Dissipative Phase Transition Research Articles

Dissipative phase transition in a mirrorless optical parametric oscillator

We experimentally demonstrate a dissipative phase transition in a mirrorless optical parametric oscillator (MOPO) using a double-$\mathrm{\ensuremath{\Lambda}}$ system in thermal atomic vapor. Bistable behavior is observed in the output power of the beams generated via the MOPO with the variation of the input power of the driving fields. We show that the long-lived hyperfine ground-state coherence induced by the Gaussian pump and the generated fields leads to the observation of optical bistability in the MOPO threshold. We further study the critical slowing-down of nonequilibrium dynamics in the vicinity of the forward threshold where the switching time of the generated fields diverges with the critical exponent, $\ensuremath{\alpha}=\ensuremath{-}0.86\ifmmode\pm\else\textpm\fi{}0.02$. Our observations pave the way to understanding and characterizing the phase transitions in driven-dissipative systems using a simple nonlinear optical system like the MOPO.

Lie-algebraic approach to one-dimensional translationally invariant free-fermionic dissipative systems

We study dissipative translationally invariant free-fermionic theories with quadratic Liouvillians. Using a Lie-algebraic approach, we solve the Lindblad equation and find the density matrix at all times for arbitrary time dependence of the Liouvillian. We then investigate the Liouvillian spectral properties and derive a generic criterion for the closure of the dissipative gap, which is believed to be linked with nonequilibrium dissipative phase transitions. We illustrate our findings with a few exotic examples. Particularly, we show the presence of gapless modes with a linear spectrum for fermions with long-range hopping, which might be related to nonunitary conformal field theories. The predicted effects can be probed in experiments with ultracold atomic and quantum-optical systems using currently available experimental facilities.

Enhanced two-parameter phase-space-displacement estimation close to a dissipative phase transition

I propose a quantum sensor based on driven-dissipative quantum system for the joint estimation of two conjugated variables characterizing the phase space displacement. The quantum probe consists of lattice system with two level atoms and bosonic modes which interact via dipolar coupling. Interplay between the coherent dynamics and dissipative processes of losses of bosonic excitations leads to a steady state which exhibits a non-analytical behaviour. I show that close to the dissipative phase transition the sensitivity of one of the conjugated parameters either the magnitude of the phase of the displacement can be significantly enhanced. Moreover, I show that the sum of the measurement uncertainties of the two parameters can overcome the standard quantum limit.

Facilitating spin squeezing generated by collective dynamics with single-particle decoherence

We study the generation of spin-squeezing in arrays of long-lived dipoles subject to collective emission, coherent drive, elastic interactions, and spontaneous emission. Counter-intuitively, it is found that the introduction of spontaneous emission leads to an enhancement of the achievable spin-squeezing, relative to that which emerges in the steady-state of the purely collective dynamics for the same model parameters. This behavior is connected to the dynamical self-tuning of the system through a dissipative phase transition that is present in the collective system alone. Our findings will be applicable to next-generation quantum sensors harnessing correlated quantum matter, including cavity-QED and trapped ion systems.

Monitoring the resonantly driven Jaynes-Cummings oscillator by an external two-level emitter: A cascaded open-systems approach

We address the consequences of backaction in the unidirectional coupling of two cascaded open quantum subsystems connected to the same reservoir at different spatial locations. In the spirit of [H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993)], the second subsystem is a two-level atom, while the first transforms from a driven empty cavity to a perturbative QED configuration and ultimately to a driven Jaynes-Cummings (JC) oscillator through a varying light-matter coupling strength. For our purpose, we appeal at first to the properties of resonance fluorescence in the statistical description of radiation emitted along two channels -- those of forwards and sideways scattering -- comprising the monitored output. In the simplest case of an empty cavity coupled to an external atom, we derive analytical results for the nonclassical fluctuations in the fields occupying the two channels, pursuing a mapping to the bad-cavity limit of the JC model to serve as a guide for the description of the more involved dynamics. Finally, we exemplify a conditional evolution for the composite system of a critical JC oscillator on resonance coupled to an external monitored two-level target, showing that coherent atomic oscillations of the target probe the onset of a second-order dissipative quantum phase transition in the source.

Gaussian trajectory approach to dissipative phase transitions: The case of quadratically driven photonic lattices

We apply the Gaussian trajectories approach to the study of the critical behavior of two-dimensional dissipative arrays of nonlinear photonic cavities, in presence of two-photon driving and in regimes of sizable loss rates. In spite of the highly mixed character of the density matrix of this system, the numerical approach is able to provide precise estimations of the steady-state expectation values, even for large lattices made of more than 100 sites. By performing a finite-size scaling of the relevant properties of the steady state, we extrapolate the behavior of the system in the thermodynamic limit and we show the emergence of a second-order dissipative phase transition, belonging to the universality class of thermal Ising model. This result indicates the occurrence of a crossover when the loss rate is increased from the weak-loss limit, in which the phase transition belongs to the universality class of the quantum Ising model

Dissipative quantum phase transition in a biased Tavis–Cummings model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11934010, U1801661, U1930402, and 11847087) and the National Key Research and Development Program of China (Grant No. 2016YFA0301200).

We study the dissipative quantum phase transition (QPT) in a biased Tavis–Cummings model consisting of an ensemble of two-level systems (TLSs) interacting with a cavity mode, where the TLSs are pumped by a drive field. In our proposal, we use a dissipative TLS ensemble and an active cavity with effective gain. In the weak drive-field limit, the QPT can occur under the combined actions of the loss and gain of the system. Owing to the active cavity, the QPT behavior can be much differentiated even for a finite strength of the drive field on the TLS ensemble. Also, we propose to implement our scheme based on the dissipative nitrogen-vacancy (NV) centers coupled to an active optical cavity made from the gain-medium-doped silica. Furthermore, we show that the QPT can be measured by probing the transmission spectrum of the cavity embedding the ensemble of the NV centers.

Effects of a dissipative coupling to the momentum of a particle in a double well potential

Double well potentials offer the possibility of coherent state preparation and therefore constitute important building blocks in the analysis of quantum information and quantum engineering devices. Here we present a study of the coherent tunneling in a parabolic double well potential in presence of different dissipative interactions. Specifically, we investigate the effects of an environmental coupling to the momentum and/or to the position of a particle in the potential. Using the semiclassical approximation to calculate instanton paths in Euclidean time, we find that momentum dissipation enhances the coherent tunnel splitting. In presence of both types of dissipation, the momentum dissipation shifts the critical coupling strength of the dissipative phase transition induced by the position dissipation.

Masked states of an atom coupled to a standing-wave cavity mode

The form of the eigenstates of an atom coupled to a cavity mode displaying a three dimensional periodic profile are obtained. It is shown that the quantized motion leads to degenerate states where the atomic degrees of freedom are masked, that is, upon detection of one component of this composite system the others remain in an entangled state. When the system is extended to include drive and dissipation it is found to undergo a dissipative quantum phase transition at a critical drive amplitude. Unlike other phase transitions reported in the literature, the degeneracy prepares the system in a superposition of incompatible states upon detection of the electromagnetic field. Probing the field hints at an order above the transition point that, due to state masking, allows for atomic coherence to survive at long times.

Relaxation dynamics and dissipative phase transition in quantum oscillators with period tripling

Period tripling in driven quantum oscillators reveals unique features absent for linear and parametric drive, but generic for all higher-order resonances. Here, we focus at zero temperature on the relaxation dynamics towards a stationary state starting initially from a domain around a classical fixed point in phase space. Beyond a certain threshold for the driving strength, the long-time dynamics is governed by a single time constant that sets the rate for switching between different states with broken time translation symmetry. By analyzing the lowest eigenvalues of the corresponding time evolution generator for the dissipative dynamics, we find that near the threshold the gap between these eigenvalues nearly closes. The closing becomes complete for a vanishing quantum parameter. We demonstrate that this behavior, reminiscent of a quantum phase transition, is associated with a transition from a stationary state which is localized in phase space to a delocalized one. We further show, that switching between domains of classical fixed points happens via quantum activation, however, with rates that differ from those obtained by a standard semiclassical treatment. As period tripling has been explored with superconducting circuits mainly in the quasi-classical regime recently, our findings may trigger new activities towards the deep quantum realm.

Thermal radiation and dissipative phase transition in a BEC with local loss

We study the dynamics of an atomic BEC subject to local dissipation in the form of atom losses. We show there is a critical loss rate at which the system undergoes a continuous dissipative phase transition from a homogeneous state into a state which contains a sonic horizon. The latter drastically alters the behavior of the system by screening the drain. Dissipation leads to two types of fluctuations. First, fluctuations are generated by particles emitted in the reservoir. Both above and below the critical loss, these result in thermal emission of phonons with a temperature set by the loss rate and the chemical potential. The second type of fluctuation results from scattering on the drain and gives rise to a particular correlation pattern that can be observed in the density–density correlation. Aside from correlations between in and out scattered modes, outgoing particles are correlated with localized modes through a process that is reminiscent of Hawking radiation. Finally, we briefly discuss the dynamics of the system when there are two drains, in which case it is possible to construct a black hole laser.

Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition.

We study a dissipative Kerr resonator subject to both single- and two-photon detuned drives. Beyond a critical detuning threshold, the Kerr resonator exhibits a semiclassical first-order dissipative phase transition between two different steady states that are characterized by a π phase switch of the cavity field. This transition is shown to persist deep into the quantum limit of low photon numbers. Remarkably, the detuning frequency at which this transition occurs depends almost linearly on the amplitude of the single-photon drive. Based on this phase-switching feature, we devise a sensitive quantum transducer that translates the observed frequency of the parametric quantum phase transition to the detected single-photon amplitude signal. The effects of noise and temperature on the corresponding sensing protocol are addressed, and a realistic circuit-QED implementation is discussed.

Symmetries and conservation laws in quantum trajectories: Dissipative freezing

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.

Scaling of the Berry Phase in the Yang-Lee Edge Singularity

We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.

Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. I. Semiclassical approach

We present a theoretical study on the nonlinear dynamics and stationary states of an inhomogeneously broadened spin ensemble coupled to a single-mode cavity driven by an external drive with constant amplitude. Assuming a sizeable number of constituents within the ensemble allows us to use a semiclassical approach and to formally reduce the theoretical description to the Maxwell-Bloch equations for the cavity and spin amplitudes. We explore the critical slowing-down effect, quench dynamics, and asymptotic behavior of the system near a steady-state dissipative phase transition accompanied by a bistability effect. Some of our theoretical findings have recently been successfully verified in a specific experimental realization based on a spin ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a single-mode microwave cavity (see Science Adv. 3, e1701626 (2017)).

Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition

We prove that the observable telegraph signal accompanying the bistability in the photon-blockade-breakdown regime of the driven and lossy Jaynes–Cummings model is the finite-size precursor of what in the thermodynamic limit is a genuine first-order phase transition. We construct a finite-size scaling of the system parameters to a well-defined thermodynamic limit, in which the system remains the same microscopic system, but the telegraph signal becomes macroscopic both in its timescale and intensity. The existence of such a finite-size scaling completes and justifies the classification of the photon-blockade-breakdown effect as a first-order dissipative quantum phase transition.

Quantum phase transitions triggered by a four-level atomic system in dissipative environments

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.

Quenching dissipative quantum Ising chain: an exact result for nonequilibrium dynamics

To create a more comprehensive understanding of nonequilibrium dynamics of open quantum many-body systems, we visit an exactly solvable example, that is a quenched transverse-field Ising chain coupled to Markovian baths, which act locally on the Jordan–Wigner fermionic space. Performing explicit calculations on the heat transfer, transverse magnetization, and kink density, we find that the imbalance of two opposite damping mechanisms play a crucial role in constructing a nontrivial nonequilibrium steady state accompanied with a dissipative quantum phase transition, also that the competition between unitary drive and decoherence does not necessarily lead to a quasi-stationary state or prethermalization under certain ordinary relaxation.

Turbulence-Induced Rogue Waves in Kerr Resonators

Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in nonequilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly nonlinear regime remains less explored, even in recent high-quality-factor resonators such as Kerr-nonlinear optical ones. Here, we investigate theoretically and experimentally the alteration of the resulting Kerr frequency combs from the weakly to the highly nonlinear regime, in the frameworks of spatiotemporal chaos, and dissipative phase transitions. We reveal the existence of a striking and easily accessible scenario of spatiotemporal chaos, free of cavity solitons, in a monostable operating regime, wherein a transition to amplitude turbulence via spatiotemporal intermittency is evidenced. Moreover, statistics of the light bursts in the resulting turbulent regime unveils the existence of rogue waves as extreme events characterized by long-tail statistics.6 MoreReceived 25 July 2018Revised 19 December 2018DOI:https://doi.org/10.1103/PhysRevX.9.011054Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBifurcationsPattern formationSpatiotemporal chaosNonlinear DynamicsGeneral Physics

Optimal stochastic unraveling of disordered open quantum systems: Application to driven-dissipative photonic lattices

We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. We prove that the optimal sampling of trajectories and disorder configurations is simply achieved by considering one random disorder configuration for each individual trajectory. As a first application, we exploit the present method to the study the role of disorder on the physics of the driven-dissipative Bose-Hubbard model in two different regimes: (i) for strong interactions, we explore the dissipative physics of fermionized bosons in disordered one-dimensional chains; (ii) for weak interactions, we investigate the role of on-site inhomogeneities on a first-order dissipative phase transition in a two-dimensional square lattice.