Generalized Dicke Model Research Articles

Dynamics of a generalized Dicke model for spin-1 atoms

Dynamics of a generalized Dicke model for spin-1 atoms

Quantum electrodynamical density functional theory for generalized Dicke model

Quantum electrodynamical density functional theory for generalized Dicke model

Quantum Phase Transitions in a Generalized Dicke Model.

We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.

Generalized Dicke model and gauge-invariant master equations for two atoms in ultrastrongly-coupled cavity quantum electrodynamics

Generalized Dicke model and gauge-invariant master equations for two atoms in ultrastrongly-coupled cavity quantum electrodynamics

Quantum multicritical behavior for coupled optical cavities with driven laser fields

Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.

Charging performance of quantum batteries based on intensity-dependent Dicke model

Recently, quantum battery based on various physical models from quantum optics model to spin model and its enhancement of charging performance have attracted increasing interest. It has been demonstrated that quantum entanglement is beneficial to the speedup of work extraction. In this paper, by an exact diagonalization approach, we investigate the charging performance of the field intensity-dependent Dicke model (also called intensity-dependent Dicke model) quantum battery, which consists of <i>N</i> qubits collectively interacting with a single-mode cavity. The considered intensity-dependent Dicke model is a generalized Dicke model with a nonlinear-coupling fashion and different weights of energy conserved term and non-conserved term. Firstly, we consider the influences of energy non-conserved term (also called anti-rotating wave term) on the maximum stored energy and maximum charging power in quantum battery. It is shown that the maximum stored energy is not very sensitive to the increase of the weight of energy non-conserved term, but the maximum charging power undergoes a significant change with the increase of the weight of energy non-conserved term. We also show that the maximum charging power increases monotonically with the increase of coupling constant between qubits and cavity, but the maximum stored energy is not monotonically related to the increase of coupling constant. Then, we further examine in detail the characteristics of the maximum stored energy, charging time, energy quantum fluctuation and maximum charging power in the quantum battery under the same weight between energy conserved term and non-conserved term. By comparing the charging performances of quantum battery based on the single-photon-Dicke model with those based on the two-photon-Dicke model, we find that the performances, specifically, the charging time and maximum charging power of the intensity-dependent Dicke quantum battery are better than those of single-photon Dicke quantum battery, but weaker than those of two-photon Dicke quantum battery. Of particular interest is that the relationship of maximum charging power with large quantum cell number in intensity-dependent Dicke quantum battery has the same form as that in the two-photon Dicke quantum battery, i.e. their maximum values of charging power are both proportional to the large quantum cell number squared, specifically, <inline-formula><tex-math id="M1">\begin{document}$ P_{\mathrm{max}}^{\mathrm{ID}}\propto N^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M1.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ P\mathrm{_{max}^{2ph}}\propto N^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M2.png"/></alternatives></inline-formula>, which are consistent with the upper bound given by the paper (Gyhm J, Šafránek D, Rosa D <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevLett.128.140501"> 2022 <i>Phys. Rev. Lett.</i> <b>128</b> 140501</ext-link>). It is worthwhile to mention that Dou et al. (Dou F Q, Zhou H, Sun J A <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevA.106.032212"> 2022 <i>Phys. Rev. A</i> <b>106</b> 032212</ext-link>) showed that using the quantum advantage of maximum charging power in the quantum battery based on cavity Heisenberg-spin-chain model <inline-formula><tex-math id="M5">\begin{document}$ P\mathrm{_{max}}\propto N^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230578_M5.png"/></alternatives></inline-formula> can be obtained. Therefore, this study of the charging performance based on the intensity-dependent Dicke quantum battery may provide an alternative approach to the further research on quantum battery.

Critical Phenomena in Light-Matter Systems with Collective Matter Interactions.

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.

Multipartite quantum correlations in a two-mode Dicke model

We analyze multipartite correlations in a generalized Dicke model involving two optical modes interacting with an ensemble of two-level atoms. In particular, we examine correlations beyond the standard bipartite entanglement and derive exact results in the thermodynamic limit. The model presents two superradiant phases involving the spontaneous breaking of either a ${\mathbb{Z}}_{2}$ or a U(1) symmetry. The latter is characterized by the emergence of a Goldstone excitation, found to significantly affect the correlation profiles. Focusing on the correlations between macroscopic subsystems, we analyze both the mutual information and the entanglement of formation for all possible bipartitions among the optical and matter degrees of freedom. It is found that while each mode entangles with the atoms, the bipartite entanglement between the modes is zero, and they share only classical correlations and quantum discord. We also study the monogamy of multipartite entanglement and show that there exists genuine tripartite entanglement, i.e., quantum correlations that the atoms share with the two modes but that are not shared with them individually, only in the vicinity of the critical lines. Our results elucidate the intricate correlation structures underlying superradiant phase transitions in multimode systems.

Multicriticality and quantum fluctuation in a generalized Dicke model

We consider an important generalization of the Dicke model in which multi-level atoms, instead of two-level atoms as in conventional Dicke model, interact with a single photonic mode. We explore the phase diagram of a broad class of atom-photon coupling schemes and show that, under this generalization, the Dicke model can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. We also calculate the atom-photon entanglement entropy for both critical and non-critical cases. We find that the order of the criticality strongly affects the critical entanglement entropy: higher order yields stronger entanglement. Our work provides deep insight into quantum phase transitions and multicriticality.

Atom-only theories for U(1) symmetric cavity-QED models

We consider a generalized Dicke model with U(1) symmetry, which can undergo a transition to a superradiant state that spontaneously breaks this symmetry. By exploiting the difference in timescale between atomic and cavity dynamics, one may eliminate the cavity dynamics, providing an atom-only theory. We show that the standard Redfield theory cannot describe the transition to the superradiant state, but including higher-order corrections does recover the transition. Our work reveals how the forms of effective theories must vary for models with continuous symmetry, and provides a template to develop effective theories of more complex models.

Quantum tricritical behavior and multistable macroscopic quantum states in generalized Dicke model

In this article, we obtain the multistable macroscopic quantum states and quantum tricritical behavior in generalized Dicke model (DM) analytically by means of spin-coherent-state (SCS) variational method for a finite atom number N. The quantum phase transition (QPT) is characterized by the ground state from the normal phase (NP) to the superradiant phases (SP). The second-order QPT turns to the first-order one at the tricritical point of phase boundary. The tricritical behavior of QPT emerges when the coupling strength of the symmetry breaking mechanism increases to a certain extent, which leads to an additional dimension of phase diagram. Beyond the ground state the symmetry-breaking coupling can manipulate the pseudospin flip of higher-level macroscopic states. The critical property of QPT is also demonstrated from the average photon-number, the atomic population as well as Berry phase.

Superradiant switching, quantum hysteresis, and oscillations in a generalized Dicke model

We demonstrate quantum signatures of deterministic nonlinear dynamics in the transition to superradiance of a generalized open Dicke model with different coupling strengths for the co- and counter-rotating light-matter interaction terms. A first-order phase transition to coexisting normal and superradiant phases is observed, corresponding with the emergence of switching dynamics between these two phases, driven by quantum fluctuations. We show that this phase coexistence gives rise to a hysteresis loop also for the quantum mechanical system. Additionally, a transition to a superradiant oscillatory phase can be observed clearly in quantum simulations.

Universal fluctuations and squeezing in a generalized Dicke model near the superradiant phase transition

In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model, we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete $\mathbb{Z}_2$ symmetry), and that of (anti-) and Tavis-Cummings $U(1)$ models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of photon number take universal values. We also find a temperature scales below which one approaches zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss Bethe ansatz solution for integrable $U(1)$ limits.

Fermionic formalism for driven-dissipative multilevel systems

We present a fermionic description of non-equilibrium multi-level systems. Our approach uses the Keldysh path integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on the Majorana fermion representation of spin-1/2 models which follows earlier applications in the context of spin and Kondo systems. We apply this formalism to problems of increasing complexity: a dissipative two-level system, a driven-dissipative multi-level atom, and a generalized Dicke model describing many multi-level atoms coupled to a single cavity. We compare our theoretical predictions with recent QED experiments and point out the features of a counter-lasing transition. Our technique provides a convenient and powerful framework for analyzing driven-dissipative quantum systems, complementary to other approaches based on the solution of Lindblad master equations.

Optimal basis for the generalized Dicke model

A methodology is devised for building optimal bases for the generalized Dicke model based on the symmetry adapted variational solution to the problem. At order zero, the matter sector is constructed by distributing $N_a$ particles in all the possible two-level subsystems connected with electromagnetic radiation; the next order is obtained when the states of $N_a-1$ particles are added and distributed again into the two-level subsystems; and so on. In the electromagnetic sector, the order zero for each mode is the direct sum of the Fock spaces, truncated to a value of the corresponding constants of motion of each two-level subsystem; by including contributions of the other modes, the next orders are obtained. As an example of the procedure we consider $4$ atoms in the $\Xi$ configuration interacting dipolarly with two modes of electromagnetic radiation. The results may be applied to situations in quantum optics, quantum information, and quantum computing.

Exploring nonequilibrium phases of the generalized Dicke model with a trapped Rydberg-ion quantum simulator

Trapped ions are a versatile platform for the investigation of quantum many-body phenomena, in particular for the study of scenarios where long-range interactions are mediated by phonons. Recent experiments have shown that the trapped ion platform can be augmented by exciting high-lying Rydberg states. This introduces controllable state-dependent interactions that are independent from the phonon structure. However, the many-body physics in this newly accessible regime is largely unexplored. We show that this system grants access to generalized Dicke model physics, where dipolar interactions between ions in Rydberg states drastically alter the collective non-equilibrium behavior. We analyze and classify the emerging dynamical phases and identify a host of non-equilibrium signatures such as multi-phase coexistence regions and phonon-lasing regimes. We moreover show how they can be detected and characterized through the fluorescence signal of scattered photons. Our study thus highlights new capabilities of trapped Rydberg ion systems for creating and detecting quantum non-equilibrium phases.

Emergent Universality in a Quantum Tricritical Dicke Model.

We propose a generalized Dicke model that supports a quantum tricritical point. We map out the phase diagram and investigate the critical behavior of the model through an exact low-energy effective Hamiltonian in the thermodynamic limit. As predicted by the Landau theory of phase transition, the order parameter shows nonuniversality at the tricritical point. Nevertheless, as a result of the separation of the classical and the quantum degrees of freedom, we find a universal relation between the excitation gap and the entanglement entropy for the entire critical line including the tricritical point. Here the universality is carried by the emergent quantum modes, whereas the order parameter is determined classically.

Superradiance in the Generalized (Non-Wiener) Dicke Model

It is shown that when nonresonant interactions between atoms and a vacuum electromagnetic field are included in analysis of emission of a localized ensemble of identical atoms, a delay must appear in the cooperative radiation pulse emitted by the atomic ensemble that is initially in a half-excited state. At the same time, the emission of cooperative radiation from a completely excited ensemble for certain parameters must begin without any delay. This contradicts the familiar facts of the conventional Dicke superradiance, in the theory of which nonresonant interactions are disregarded. The model taking into account nonresonant interactions along with other factors of the Dicke model is called the generalized Dicke model.

Extreme spin squeezing in the steady state of a generalized Dicke model

We present a scheme to generate steady-state atomic spin squeezing in a cavity QED system using cavity-mediated Raman transitions to engineer effective atom-photon interactions, which include both linear and nonlinear (dispersive) atom-cavity couplings, on a potentially equal footing. We focus on a regime where the dispersive coupling is very large and find that the steady state of the system can in fact be a strongly spin-squeezed Dicke state $|N/2,0\ensuremath{\rangle}$ of the atomic ensemble. These states offer Heisenberg-limited metrological properties and feature genuine multipartite entanglement among the entire atomic ensemble.

Delay of Superradiance as a Signature of the Non-Wiener Dynamics of the Generalized Dicke Model

Delay of a superradiance pulse of an ensemble of identical atoms in a half-excited state has been detected. No such delay has been detected for an ensemble of fully excited atoms. These effects are due to the nonresonant interaction of a localized atomic ensemble with vacuum broadband environment, which is disregarded within the traditional Dicke model but is taken into account within the generalized Dicke model.