We introduce an auxiliary-particle field theory to treat the non-Markovian dynamics of driven-dissipative quantum systems of the Jaynes-Cummings type. It assigns an individual quantum field to each reservoir state and provides an analytic, faithful representation of the coupled system-bath dynamics. We apply the method to a driven-dissipative photon Bose-Einstein condensate (BEC) coupled to a reservoir of dye molecules with electronic and vibronic excitations. The complete phase diagram of this system exhibits a hidden, non-Hermitian phase transition separating temporally oscillating from biexponentially decaying photon density correlations within the BEC. On one hand, this provides a qualitative distinction of the thermal photon BEC from a laser. On the other hand, it shows that one may continuously tune from the BEC to the lasing phase by circumventing a critical point. This auxiliary-particle method is generally applicable to the dynamics of open, non-Markovian quantum systems. Published by the American Physical Society 2024
We introduce an auxiliary-particle field theory to treat the non-Markovian dynamics of driven-dissipative quantum systems of the Jaynes-Cummings type. It assigns an individual quantum field to each reservoir state and provides an analytic, faithful representation of the coupled system-bath dynamics. We apply the method to a driven-dissipative photon Bose-Einstein condensate (BEC) coupled to a reservoir of dye molecules with electronic and vibronic excitations. The complete phase diagram of this system exhibits a hidden, non-Hermitian phase transition separating temporally oscillating from biexponentially decaying photon density correlations within the BEC. On one hand, this provides a qualitative distinction of the thermal photon BEC from a laser. On the other hand, it shows that one may continuously tune from the BEC to the lasing phase by circumventing a critical point. This auxiliary-particle method is generally applicable to the dynamics of open, non-Markovian quantum systems. Published by the American Physical Society 2024
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.
Open quantum many body systems describe several quantum simulators, ranging from arrays of superconducting circuits hosting correlated states of light, to ultracold atoms in optical lattices in presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work we extend Dynamical Mean Field Theory (DMFT), a powerful nonperturbative technique developed for strongly correlated quantum many-body systems, to Markovian open quantum systems. Within Open-DMFT, a master equation describing a lattice of bosonic particles is mapped, at large but finite connectivity, onto an impurity problem describing a single site coupled to Markovian and non-Markovian environments, where the latter accounts for quantum fluctuations beyond Gutzwiller mean-field theory. We introduce a new non-perturbative approach to solve the impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of non-crossing diagrams. Finally, we apply our Open-DMFT to solve a driven-dissipative Bose-Hubbard model, which is relevant to current experiments with dissipative ultracold bosons. We show that this model undergoes a dissipative phase transition towards a superfluid phase, which can be equally interpreted as a quantum many-body synchronization transition of an array of quantum van der Pol oscillators. We show how Open-DMFT captures crucial effects due to finite lattice connectivity, such as hopping-induced dissipation and heating, which are completely missed by mean field theories and which lead to a drastic reduction of the broken symmetry phase that we interpret as a desynchronization driven by quantum fluctuations.
We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.
A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.
The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature are studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics are completely determined by the propagating (retarded) and correlation Green functions. Comparing the non-Markovian behavior at finite temperature with those at the zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory effect can dramatically change the coherent and thermal dynamics of the cavity. We also numerically study the dissipation dynamics of the cavity through the mean mode amplitude decay and the average photon number decay in the microwave regime. It is shown that the strong coupling between the cavity and the reservoir results in a long-time dissipationless evolution to the cavity field amplitude, and its noise dynamics undergo a critical transition from the weak to the strong coupling due to the non-Markovian memory effect.
We develop an exact analytical framework for studying the nonequilibrium dynamics of interacting quantum harmonic oscillators coupled to a modelled thermal reservoir and driven by external classical fields. The total Hamiltonian is diagonalized via successive Bogoliubov transformations, enabling a nonperturbative treatment of dissipation and driving. For two coupled oscillators with an external source applied to the first, we derive explicit energy expressions and analyze their dependence on coupling and bath parameters. The phase-space structure is characterized through Husimi Q-functions for initial separable coherent and number states. We obtain the reduced density matrix elements in the number-state basis and demonstrate that, in the absence of driving and at zero temperature, the reduced density matrix of the main system satisfies the Lindblad master equation. A generating function for the Husimi function is introduced to facilitate computation of higher-order correlations. The analysis is then generalized to n interacting oscillators, with analytical energy expressions provided and the case n=3 examined in detail. Our results establish a versatile and exact framework for driven-dissipative quantum systems, with potential applications in quantum thermodynamics, open quantum systems, and many-body physics.