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Journal of Physics B Atomic Molecular and Optical Physics

Dicke quantum phase transition with a degenerate Fermi gas in an optical cavity

Shuai Yang, M. Al-Amri, Muhammad Suhail Zubairy

Published Jun 25, 2014• 4 citations
Publisher

Abstract

A quantum-degenerate Fermi gas in an optical cavity is investigated. It is shown that there exists a self-organization phase transition. This phase transition can be identified as the Dicke quantum phase transition. This investigation opens the door to include degenerate Fermi gases in the group of atomic systems which exhibit a self-organization threshold.

DOI
10.1088/0953-4075/47/13/135503

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A quantum-degenerate Fermi gas in an optical cavity is investigated. It is shown that there exists a self-organization phase transition. This phase transition can be identified as the Dicke quantum phase transition. This investigation opens the door to include degenerate Fermi gases in the group of atomic systems which exhibit a self-organization threshold.
A phase transition describes the sudden change of state in a physical system, such as the transition between a fluid and a solid. Quantum gases provide the opportunity to establish a direct link between experiment and generic models which capture the underlying physics. A fundamental concept to describe the collective matter-light interaction is the Dicke model which has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose-Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-ranged interactions between the condensed atoms. These are induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. The work opens the field of quantum gases with long-ranged interactions, and provides access to novel quantum phases.
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.
Coupling Bose-Einstein condensates to optical cavities has enabled the study of many-body states with long-range interactions. However, equivalent experiments with ultracold Fermi gases have remained largely unexplored. Here, we report an experimental realization of a superradiant quantum phase transition of a degenerate Fermi gas in a transversely pumped optical cavity. The self-ordering checkerboard density pattern of Fermi gases and superradiant transitions of the cavity field spontaneously emerge by increasing the pumping intensity above a threshold value. The effects of Fermi statistics are manifested by an inverse square root scaling of the threshold with atom number and the slow dynamics of low–atomic momentum states. Our work provides an ideal platform for studying nonequilibirium dynamics of many-body states for long-range interacting Fermi gases.
Understanding the interplay between collective optical response and disorder presents significant challenges in modern many-body physics. While there has been considerable interest and a wealth of theoretical work in recent years, the experimental investigation of the superradiant phase transition and disorder has been unexplored. Here, we report an observation of the localization-driven superradiance with a degenerate Fermi gas in an optical cavity. We show that the dynamics of Fermi gases exhibits Anderson localization in an intracavity incommensurate lattice. The exponential localization is directly observed in both spatial and momentum spaces. We observe the localization driving a nearly vanishing pump threshold in fermionic superradiance when the system is in the localized state. The underlying mechanism of the self-organization and the quantum statistic of the atoms are revealed by measuring the atom momentum distribution and characteristic growth of the superradiant field. Our work provides a platform for studying superradiant quantum phase transition and localization in photon-mediated long-range interacting Fermi gases.
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.