In this paper we investigate the ground-state properties and related quantum phase transitions for the two-component Bose-Einstein condensate in a single-mode optical cavity. Apart from the usual normal and superradiant phases, multi-stable macroscopic quantum states are realized by means of the spin-coherent-state variational method. We demonstrate analytically the stimulated radiation from a collective state of atomic population inversion, which does not exist in the normal Dicke model with single-component atoms. It is also revealed that the stimulated radiation can be generated only from one component of atoms and the other remains in the ordinary superradiant state. However, the order of superradiant and stimulated-radiation states is interchangeable between two components of atoms by tuning the relative atom-field couplings and the frequency detuning as well.
In this paper we investigate the ground-state properties and related quantum phase transitions for the two-component Bose-Einstein condensate in a single-mode optical cavity. Apart from the usual normal and superradiant phases, multi-stable macroscopic quantum states are realized by means of the spin-coherent-state variational method. We demonstrate analytically the stimulated radiation from a collective state of atomic population inversion, which does not exist in the normal Dicke model with single-component atoms. It is also revealed that the stimulated radiation can be generated only from one component of atoms and the other remains in the ordinary superradiant state. However, the order of superradiant and stimulated-radiation states is interchangeable between two components of atoms by tuning the relative atom-field couplings and the frequency detuning as well.
In this paper we explore the rich structure of macroscopic many-particle quantum states for a Bose-Einstein condensate in an optical cavity with a tunable nonlinear atom-photon interaction [K. Baumann et al., Nature (London) 464, 1301 (2010)]. Population inversion, bistable normal phases, and the coexistence of normal-superradiant phases are revealed by adjusting the experimentally realizable interaction strength and pump-laser frequency. For the negative (effective) cavity frequency we observe, remarkably, an inverted quantum phase transition (QPT) from the superradiant to the normal phases with an increase in atom-field coupling, which is just opposite the QPT in the normal Dicke model. Bistable macroscopic states are derived analytically in terms of the spin-coherent-state variational method by taking into account both normal and inverted pseudospin states.
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.
We investigate the multiple stable macroscopic quantum states of a Bose-Einstein condensate in an optomechanical cavity with pump-cavity field detuning and atom-photon interaction following the experimental realization of the quantum phase transition [Nature (London) 464, 1301 (2010)]. The spin-coherent-state variational method is useful in exploring the multistability since it has the advantage of including both normal and inverted pseudospin states. In the blue detuning regime the usual transition from normal to superradiant phases still exists, however, when the atom-field coupling increases to a certain value, called the turning point, the superradiant phase collapses due to the resonant damping of the mechanical oscillator. As a consequence, the system undergoes at this point an additional phase transition to the normal phase of the atomic population inversion state. In particular, the superradiant phase disappears completely at strong photon-phonon interaction, resulting in the direct atomic population transfer between two atomic levels. Moreover, the coupling-induced collapse and revival of the superradiant state are also found in the red detuning region.
Abstract Based on spin-coherent-state variational method, we mainly study the multiple stable macroscopic quantum states and quantum phase transitions of a Bose-Einstein Condensate in an optomechanical dual-cavity by modulating the dual-cavity interaction and the nonlinear phonon-photon interaction. Especially, the collapse of superradiant phase can be tuned in the existing nonlinear photon-phonon interaction, but the critical quantum phase transition point or boundary hasn’t been inflfluenced. As a result, the system occurs an additional phase transition from the superradiant phase to the inversely atomic populated state. Moreover, when dual-cavity coupling interaction increases to a certain value, a new quantum phase transition from the normal phase to the inversely atomic populated state will appear. Finally, the superradiant phase completely collapses and the normal phase also collapses into an unstable macroscopic vacuum state for a strong dual-cavity coupling interaction.
In this paper we reveal the rich ground-state properties induced by the strong nonlinear atom-photon interaction which has been found in the recent experiment about a Bose-Einstein condensate coupling with a high-finesse cavity [Nature (London) 464, 1301 (2010)]. Two detuning-dependent phase diagrams are revealed by investigating the experimentally measurable atomic population. In particular, two quantum phase transitions from the superradiant phase or the normal phase to a dynamically unstable phase are predicted in the blue detuning. Moreover, the three-phase coexistence points are found. It is also demonstrated that these predicted quantum phase transitions are the intrinsic transitions governed only by the second-order derivative of the ground-state energy. Finally, we also point out that the region involving coexistence of the superradiant phase and the normal phase previously predicted cannot happen in the ground state.
An extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted a second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, second-order phase transition from the superradiant phase to the ``Mott'' phase is also revealed. In addition, a rich and exotic phase diagram is presented.