Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.
Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.
We study the quantum phase diagram and the onset of quantum critical phenomena in a generalized Dicke model that includes collective qubit-qubit interactions. By employing semiclassical techniques, we analyze the corresponding classical energy surfaces, fixed points, and the smooth Density of States as a function of the Hamiltonian parameters to determine quantum phase transitions in either the ground (QPT) or excited states (ESQPT). We unveil a rich phase diagram, the presence of new phases, and new transitions that result from varying the strength of the qubits interactions in independent canonical directions. We also find a correspondence between the phases emerging due to qubit interactions and those in their absence but with varying the strength of the non-resonant terms in the light-matter coupling. We expect our work to pave the way and stimulate the exploration of quantum criticality in systems combining matter-matter and light-matter interactions.
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-Ising model describes cavity quantum electrodynamics setups in which dipoles couple not only with the photonic cavity field but also with each other through dipole-dipole interaction. In this work we diagonalize such a model in terms of bosonic polaritonic operators for arbitrarily large values of the light-matter coupling and for values of the dipole-dipole interaction until the onset of the ferromagnetic Ising phase transition. In order to accomplish this task we exploit higher-order terms of the Holstein-Primakoff transformation, developing a general method which allows us to solve the normal phase of the Ising model in terms of bosonic excitations for large values of the dipole-dipole interaction. Our results shed light on the interplay between the dipole-dipole and light-matter coupling strengths and their effect on the virtual excitations which populate the ground state when the interactions become comparable with the bare transition frequency.
In this doctoral thesis, the thermodynamic phases und phase transitions of a generalised Dicke model are studied and characterised. Both, finite and vanishing temperatures are considered. The Dicke model of quantum optics describes collective phenomena which occur when light interacts with a many-atom system. In the thermodynamic limit, a so-called Hepp–Lieb superradiant phase transition sets in. A superradiant phase develops for low temperatures or strong coupling between light and atoms, which is characterised by a macroscopic excitation of the light field and a spontaneous, collective polarisation of the atoms. This thesis discusses a generalised version of the Dicke model, which is described by a quantum mechanical system consisting of three-level atoms in Lambda-configuration and two modes of a resonator. By means of the Holstein–Primakoff transformation, the Hamiltonian of this system is written in terms of four interacting, non-linear oscillators, which can be linearised in the thermodynamic limit, yielding the ground-state energy as well as the low-energy excitations. The phase diagram consisting of two superradiant phases separated by continuous and first-order phase transitions is derived. In order to clarify the question whether or not the superradiant phase transition of this generalised Dicke model can be observed experimentally for real atoms, the significance of the diamagnetic term is discussed. In contrast to the original Dicke model, superradiant phase transitions are possible in principle. This is due to the first-order phase transitions. In addition, a no-go theorem for continuous superradiant phase transitions is presented. The argument is based on the Thomas–Reiche–Kuhn sum rule. Last, we study the superradiant phase transition of the generalised Dicke model at finite temperatures. Therefore, the partition sum is computed and analysed in the thermodynamic limit using Laplace’s method. At finite temperatures, the properties of the phase diagram and phases remain. However, here all phase transitions are of first order.
The multi-mode Dicke model, which describes many atoms interacting with the multi-mode photons, has attracted much attention; it not only exhibits rich quantum phases, but also has an important application in quantum information. In this paper, we explore the ground-state properties of the two-mode Dicke model by the Holstein-Primakoff transformation and Boson expansion method, and theoretically predict a new first-order quantum phase transition. In the experiment, this quantum phase transition could be detected by measuring the mean-photon number or the atom population.
We study the coherent cooperative phenomena of the system composed of two interacting atomic ensembles in the thermodynamic limit. Remarkably, the system exhibits the Dicke-like quantum phase transition and entanglement behavior although the governing Hamiltonian is fundamentally different from the spin-boson Dicke Hamiltonian, offering the opportunity for investigating collective matter-light dynamics with pure matter waves. The model can be realized with two Bose-Einstein condensates or atomic ensembles trapped in two optical cavities coupled to each other. The interaction between the two separate samples is induced by virtual photon exchange.