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.
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.
We demonstrate that the open quantum Rabi model (QRM) exhibits a second-order dissipative phase transition (DPT) and propose a method to observe this transition with trapped ions. The interplay between the ultrastrong qubit-oscillator coupling and the oscillator damping brings the system into a steady state with a diverging number of excitations, in which a DPT is allowed to occur even with a finite number of system components. The universality class of the open QRM, modified from the closed QRM by a Markovian bath, is identified by finding critical exponents and scaling functions using the Keldysh functional integral approach. We propose to realize the open QRM with two trapped ions where the coherent coupling and the rate of dissipation can be individually controlled and adjusted over a wide range. Thanks to this controllability, our work opens a possibility to investigate potentially rich dynamics associated with a dissipative phase transition.
We demonstrate a novel mechanism driving complex critical phenomena in open light-atom interacting systems by investigating a parametrically amplified quantum Rabi model (QRM) subject to both single- and two-photon decay. In the classical oscillator limit, four composite phases emerge, arising from the possible normal or superradiant regimes across the upper and lower spin branches. A mean-field analysis reveals that the two-photon decay activates the intrinsic nonlinearity of the QRM. The synergy of the coherent and dissipative two-photon processes, together with the spin-boson coupling, constitutes an ``inverted" regime where superradiance emerges exclusively at weak coupling. This regime features first- and second-order superradiant DPTs separated by a tricritical point. Utilizing an adiabatic approach and the semi-classical Langevin formalism, we further study the steady-state structure beyond the mean-field level. The universality classes of the DPTs are identified, with the corresponding critical and finite-size scaling exponents derived and a scaling ansatz proposed to describe the critical behavior.
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 and characterize the emergence of finite-component dissipative phase transitions (DPTs) in nonlinear photon resonators subject to n -photon driving and dissipation. Exploiting a semiclassical approach, we derive general results on the occurrence of second-order DPTs in this class of systems. We show that for all odd n , no second-order DPT can occur while, for even n , the competition between higher-order nonlinearities determines the nature of the criticality and allows for second-order DPTs to emerge only for n = 2 and n = 4 . As pivotal examples, we study the full quantum dynamics of three- and four-photon driven-dissipative Kerr resonators, confirming the prediction of the semiclassical analysis on the nature of the transitions. The stability of the vacuum and the typical timescales needed to access the different phases are also discussed. We also show a first-order DPT where multiple solutions emerge around zero, low, and high-photon numbers. Our results highlight the crucial role played by s t r o n g and w e a k symmetries in triggering critical behaviors, providing a Liouvillian framework to study the effects of high-order nonlinear processes in driven-dissipative systems, that can be applied to problems in quantum sensing and information processing.
The dissipative quantum phase transitions experienced by a driven optical system are studied in order to understand the underlying light-matter coupling. The primary system under study is composed of a cavity mode coupled to a two-level system with dissipation being introduced through the interaction with a surrounding environment; an external coherent field is included to drive the system out of the ground state. The coupling is given by a generalized Rabi Hamiltonian, where rotating, gr, and counter-rotating, ngr, couplings are both present and can be adjusted independently. A comprehensive study of the different phases the system can exhibit as gr and n are varied is presented. From this, we construct a bridge between two limiting scenarios: (i) the Jaynes-Cummings limit (n = 0), where the system undergoes a phase transition by means of the breakdown of the photon blockade, and (ii) the driven Dicke limit ( = 1 ), where the normal to super-radiant phase transition is found. Novel behaviour encountered in an intermediate regime (1 > n > 0) is discussed. Attention is drawn towards the strong coupling regime, where changes at the one-photon level induce nonlinear effects and behaviour reminiscent of phase transitions is encountered with just a few photons present. A comparison between weak and strong coupling regimes, and, thus, an exploration of the effect of fluctuations over quantum phase transitions of light, is given through a survey of the phases an auxiliary optical system exhibits. This system is composed of two coupled nonlinear cavities that are driven coherently and damped through the interaction with the environment; it is seen to exhibit three phases. Two phases present high-correlation between the cavities and are differentiated by the photon statistics, transitioning from classical to quantum. The third phase is characterized by a highly localized field in one of the cavities. The departure from mean-field results is highlighted and a new way to characterize the possible phases of the system is proposed. Finally, the crucial role of quantum fluctuations is quantified and used to define the phases at hand.
We investigate the quantum phase transition in the dissipative anisotropic quantum Rabi model in the framework of quantum dressed master equation. From perspectives of both numerical and analytical analysis, we unravel the implication of the giant photon-bunching feature on the first-order quantum phase transition. The observed two-photon statistics can be well described analytically within a few lowest eigenstates at the low temperature. Moreover, such significant photon-bunching peak is generally exhibited at the deep-strong qubit-photon coupling, which is however lacking in the dissipative isotropic quantum Rabi model. Therefore, we suggest that the photon-bunching measurement is helpful to characterize the first-order QPT of the qubit-photon hybrid systems.