Characteristics of superradiant optical phases occurring in the system of nondegenerate Λ atoms and radiation that are interacting inside a nonlinear quantum cavity
In the present article, we investigate the behavior of a large collection of three-level $\mathrm{\ensuremath{\Lambda}}$ atoms interacting with two quantized electromagnetic fields inside a second-order nonlinear quantum cavity. The nonlinearity of the cavity is supposed to be activated by the application of two classical pump fields. The total Hamiltonian of the combination, with due attention to the nonlinearity effects, is diagonalized. The corresponding ground-state energy then follows from minimizing the total Hamiltonian. The structure of the ground state indicates that four distinct optical phases can occur in such a system. These possible phases turn out to be trivial, dark, left-arm and right-arm superradiant ones. Conditions under which any of the four optical phases can actually occur are also analyzed and discussed. The analysis of the conditions, accompanied by several figures, then reveals that with a suitable choice of the pump field amplitudes and/or geometrical phases, one can intensify the two superradiant phases drastically. Moreover, we demonstrate that the dark optical phase cannot occur at all, while the trivial and superradiant ones can, in fact, coexist. Our calculations also show that transition from the trivial phase to left-arm (right-arm) superradiant one is continuous (discrete) and second (first) order in nature. Another important result of our investigation is that by adjusting the pump field strength, one can switch from the left-arm superradiant phase to the right-arm one and vice versa. This point, in turn, provides an alternative mechanism for the development of quantum optical switching devices.
In the present article, we investigate the behavior of a large collection of three-level \ensuremathΛ atoms interacting with two quantized electromagnetic fields inside a second-order nonlinear quantum cavity. The nonlinearity of the cavity is supposed to be activated by the application of two classical pump fields. The total Hamiltonian of the combination, with due attention to the nonlinearity effects, is diagonalized. The corresponding ground-state energy then follows from minimizing the total Hamiltonian. The structure of the ground state indicates that four distinct optical phases can occur in such a system. These possible phases turn out to be trivial, dark, left-arm and right-arm superradiant ones. Conditions under which any of the four optical phases can actually occur are also analyzed and discussed. The analysis of the conditions, accompanied by several figures, then reveals that with a suitable choice of the pump field amplitudes and/or geometrical phases, one can intensify the two superradiant phases drastically. Moreover, we demonstrate that the dark optical phase cannot occur at all, while the trivial and superradiant ones can, in fact, coexist. Our calculations also show that transition from the trivial phase to left-arm (right-arm) superradiant one is continuous (discrete) and second (first) order in nature. Another important result of our investigation is that by adjusting the pump field strength, one can switch from the left-arm superradiant phase to the right-arm one and vice versa. This point, in turn, provides an alternative mechanism for the development of quantum optical switching devices.
In the present work, the role of temperature in the occurrence of optical phases in a system of a large number of atoms interacting with photons is reported. To this end, it is assumed that the cavity inside which the constituents interact is in equilibrium with a heat reservoir, held at a fixed temperature. To achieve this goal, we start with the conventional density operator to calculate the mean values of electromagnetic quadratures. To make the realization of three distinct optical phases, trivial, electric, and magnetic superradiance, possible, the medium inside the cavity is assumed to be a second-order nonlinear one. The nonlinearity of the medium is further assumed to be activated by an externally applied classical pump field. As a consequence, now there are two external controlling agents, the temperature and nonlinearity strength. We then proceed to calculate the quadrature mean values in the thermodynamical limit and for a large number of atoms as a function of temperature. An analysis of the calculated mean values, along with relevant figures, reveals temperature-dependent conditions for realizing trivial, electric, and magnetic optical phases. Moreover, we shall demonstrate that the atom-field coupling strength gives rise to two distinct regimes where the optical phases behave quite differently. In one of the two regimes it is possible for the phases to coexist, while in the other it is not. As a profound result, it is demonstrated that for such a system there can exist a unique temperature (triple point) at which the three optical phases coexist.
In the present report, the question of U(1) symmetry breaking in a system of atoms and electromagnetic fields, interacting inside a leaky cavity, filled with a nonlinear medium, is addressed. In particular, the Z2 discrete symmetry of the system and the emergence of optical phases are fully discussed. For the nonlinearity of a general order, with an electromagnetic field of any number of modes, conditions under which the resulting field-field interactions destroy the U(1) (and Z2) symmetry are determined. We then apply the theory to the case of a collection of two-level atoms and three electromagnetic modes. Taking one of the fields as a classically adjustable pumping one, it is demonstrated that the quantized field-field coupling profoundly depends upon the pump field strength. The presence of two competing phenomena, namely, the cavity photonic dissipation and nonlinearity, is shown to lead the system towards steady behavior. The steady-state solutions to the atomic population and field quadratures exhibit the normal and superradiant phases, depending on the strengths of pumping field and atom-field couplings. The conditions for the stability of such steady-state solutions are also discussed in detail. A notable result of the present article is that by adjusting the parameters involved in the system one can switch from the normal to electric and/or magnetic superradiant phases.
We demonstrate the emergence of nonreciprocal superradiant phase transitions and novel multicriticality in a cavity quantum electrodynamics system, where a two-level atom interacts with two counterpropagating modes of a whispering-gallery-mode microcavity. The cavity rotates at a certain angular velocity and is directionally squeezed by a unidirectional parametric pumping χ^{(2)} nonlinearity. The combination of cavity rotation and directional squeezing leads to nonreciprocal first- and second-order superradiant phase transitions. These transitions do not require ultrastrong atom-field couplings and can be easily controlled by the external pump field. Through a full quantum description of the system Hamiltonian, we identify two types of multicritical points in the phase diagram, both of which exhibit controllable nonreciprocity. These results open a new door for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering various integrated nonreciprocal quantum devices.
In this paper, the quantum phase transitions caused by the interactions between light and atoms, as well as between light and mechanical oscillators, are discussed theoretically in a coupled optomechanical cavity containing two optical field modes (N atoms and mechanical oscillator). By using Holstein-Primak off transformation method, new translational boson operators and four parameters are assumed. The ground state energy functional of the system and a set of equations composed of four parameters are given. The correctness of the assumed translation boson operators is proved by two special cases. In the case of resonance, the characteristics of the obtained solutions are shown by solving the equations, graphical method and Hessian matrix judgment. The stable zero solution is called the normal phase, the unstable zero solution is named the unstable vacuum macroscopic phase, and the stable non-zero solution is referred to as the superradiation phase. The phase can transition from normal phase to superradiation phase, and the point of phase transition can be changed by adjusting the coupling intensity of the two cavity light fields. When the nonlinear photon-phonon interaction caused by radiation pressure is considered, the phase diagram of the system is expanded from the original two phase regions to three phase regions, including the coexistent normal phase and superradiation phase, the bistable superradiation phase, and the unstable vacuum macroscopic phase region, where the bistable superradiation phase is similar to the optical bistable phenomenon. At the same time, there is also a turning point curve, which overlaps with the phase transition point curve, indicating the existence of multiple quantum phase transitions in the system. These predictions can be detected by measuring the average number of photons. The coupled optomechanical cavity that we studied, when considering the coupling of the two-mode optical field and the atomic ensemble but no mechanical oscillator, reflects the interaction between the two-mode optical field and the atom, thus concluding that the transformation point is small and the quantum phase transition is easy to occur. When the coupling between the mechanical oscillator and the two-mode optical field is not considered, the interaction between the single-mode optical field and the atom is reflected, returning to the quantum phase transition of the Dicke model under rotating wave approximation.
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.
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.