The emergent behavior that arises in many-body systems of increasing size follows universal laws that become apparent in order-to-disorder transitions. While this behavior has been traditionally studied for large numbers of emitters, recent progress allows for the exploration of the few-emitter limit, where correlations can be measured and connected to microscopic models to gain further insight into order-to-disorder transitions. We explore this few-body limit in the driven and damped Tavis–Cummings model, which describes a collection of atoms interacting with a driven and damped cavity mode. Our exploration revolves around the dressed states of the atomic ensemble and field, whose energies are shown to collapse as the driving field is increased to mark the onset of a dissipative quantum phase transition. The collapse occurs in stages and is an effect of light-matter correlations that are overlooked for single atoms and neglected in mean-field models. The implications of these correlations over the macroscopic observables of the system are presented. We encounter a shift in the expected transition point and an increased number of parity-broken states to choose from once the ordered phase is reached.
The emergent behavior that arises in many-body systems of increasing size follows universal laws that become apparent in order-to-disorder transitions. While this behavior has been traditionally studied for large numbers of emitters, recent progress allows for the exploration of the few-emitter limit, where correlations can be measured and connected to microscopic models to gain further insight into order-to-disorder transitions. We explore this few-body limit in the driven and damped Tavis–Cummings model, which describes a collection of atoms interacting with a driven and damped cavity mode. Our exploration revolves around the dressed states of the atomic ensemble and field, whose energies are shown to collapse as the driving field is increased to mark the onset of a dissipative quantum phase transition. The collapse occurs in stages and is an effect of light-matter correlations that are overlooked for single atoms and neglected in mean-field models. The implications of these correlations over the macroscopic observables of the system are presented. We encounter a shift in the expected transition point and an increased number of parity-broken states to choose from once the ordered phase is reached.
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 photon emission properties of the driven-dissipative Rabi model in the so-called ultrastrong- and deep strong-coupling regimes where the atom-cavity coupling rate g becomes comparable or larger than the cavity frequency ${\ensuremath{\omega}}_{c}$. By solving numerically the master equation in the dressed-state basis, we compute the output field correlation functions in the steady-state for a wide range of coupling rates. We find that, as the atom-cavity coupling strength increases, the system undergoes multiple transitions in the photon statistics. In particular, a first sharp antibunching-to-bunching transition, occurring at $g\ensuremath{\sim}0.45{\ensuremath{\omega}}_{c}$, leading to the breakdown of the photon blockade due to the counter-rotating terms, is shown to be the consequence of a parity shift in the energy spectrum. A subsequent revival of the photon blockade and the emergence of the quasicoherent statistics for even larger coupling rates are attributed to an interplay between the nonlinearity in the energy spectrum and the transition rates between the dressed states.
Nonequilibrium phase transitions exist in damped-driven open quantum systems when the continuous tuning of an external parameter leads to a transition between two robust steady states.In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can coexist in a critical hysteresis domain.Here, we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics system.It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power.The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength.Our measurements show an improved stabilization of the classical attractors up to the millisecond range when the size of the quantum system is increased from one to three artificial atoms.The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multiphoton phases of finite-size, nonlinear, open quantum systems.
Quantum phase transition in Ξ-configuration Tavis-Cummings model driven by an electromagnetic field for a finite number of atoms
The quantum phase transitions of a three-level Tavis-Cummings model in the \Xi Ξ -configuration driven by a single-mode electromagnetic field in a QED cavity are studied for n_a=1,\,2 n a = 1 , 2 , and 4 4 atoms. Although conventional observables like photon number and energy level populations suffice to locate quantum phase transitions, they often lack sensitivity to finite-size effects. Here, we show that the expectation values of the quadratic Casimir invariants associated with the atomic subsystems offer a more robust measure, exhibiting sharp signatures of criticality that are validated by fidelity calculations. Additionally, the von Neumann entropy is employed to map the entanglement landscape between matter and the quantized field. A key finding is that the external driving field acts as a control parameter that shrinks the normal phase region; as the driving intensity increases, the separable ground state vanishes, leading to the dominance of field-matter entanglement across the parameter space.
Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons.We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes-Cummings model, in which case the photon blockade breaks down in a second-order phase transition at a critical drive strength.We show that this transition is associated to the spontaneous breaking of an antiunitary PT symmetry.Within a semiclassical approximation, we calculate the expectation values of observables in the steady state.We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve.The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power law, allowing us to calculate the critical scaling of steady-state observables without invoking mean-field theory.We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state.We list several experimental platforms where this phenomenon may be observed.
Abstract We investigate the steady-state quantum phases and associated collective phenomena of an open Tavis–Cummings (TC) model driven by a two-photon source. The standard (non-dissipative) TC model describes the quantum phases of an ensemble of N q two-level quantum emitters interacting with a single-mode electromagnetic field. The interplay among coherent driving, dissipation, and dipole interactions of the open TC model results in emergent collective phenomena, leading to a dissipative or non-equilibrium phase transition from the normal to the superradiant phase. We solve the Liouvillian equation analytically using the semi-classical mean-field approximation. We carry out stability analysis of the steady-state phases and determine the phase boundary. The use of Holstein–Primakoff transformation in the thermodynamic limit N q → ∞ reduces the system to an effective coupled-oscillator model, the solution of which yields collective modes.