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.
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.
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.
Dissipative light-matter coupling plays a vital role in non-Hermitian physics, but it remains largely unexplored in waveguide QED systems. In this work, we find that by employing pseudo-Hermitian symmetry rather than anti- PT symmetry, the concept of dissipative coupling could be generalized and applied to the field of waveguide QED. This leads to a series of intriguing results, such as spontaneous breaking of pseudo-Hermitian symmetry across the exceptional points (EPs), level attraction between the bound states, and critical transition across the EPs for the population of quantum emitters in the bound state. Thanks to the tunability of photonic bands in crystal waveguides, we also demonstrate that dissipative light-matter coupling leads to the emergence of nonstandard third-order exceptional points with chiral spatial profiles in a topological waveguide QED system. This work provides a promising paradigm for studying non-Hermitian quantum phenomena in waveguide QED systems.
Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.
The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate.
We investigate in this paper the macroscopic quantum states of multiple atoms in an optical cavity with non-Hermitian coupling motivated by recent experiments. The tunable atom-photon nonlinear interaction is included to demonstrate the variety of quantum phases in the realistic realization of Dicke phase transition with cold atoms. The energies of macroscopic quantum states are obtained in terms of the spin-coherent-state variational method, in which the nonunitary operator of the similarity transformation is used to diagonalize the effective non-Hermitian Hamiltonian, which is pseudo-Hermitian below the exceptional point (EP). The superradiant phase (SP) and related quantum phase transition (QPT) disappear completely for the non-Hermitian Dicke model (DM) because of imaginary coupling, which leads to instability of states with nonzero photons. The situation is dramatically changed by including the nonlinear atom-photon interaction generated by the pump field. It is found that the second EP emerges at a higher value of coupling. The spectrum is complex between the two EPs and real otherwise. Phase diagrams are obtained for red and blue cavity pump field detunings, showing explicitly the revival of the SP and QPT, respectively. However, the QPT from the SP to the normal phase with the increase of coupling is opposite to the transition in the normal DM. The critical property of the Berry phase indicates the first-order nature of the QPT, which again is different from the DM, where the QPT is known as the second order.