Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts.However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin.In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior.Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high-to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase.Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z 2 symmetry.However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a Z 2 × Z 2 symmetry.Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system.We elucidate various exotic features of these NEFPs.In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance.This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition.As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths.Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts.However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin.In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior.Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high-to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase.Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z 2 symmetry.However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a Z 2 × Z 2 symmetry.Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system.We elucidate various exotic features of these NEFPs.In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance.This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition.As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths.Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
Nonequilibrium dynamics play an important role in all contexts of physics, both classical and quantum as well as living and nonliving, so it is crucial to develop a foundational understanding of nonequilibrium phase transitions. In this work we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular we study how nonreciprocal coupling between two O(n_{i}) order parameters (with i=1,2) affects the universality at a multicritical point, extending the analysis of J. T. Young et al. [Phys. Rev. X 10, 011039 (2020)2160-330810.1103/PhysRevX.10.011039], which considered the case n_{1}=n_{2}=1, i.e., a Z_{2}×Z_{2} model. We show that nonequilibrium fixed points (NEFPs) emerge for a broad range of n_{1},n_{2} and exhibit intrinsically nonequilibrium critical phenomena, namely a violation of fluctuation-dissipation relations at all scales and underdamped oscillations near criticality in contrast to the overdamped relaxational dynamics of the corresponding equilibrium models. Furthermore, the NEFPs exhibit an emergent discrete scale invariance in certain physically relevant regimes of n_{1},n_{2}, but not others, depending on whether the critical exponent ν is real or complex. The boundary between these two regions is described by an exceptional point in the renormalization group (RG) flow, leading to distinctive features in correlation functions and the phase diagram. Another contrast with the previous work is the number and stability of the NEFPs as well as the underlying topology of the RG flow. Finally, we investigate an extreme form of nonreciprocity where one order parameter is independent of the other order parameter but not vice versa. Unlike the Z_{2}×Z_{2} model, which becomes nonperturbative in this case, we identify a distinct nonequilibrium universality class whose dependent field similarly violates fluctuation-dissipation relations but does not exhibit discrete scale invariance or underdamped oscillations near criticality.
Due to the variety of tools available to control atomic, molecular, and optical (AMO) systems, they provide a versatile platform for studying many-body physics, quantum simulation, and quantum computation. Although extensive efforts are employed to reduce coupling between the system and the environment, the effects of the environment can never fully be avoided, so it is important to develop a comprehensive understanding of open quantum systems. The system-environment coupling often leads to loss via dissipation, which can be countered by a coherent drive. Open quantum systems subject to dissipation and drive are known as driven-dissipative systems, and they provide an excellent platform for studying many-body nonequilibrium physics. The first part of this dissertation will focus on driven-dissipative phase transitions. Despite the nonequilibrium nature of these systems, the corresponding phase transitions tend to exhibit emergent equilibrium behavior. However, we will show that in the vicinity of a multicritical point where multiple phase transitions intersect, genuinely nonequilibrium criticality can emerge, even though the individual phase transitions on their own exhibit equilibrium criticality. These nonequilibrium multicritical points can exhibit a variety of exotic phenomena not possible for their equilibrium counterparts, including the emergence of complex critical exponents, which lead to discrete scale invariance and spiraling phase boundaries. Furthermore, the Liouvillian gap can take on complex values, and the fluctuation-dissipation theorem is violated, corresponding to an effective temperature which gets "hotter" and "hotter" at longer and longer wavelengths. The second part of this dissertation will focus on Rydberg atoms. In particular, we study how the spontaneous generation of contaminant Rydberg states drastically modifies the behavior of a driven-dissipative Rydberg system due to the resultant dipole-dipole interactions. These interactions lead to a complicated competition of both blockade and anti-blockade effects, leading to strongly enhanced Rydberg populations for far-detuned drive and reduced Rydberg populations for resonant drive.
Nonequilibrium universality of the nonreciprocally coupled O(n1)×O(n2) model
In this work, we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular, we study how nonreciprocal coupling between two O(ni) order parameters (with i=1,2) affects the universality at a multicritical point, extending the analysis of [J.T. Young et al., Phys. Rev. X 10, 011039 (2020)], which considered the case n1=n2=1, i.e., a Z2×Z2 model. We show that nonequilibrium fixed points (NEFPs) emerge for a broad range of n1,n2 and exhibit intrinsically nonequilibrium critical phenomena, namely a violation of fluctuation-dissipation relations at all scales and underdamped oscillations near criticality in contrast to the overdamped relaxational dynamics of the corresponding equilibrium models. Furthermore, the NEFPs exhibit an emergent discrete scale invariance in certain physically-relevant regimes of n1,n2, but not others, depending on whether the critical exponent ν is real or complex. The boundary between these two regions is described by an exceptional point in the renormalization group (RG) flow, leading to distinctive features in correlation functions and the phase diagram. Another contrast with the previous work is the number and stability of the NEFPs as well as the underlying topology of the RG flow. Finally, we investigate an extreme form of nonreciprocity where one order parameter is independent of the other order parameter but not vice versa. Unlike the Z2×Z2 model, which becomes non-perturbative in this case, we identify a distinct nonequilibrium universality class whose dependent field similarly violates fluctuation-dissipation relations but does not exhibit discrete scale invariance or underdamped oscillations near criticality.
A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large class of nonequilibrium systems. For such a manifestly nonlinear nonequilibrium strongly fluctuating system, we show that there exists universal nonequilibrium critical behavior that is incredibly well described by its equilibrium critical properties. A dynamic renormalization-group theory is developed to account for the behavior. The weak driving may give rise to several time scales depending on its form and thus rich nonequilibrium phenomena of various regimes and their crossovers, negative susceptibilities, as well as a violation of fluctuation-dissipation theorem and hysteresis. An initial condition that can be in either equilibrium or nonequilibrium but has longer correlations than the driving scales also results in a unique regime and complicates the situation. The implication of the results on measurement is also discussed. The theory may shed light on the study of other nonequilibrium systems and even nonlinear science.
The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved diffusive density. Below dc=4, the renormalization group flows to a fast-diffusion fixed point at which the density acts as a long-range multiplicative noise, producing a novel universality class. The non-equilibrium nature of the fixed point is manifest in the large-scale violation of the fluctuation-dissipation relations, reflected in a splitting of the scaling exponents of the two-point correlation and response functions--a measurable hallmark of non-equilibrium critical fluctuations. A two-loop calculation establishes the stability of this fixed point but yields a small correction-to-scaling exponent ω≈0.020 in d=3, implying strong finite-size corrections. An all-orders modified Harris criterion ν>2/(d+z−2) confirms that the BIM fixed point governs criticality in d=3, with Ising universality recovered only at d=2.
Driven-dissipative many-body systems are difficult to analyze analytically due to their nonequilibrium dynamics, dissipation, and many-body interactions. In this paper, we consider a driven-dissipative infinite-range Ising model with local spontaneous emission, which naturally emerges from the open Dicke model in the large-detuning limit. Utilizing an adaptation of the Suzuki-Trotter quantum-to-classical mapping, we develop an exact field-theoretical analysis and a diagrammatic representation of the spin model that can be understood from a simple scattering picture. With this representation, we are able to analyze critical behavior, finite-size scaling, and the effective temperature near the respective phase transition. Our formalism further allows a detailed study of the ordered phase where we find a ``heating'' region within which the effective temperature becomes negative, thereby exhibiting a truly nonequilibrium behavior. At the phase transition, we find two distinct critical behaviors with overdamped and underdamped critical dynamics at generic and weakly dissipative critical points, respectively. We further show that the underdamped critical behavior is robust against short-range perturbations and is not an artifact of the mean-field nature of the model. To treat such perturbations, we extend our diagrammatic representation to include the coupling to spin waves due to the short-range interactions. The field-theoretical approach and the diagrammatics developed in this work should prove useful in applications to generic short-range driven-dissipative spin systems.