 1(a), offer a unique system to study relaxation in long-range interacting systems. Here, multiple photon scattering mediates particleparticle interactions whose range scales with the system size in a single-mode cavity [15][16][17][18]. In this limit, atomic ensembles in cavities are expected to share several features with other long-range interacting systems such as gravitational clusters and non-neutral plasmas in two or more dimensions [3,16,19]. The equilibrium thermodynamics of these systems can exhibit ensemble inequivalence [3,20], while quasi-stationary states (QSS) typically characterise the out-of-equilibrium dynamics [3,[21][22][23]. QSS are metastable states in which the system is expected to remain trapped in the thermodynamic limit, they are Vlasov-stable solutions and thus depend on the initial state. So far, however, evidence of QSS has been elusive. It has been conjectured that noise and dissipation can set a time scale that limits the QSS lifetime [24][25][26][27], and possibly gives rise to dynamical phase transitions [25]. In Ref. [28] it was shown that, in pr...

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“…[34]). Our analysis sets the stage for the development of a kinetic equation that is valid in the full quantum regime [47][48][49][50][51].…”

Section: Arxiv:151205243v2 [Quant-ph] 20 Jul 2016mentioning

confidence: 99%

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

2016

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“…Here pumping and dissipation play a key role. For example, they facilitate superradiance -a macroscopic population of photons in the cavity mode [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In addition to providing a platform for studying far-from-equilibrium physics, atom-cavity systems have interesting technological applications, such as an ultrastable superradiant laser [28][29][30][31].…”

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confidence: 99%

Driven-dissipative dynamics of atomic ensembles in a resonant cavity: Nonequilibrium phase diagram and periodically modulated superradiance

2019

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We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two parameters -detuning between the clocks and the repump rate. There are three main phases -trivial steady state (Phase I), where all atoms are maximally pumped, nontrivial steady state corresponding to monochromatic superradiance (Phase II), and amplitude-modulated superradiance (Phase III). Phases I and II are fixed points of the mean-field dynamics, while in most of Phase III stable attractors are limit cycles. Equations of motion possess an axial symmetry and a Z2 symmetry with respect to the interchange of the two clocks. Either one or both of these symmetries are spontaneously broken in various phases. The trivial steady state loses stability via a supercritical Hopf bifurcation bringing about a Z2-symmetric limit cycle. The nontrivial steady state goes through a subcritical Hopf bifurcation responsible for coexistence of monochromatic and amplitude-modulated superradiance. Using Floquet analysis, we show that the Z2-symmetric limit cycle eventually becomes unstable and gives rise to two Z2-asymmetric limit cycles via a supercritical pitchfork bifurcation. Each of the above attractors has its own unique fingerprint in the power spectrum of the light radiated from the cavity. In particular, limit cycles in Phase III emit frequency combs -series of equidistant peaks, where the symmetry of the frequency comb reflects the symmetry of the underlying limit cycle. For typical experimental parameters, the spacing between the peaks is several orders of magnitude smaller than the monochromatic superradiance frequency, making the lasing frequency highly tunable.

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“…This driven dissipative system is able to show a transition very similar to the ground state transition described above. These experiments prompted much theoretical investigation [18][19][20][21][22][23][24][25][26][27] into the nature of the phase transition.…”

Section: Introductionmentioning

confidence: 99%

Superradiant and lasing states in driven-dissipative Dicke models

2018

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We present the non-equilibrium phase diagram of a model which can demonstrate both DickeHepp-Lieb superradiance and regular lasing by varying the coherent and incoherent driving terms We find that the regions in the phase diagram corresponding to superradiance and standard lasing are always separated by a normal region. We analyse the behaviour of the system using a combination of exact numerics based on permutation symmetry of the density matrix for small to intermediate numbers of molecules, and second order cumulant equations for large numbers of molecules. We find that the nature of the photon distribution in the superradiant and lasing states are very similar, but the emission spectrum is very different. We also show that in the presence of both coherent and incoherent driving, a period-doubling route to a chaotic state occurs.

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Nonequilibrium Quantum Criticality and Non-Markovian Environment: Critical Exponent of a Quantum Phase Transition

Cited by 64 publications

References 43 publications

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

Driven-dissipative dynamics of atomic ensembles in a resonant cavity: Nonequilibrium phase diagram and periodically modulated superradiance

Superradiant and lasing states in driven-dissipative Dicke models

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