We study a generalized Dicke model, as recently realized in an atomic quantum gas experiment, describing the collective interaction of N two-level atoms with a single cavity mode. The model takes account of dissipation of the cavity field, and includes a non-linear atom-photon coupling, not present in the conventional Dicke model. We extend previous theoretical investigations of a semiclassical model by including all quantum effects and considering finite atom number N . Our results show good agreement between quantum expectation values and the semiclassical model as N is increased, but also show exotic behaviour for the corresponding quantum state as the non-linear atom-photon coupling is varied.
We study a generalized Dicke model, as recently realized in an atomic quantum gas experiment, describing the collective interaction of N two-level atoms with a single cavity mode. The model takes account of dissipation of the cavity field, and includes a non-linear atom-photon coupling, not present in the conventional Dicke model. We extend previous theoretical investigations of a semiclassical model by including all quantum effects and considering finite atom number N . Our results show good agreement between quantum expectation values and the semiclassical model as N is increased, but also show exotic behaviour for the corresponding quantum state as the non-linear atom-photon coupling is varied.
Abstract The Dicke model, which describes the collective interaction between an ensemble of atoms and a single-mode photon field, serves as a fundamental framework for studying light-matter interactions and quantum electrodynamic phenomena. In this work, we investigate the manifestation of non-Hermitian effects in a generalized Dicke model, where two dissipative atom ensembles interact with a single-mode photon field. We explore the system in the semiclassical limit as a non-Hermitian Dicke model, revealing rich exceptional points (EPs) and diabolic points. Furthermore, we explore the quantum signature of EPs in the Hilbert space, relying on discrete photon numbers. The transition of photons from antibunching to bunching at steady state is unravelled. Our findings deepen the understanding of non-Hermitian physics in light-matter interaction, which is instructive for the design of advanced photonic devices.
The Dicke model, which describes the collective interaction between an ensemble of atoms and a single-mode photon field, serves as a fundamental framework for studying light-matter interactions and quantum electrodynamic phenomena. In this work, we investigate the manifestation of non-Hermitian effects in a generalized Dicke model, where two dissipative atom ensembles interact with a single-mode photon field. By applying the Holstein-Primakoff transformation, we explore the system in the semiclassical limit as a non-Hermitian Dicke model, revealing rich exceptional points (EPs) and diabolic points in such a system. We find that, by introducing the nonlinear saturation gain into an atomic ensemble, higher-order EP can be induced, leading to intriguing properties. Furthermore, if the system is extended to a one-dimensional chain, then the band topology will interplay with the non-Hermitian effect. In the quantum regime, we explore the quantum signature of EPs, noting that the conditions for their emergence are influenced by discrete photon numbers. We further study the transition from photon anti-bunching to bunching at a steady state, driven by non-Hermitian dynamics. Our findings deepen the understanding of non-Hermitian physics in light-matter interaction which is instructive for the design of advanced photonic and quantum systems.
The Dicke model describes the coherent interaction of a laser-driven ensemble of two-level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to, e.g., atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced collective decay of an excitation that is shared by N atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by nonthermal Markovian noise. The interplay between dissipative and coherent elements leads to a genuine nonequilibrium dynamics in the bistable regime, which is expressed via a nonconservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke model become exact in the large-N-limit. The absence of an effective free-energy functional, however, necessitates the inclusion of fluctuation corrections with O(1/N) for finite $N<\ensuremath{\infty}$ to locate the nonthermal first-order phase transition between the superradiant and the empty cavity.
The Dicke model is a staple of theoretical cavity quantum electrodynamics (cavity QED), describing the interaction between an ensemble of atoms and a single radiation mode of an optical cavity. It is studied both quantum mechanically and semiclassically for two-level atoms, and demonstrates a rich variety of dynamics such as phase transitions, phase multistability, and chaos. In this work we explore an open, spin-1 Dicke model with independent co and counterrotating coupling terms as well as a quadratic Zeeman shift enabling control over the atomic energy-level structure. We investigate the stability of operator and moment equations under two approximations and show the system undergoes phase transitions. To compliment these results, we relax the aforementioned approximations and investigate the system semiclassically. We show evidence of phase transitions to steady-state and oscillatory superradiance in this semiclassical model, as well as the emergence of chaotic dynamics. The varied and complex behaviors admitted by the model highlights the need to more rigorously map its dynamics.
Interactions among emitters provide a powerful means of controlling collective light--matter phenomena, yet their role in superradiant criticality has not been thoroughly investigated. Here we construct a minimal model that can yield analytical insights --- a Dicke model with two interacting atoms coupled to a single mode cavity --- to study such interaction effects. We show that interaction changes the phase boundary, and may even completely suppress the atom-photon coupling threshold for superradiance and change the universality class of the phase transition. We further study the dissipative phase transition and quantum dynamics in the presence of dissipation channels such as photon loss and spin relaxation. Our results demonstrate important roles played by the atom-atom interaction and how it can be engineered to control atom-photon coupling.
Dicke model, as an important many-body model in quantum optics, describes the interaction between multiple identical two-level atoms and a quantized electromagnetic field. This spin-boson model shows collective phenomena in light-matter interaction systems and can undergo a second-order quantum phase transition from a normal phase to a superradiant phase when the coupling strength between the two-level atoms and the optical field exceeds a critical value. Dicke model embodies unique many-body quantum theories. And it has been widely studied and obtained many significant research results in quantum information, quantum process, and other quantum systems. Meanwhile, Dicke model also has wide applications in quantum optics and condensed matter physics. The extended Dicke model, describing the interaction of a Bose-Einstein condensate in an optical cavity, provides a remarkable platform for studying extraordinary quantum phase transitions in theory and experiment. Based on the recent experiment on non-Hermitian coupling between two long-lived atomic spin waves in an optical cavity, in this work we use spin-coherent-state variational method and present the macroscopic quantum-state energy of the non-Hermitian Dicke model. The spin coherent state variational method has an advantage in the theoretical research of macroscopic quantum states, especially in the normal and the inverted pseudospin states. In the variational method, optical coherent states and atomic extremum spin coherent states are used as the trial wave functions. A Hermitian transformation operator is proposed to diagonalize the non-Hermitian Hamiltonian, which is different from the ordinary quantum mechanics where the transformation operator must be unitary. Herein, the energy function is not necessarily real in the entire coupling region. Beyond an exceptional point, the spectrum becomes complex and introducing biorthogonal sets of atomic extremum states is necessary to evaluate the average quantities. The normal phase (for the zero average photon number) possesses real energy and atomic population. The non-Hermitian interaction destroys the superradiant phase (for the stable nonzero average photon number) and leads to the absence of quantum phase transition. However, the introduced atom-photon interaction, which is induced by the pump field experimentally, can change the situation, dramatically. The pump field can balance the loss by the non-Hermitian atom-photon interaction to achieve the superradiant phase. An interesting double exceptional point are observed in the energy functional. There is the real spectrum below the first exceptional point and beyond the second exceptional point, while there is a complex spectrum between these two exceptional points. The superradiant phase appears only beyond a critical value, which is related to the nonlinear interaction and the pump laser. A new and inverted quantum phase transition from the superradiant phase to the normal phase, is observed by modulating the atom-field coupling strength. The superradiant phase of the population inversion state appears for a negative effective frequency and a large atom-photon interaction. The influence of the dissipative coupling may be observed in cold atom experiment in an optical cavity. All the parameters adopted in this work are the actual experimental parameters.