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arXiv:0802.3972 · Physical Review A

Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity

Gang Chen, Xiaoguang Wang, J.-Q. Liang, Z. D. Wang

Published Aug 29, 2008• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.78.023634

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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.
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.
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.
When an atomic ensemble is coupled with a cavity field governed by the well-known Dicke model , an important quantum phase transition (QPT) from the normal phase to the superradiant phase occurs, which was predicted more than 30 years ago. In this paper, both the atom-photon nonlinear interaction and the driving field are added to the Dicke's Hamiltonian. With the method of Holstein-Primafoff transformation, the ground state energy is given by the theoretical calculation, and the rich phase figures are presented. Meanwhile, these properties are observed experimentally. We mainly dicuss the effects of the atom-photon nonlinear interaction and the driving field on QPT.
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.
The coupling of ultracold fermions to a high-finesse optical cavity can result in novel many-body phenomena, and has attracted significant interests at present. Here we consider a realization of the Fermi-Dicke model with controllable parameters, based on a two-dimensional polarized degenerate Fermi gas coupled to an optical cavity. We analytically investigate the ground-state properties of such system under the mean-field approximation. We find the system can exhibit a rich phase diagram depending on the fermion-photon coupling strength and the atomic resonant frequency. Contrasting to the bosonic counterpart, a first-order quantum phase transition between the superradiant phase and the normal phase featuring two Fermi surfaces can occur for the weak atomic resonant frequency, and there is a unique mixed phase where this normal phase and the superradiant phase coexist. The experimental detection of our results is also discussed.