Abstract Dissipative phase transitions are a characteristic feature of open systems. One of the paradigmatic examples for a first order dissipative phase transition is the driven nonlinear single-mode optical resonator. In this work, we study a realization with an ultracold bosonic quantum gas, which generalizes the single-mode system to many modes and stronger interactions. We measure the effective Liouvillian gap of the system and find evidence for a first order dissipative phase transition. Due to the multi-mode nature of the system, the microscopic dynamics is much richer and allows us to identify a non-equilibrium condensation process.
Abstract Dissipative phase transitions are a characteristic feature of open systems. One of the paradigmatic examples for a first order dissipative phase transition is the driven nonlinear single-mode optical resonator. In this work, we study a realization with an ultracold bosonic quantum gas, which generalizes the single-mode system to many modes and stronger interactions. We measure the effective Liouvillian gap of the system and find evidence for a first order dissipative phase transition. Due to the multi-mode nature of the system, the microscopic dynamics is much richer and allows us to identify a non-equilibrium condensation process.
We theoretically investigate the critical properties of a single driven-dissipative nonlinear photon mode. In a well-defined thermodynamical limit of large excitation numbers, the exact quantum solution describes a first-order phase transition in the regime where semiclassical theory predicts optical bistability. We study the behavior of the complex spectral gap associated with the Liouvillian superoperator of the corresponding master equation. We show that in this limit the Liouvillian gap vanishes exponentially and that the bimodality of the photon Wigner function disappears. The connection between the considered thermodynamical limit of large photon numbers for the single-mode cavity and the thermodynamical limit of many cavities for a driven-dissipative Bose-Hubbard system is discussed.
Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the dissipative transverse field Ising model. It has been shown recently that the steady state of this model with all-to-all interactions is genuinely non-equilibrium near criticality, exhibiting a modified time-reversal symmetry and violating the fluctuation-dissipation theorem. Experimental study of such non-equilibrium steady-state phase transitions is however lacking. Here we propose realistic experimental setups and measurement schemes for current trapped-ion quantum simulators to demonstrate this phase transition, where controllable dissipation is engineered via a continuous weak optical pumping laser. With extensive numerical calculations, we show that strong signatures of this dissipative phase transition and its non-equilibrium properties can be observed with a small system size across a wide range of system parameters. In addition, we show that the same signatures can also be seen if the dissipation is instead achieved via Floquet dynamics with periodic and probabilistic resetting of the spins. Dissipation engineered in this way may allow the simulation of more general types of driven-dissipative systems or facilitate the dissipative preparation of useful many-body entangled states.
The study of phase transitions and critical phenomena arising in quantum driven-dissipative systems, and whether a correspondence can be drawn to their equilibrium counterparts, is a pressing question in contemporary physics. The development of large-scale superconducting circuits provides an experimental platform for these theoretical models. We report an experimental study of a multimode dissipative first-order phase transition in a 1D Bose-Hubbard chain consisting of 21 superconducting resonators. This phase transition manifests itself as a simultaneous frequency jump in all resonator modes as the frequency or power of a pump tone is swept. By measuring the system’s emission spectrum through the transition, we characterize the dim-to-bright phase transition and construct the full phase diagram. We further perform time-dependent measurements of the switching between the two phases in the transition region, from which we corroborate the transition line and extract transition times ranging from a few ms up to 143 s. Our model, based on single-mode mean-field theory and cross-Kerr interactions, captures the features at moderate pump powers and quantitatively reproduces the transition line. Our results open a new window into nonequilibrium quantum many-body physics and mark a step toward realizing and understanding dissipative phase transitions in the thermodynamic limit using superconducting quantum circuits. In addition, our study opens new possibilities for sensing and cryo-switching applications.
Motivated by recent experiments on light-matter interacting systems, we investigate a dilute Bose gas and self-bound quantum droplets in a one-dimensional optical lattice coupled to a lossy cavity mode. Using a classical-field approach, we determine the stationary states and collective excitations of this non-equilibrium system. Apart from the usual Bogoliubov modes, we identify a polariton-like gapped excitation, the frequency of which softens as a precursor of the density ordering transition. Moreover, its relaxation time diverges as the critical point is approached, signaling the non-equilibrium nature of this transition. Dynamically, this polariton-like mode can be probed by inducing cavity field fluctuations, which in turn generates spatio-temporal oscillations of both the condensate and droplet states. In the droplet regime, we also analyze the bound modes which bear the characteristics of such non-equilibrium self-bound state. In addition, we uncover solitonic non-equilibrium states, including condensate with kink-like configuration and double-droplet state, and investigate their robustness following a sudden quench. Remarkably, although these states become unstable beyond a critical coupling, they continue to manifest in the dynamics, akin to the scarring phenomena. Our results demonstrate that dissipative cavity coupling provides a versatile route for exploring rich non-equilibrium dynamics of condensates and quantum droplets within experimentally accessible settings.
It presents a significant challenge to elucidate the relationship between the phases of open quantum many-body systems and the spectral structure of their governing Liouvillian, which determines how the density matrix evolves. Previous studies have focused on the Liouvillian gap, defined as the decay rate of the most slowly decaying mode, as a key indicator of dissipative phase transition, noting its closure in symmetry-broken phases and opening in disordered phases. In this work, we propose an additional spectral gap, termed the oscillating-mode gap, defined as the decay rate of the most slowly decaying oscillating mode. Through the analysis of a prototype dissipative boson system, we demonstrate the necessity of both the Liouvillian gap and the oscillating-mode gap for the comprehensive characterization of the system's phases and the transitions between them.
Quantum many-body systems coupling photonic and matter degrees of freedom are ideal for the realization of driven open quantum dynamics at the intersection of quantum optics and condensed matter. They offer the possibility to address unresolved issues regarding a variety of non-equilibrium phenomena. In such open systems, the substructure of the reservoir then introduces further timescales that may enter into competition with rapid system processes, raising long-standing questions about the influence of non-Markovian effects on dynamics and equilibration out of equilibrium. \n \nThe central result of this thesis is a general pseudo-particle technique that can be applied to a large class of models of interacting light and matter and allows for realistic and efficient simulations of the full non-equilibrium dynamics of these systems. Since organic molecules, as used in experiments with photon condensates, which provide the main area of application for this thesis, possess an electronic transition coupled to vibrational phonon modes, we construct a representation where an auxiliary boson is assigned to each vibrational state of the molecule. An operator constraint then enforces single occupation across all of these states. We emphasize that we implement the operator constraint exactly and that we are the first to apply a faithful auxiliary-boson representation to open quantum systems. \n \nAs a contribution to bridging the gap between well-understood equilibrium and less explored non-equilibrium phenomena, we investigate photon condensates as they are driven away from equilibrium. The earliest signs of the non-equilibrium character of the driven-dissipative photon gas do not manifest in the spectrally resolved intensity distribution but in the time dependence of the intensity fluctuations. The energy flow through the system renders it {non-Hermitian} and induces a novel driven-dissipative transition in the second-order correlations characterized by the appearance of exceptional points. If only the static intensity spectrum is monitored, this transition remains unnoticed, as does the fact that the system is not truly in equilibrium. Non-Markovian effects due to the non-separability of system and reservoir timescales are shown to become important far away from equilibrium. Furthermore, we derive a novel photon-condensate Gross-Pitaevskii equation, which is capable of describing photo-molecular coherence. Such effects cannot be captured by existing theories and hence serve as a validation of our auxiliary-boson method. These results provide a building block to understanding the properties of the photon condensates in stationary operation where they act as fluctuating light sources. In the future, lattice systems of coupled photon condensates may lead to the appearance of novel driven-dissipative phases of light.