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arXiv:1701.02897

Quantum phases of a two-dimensional polarized degenerate Fermi gas in an optical cavity

Yanlin Feng, Kuang Zhang, Jingtao Fan, Feng Mei, Gang Chen, Suotang Jia

Published Jan 11, 2017• 1 citation
arXivHTMLPDF

Abstract

In this paper we analytically investigate the ground-state properties of a two-dimensional polarized degenerate Fermi gas in a high-finesse optical cavity, which is governed by a generalized Fermi-Dicke model with tunable parameters. By solving the photon-number dependent Bogoliubov-de-Gennes equation, we find rich quantum phases and phase diagrams, which depend crucially on the fermion-photon coupling strength, the fermion-fermion interaction strength, and the atomic resonant frequency (effective Zeeman field). In particular, without the fermion-fermion interaction and with a weak atomic resonant frequency, we find a mixed phase that the normal phase with two Fermi surfaces and the superradiant phase coexist, and reveal a first-order phase transition from this normal phase to the superradiant phase. With the intermediate fermion-fermion interaction and fermion-photon coupling strengths, we predict another mixed phase that the superfluid and superradiant phases coexist. Finally, we address briefly how to detect these predicted quantum phases and phase diagrams in experiments.

DOI
10.48550/arxiv.1701.02897

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In this paper we analytically investigate the ground-state properties of a two-dimensional polarized degenerate Fermi gas in a high-finesse optical cavity, which is governed by a generalized Fermi-Dicke model with tunable parameters. By solving the photon-number dependent Bogoliubov-de-Gennes equation, we find rich quantum phases and phase diagrams, which depend crucially on the fermion-photon coupling strength, the fermion-fermion interaction strength, and the atomic resonant frequency (effective Zeeman field). In particular, without the fermion-fermion interaction and with a weak atomic resonant frequency, we find a mixed phase that the normal phase with two Fermi surfaces and the superradiant phase coexist, and reveal a first-order phase transition from this normal phase to the superradiant phase. With the intermediate fermion-fermion interaction and fermion-photon coupling strengths, we predict another mixed phase that the superfluid and superradiant phases coexist. Finally, we address briefly how to detect these predicted quantum phases and phase diagrams in experiments.
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.
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.
We study the superradiance transition of a two-component three-dimensional Fermi gas interacting with a single-mode light field of Dicke-type coupling. We find that for a noninteracting gas, due to the Fermi blocking, a unique superradiant state with a superradiant outer shell surrounding an inner Fermi sea may appear, and the critical atom-light coupling strength gc{g}_{c}gc​ to trigger the superradiance approaches $\sqrt{{\ensuremath{\omega}}_{c}{E}_{F}/3}$ even for a vanishing transition frequency between a two-spin state (${\ensuremath{\omega}}_{a}\ensuremath{\rightarrow}0$), in contrast to ${g}_{c}\ensuremath{\sim}\sqrt{{\ensuremath{\omega}}_{c}{\ensuremath{\omega}}_{a}}\ensuremath{\rightarrow}0$ for a bosonic or spin system. When the atom-atom attraction is included, we find that the atomic superfluid would compete with the superradiance directly and both orders cannot coexist, giving rise to an interesting ground-state phase diagram with a tricritical point. The resultant phases and phase transitions are characterized by the unique fluctuation spectrum beyond the mean-field level. We further analyze the effects caused by the decay of the light field, which is inevitable for a possible realization in a cavity with a cold atom system. Our results would be beneficial for the understanding of the interplay between Fermi superfluid and superradiance.
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.
Abstract We investigate the ground-state properties and quantum phase transitions of an ensemble consisting of NNN four-level atoms within an optical cavity coupled to the single cavity mode and external laser fields. The system is described by an extended imbalanced Dicke model, in which the co- and counterrotating coupling terms are allowed to have different coupling strengths. Some novel polarized phases characterized by the phase differences between the cavity field or the atomic spin excitation and the Raman laser are found analytically. Meanwhile, the full phase diagram and quantum phase transitions are also revealed. Two sign-dependent coexisting phases have been identified, where the normal phase persists as a metastable state alongside the superradiant ground state. Finally, the breaking or restoration of the intrinsic symmetry in this system is addressed. It is found that besides the continuous U(1)U(1)U(1) and discrete Z2\mathbb{Z}_2Z2​ symmetries, the system also exhibits two reflection symmetries σv\sigma_vσv​s, a central symmetry C2C_2C2​ in the abstract position-momentum representation, and a discrete reflection parity-time (PT\mathcal{PT}PT) symmetry, a parameter exchange symmetry Tex\mathcal{T}_\mathrm{ex}Tex​ in the parameters space. These additional symmetries are governed by two Coxeter groups.