This paper is devoted to a study of a kind of chirality appearing in a model in cavity or circuit quantum electrodynamics. The model especially describes an artificial atom fully coupled to a 1-mode photon in a cavity. This chirality is played in the fully coupled (FC) Hamiltonian by two modified Jaynes-Cummings (JC) Hamiltonians. The modified JC Hamiltonian as well as the standard one has the superradiant ground state energy for sufficiently large coupling strength. The superradiance is caused by a phase transition found by Preparata, called the Dicke-Preparata (DP) superradiance. Using the one common Hamiltonian formalism with the chirality, we theoretically prove the followings: (i) when the coupling strength makes the weak or standard strong coupling regime, the ground state energy of the FC Hamiltonian can be well approximated with that of the standard and modified JC Hamiltonians since the chirality does not work in the regime; (ii) once the coupling strength plunges into the ultra-strong coupling regime, the effect of the chirality is turned on and works in the ground state energy of the FC Hamiltonian. That is, there is a kind of a phase transition concerning the chirality associated with the DP superradiance between the strong coupling regime and the ultra-strong coupling one.
This paper is devoted to a study of a kind of chirality appearing in a model in cavity or circuit quantum electrodynamics. The model especially describes an artificial atom fully coupled to a 1-mode photon in a cavity. This chirality is played in the fully coupled (FC) Hamiltonian by two modified Jaynes-Cummings (JC) Hamiltonians. The modified JC Hamiltonian as well as the standard one has the superradiant ground state energy for sufficiently large coupling strength. The superradiance is caused by a phase transition found by Preparata, called the Dicke-Preparata (DP) superradiance. Using the one common Hamiltonian formalism with the chirality, we theoretically prove the followings: (i) when the coupling strength makes the weak or standard strong coupling regime, the ground state energy of the FC Hamiltonian can be well approximated with that of the standard and modified JC Hamiltonians since the chirality does not work in the regime; (ii) once the coupling strength plunges into the ultra-strong coupling regime, the effect of the chirality is turned on and works in the ground state energy of the FC Hamiltonian. That is, there is a kind of a phase transition concerning the chirality associated with the DP superradiance between the strong coupling regime and the ultra-strong coupling one.
Abstract We carefully investigate the comprehensive impact of atom-cavity interaction and artificial magnetic fields on quantum phase transitions of anti-Jaynes-Cummings triangle model in the infinite frequency limit. We discover that ground states of the optical field can be a gapped normal phase (NP) or three kinds of gapless superradiant phases with infinite degeneracy. When the atom-cavity coupling is weak, the optical field is in a NP, which is a vacuum with no photons. Otherwise, it will stay at one of the superradiant phases: a normal superradiant phase without photon currents and another two chiral superradiant phases with opposite photon currents. The former only breaks the continuous U (1) symmetry and its gapless excitations are normal Goldstone modes. Nevertheless, the latter, mainly induced by an external synthetic gauge field, break both the continuous U (1) symmetry and chiral symmetry, thereby corresponding gapless excitations are chiral Goldstone modes. In addition, we also propose a detecting scheme to distinguish these superradiant phases.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.
The four standard quantum optics model in cavity QED such as Rabi, Dicke, Jaynes-Cummings ( JC ) and Tavis-Cummings (TC) model were proposed many decades ago. Despite their relative simple forms and many previous theoretical works, their solutions at a finite $ N $ inside the superradiant regime remain unknown. In view of recent remarkable experimental advances in several experimental systems such as cold atoms inside a cavity or superconducting qubits inside a microcavity to realize these models, it becomes topical and important to understand what would be the new phenomena in these models at a finite $ N $, especially inside the superradaint regime. In this work, we resolved this outstanding problem. We use three independent methods such as $ 1/J $ expansion, the strong coupling expansion and exact diagonization (ED) to study $ U(1)/Z_2 $ Dicke model at a finite $ N $ and different anisotropy parameters $ 0 \leq \beta \leq 1 $ as the atom-photon interaction strength increases. This model include the four standard quantum optics model as its special limit. We identify 4 different regimes: the normal, $ U(1) $, strong quantum tunneling (QT) and weak QT regime. We map out the evolution of energy level structures, compute all kinds of photon correlation functions and find nearly perfect agreements between the strong coupling expansion and the ED not only in the weak and strong QT regimes, but also in the $ U(1) $ regime not too close to the critical point at $ N=\infty $.
The Dicke model can exhibit quantum phase transition between the normal and the superradiant phases when the strength of the light-matter coupling exceeds the ultrastrong-coupling regime. However, it is challenging to observe this phase transition in practical systems due to limited coupling strength or finite two-photon A2 terms. Here we show that by applying a periodic modulation to the frequency of the two-level systems in a standard Dicke model in the strong-coupling regime, an anisotropic Dicke model with tunable rotating and counter-rotating terms in the ultrastrong-coupling regime can be achieved. We calculate the ground state and the excitation spectrum of this model in terms of the modulation parameters. Our result shows that the superradiant phases can be observed in cavity- or circuit-quantum electrodynamics systems with strong coupling.
The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous U(1) symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a U(1)-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from zν=1 to zν=1/2. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.
The Dicke Hamiltonian describes the simplest quantum system with atoms interacting with photons: N two level atoms inside a perfectly reflecting cavity which allows only one electromagnetic mode. It has also been successfully employed to describe superconducting circuits which behave as artificial atoms coupled to a resonator. The system exhibits a transition to a superradiant phase at zero temperature. When the interaction strength reaches its critical value, both the number of photons and of atoms in excited states in the cavity, together with their fluctuations, exhibit a sudden increase from zero. Employing symmetry-adapted coherent states it is shown that these properties scale with the number of atoms, that their reported divergences at the critical point represent the limit when this number goes to infinity, and that in this limit they remain divergent in the superradiant phase. Analytical expressions are presented for all observables of interest, for any number of atoms. Comparisons with exact numerical solutions strongly support the results.