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arXiv:1801.08254 · Physical Review A

Magnetic order in a Fermi gas induced by cavity-field fluctuations

Jingtao Fan, Xiaofan Zhou, Wei Zheng, Wei Yi, Gang Chen, Suotang Jia

Published Oct 12, 2018• 25 citations
arXivHTMLPDF

Abstract

We show that cavity-field fluctuations can induce interesting magnetic phases and phase transitions in an atom-cavity coupled system. Adopting a numerical density-matrix-renormalization-group method, we study the steady state of a two-component Fermi gas subject to cavity-assisted Raman coupling in a one-dimensional lattice at half filling. The cavity-enhanced atom-photon coupling introduces a dynamic long-range interaction in the atoms, which competes with the short-range on-site interactions and leads to a rich phase diagram with a variety of magnetic orders. Importantly, as all the phase transitions take place outside the superradiant regime, the magnetic orders are associated with cavity-field fluctuations with a vanishing number of photons on the mean-field level.

DOI
10.1103/physreva.98.043613

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We explore the density and spin self-ordering of driven spin-1/2 collisionless fermionic atoms coupled to the electromagnetic fields of a ring resonator. The two spin states are two-photon Raman-coupled via a pair of degenerate counterpropagating cavity modes and two transverse pump fields. In this one-dimensional configuration the coupled atom-field system possesses a continuous U (1) translational symmetry and a discrete Z 2 spin inversion symmetry. At half filling for sufficiently strong pump strengths, the combined U (1) × Z 2 symmetry is spontaneously broken at the onset of a superradiant phase transition to a state with self-ordered density and spin structures. We predominately find an antiferromagnetic lattice order at the cavity wavelength. The self-ordered states exhibit unexpected positive momentum pair correlations between fermions with opposite spin. These strong cavity-mediated correlations vanish at higher pump strength.
In this work we show that the superradiance of the cavity photons can give rise to a magnetic transformation for the atomic system when the quasi one-dimensional Fermi gases are coupled to an optical cavity. This magnetic transformation has a close relationship with the atomic detuning and the filling number. When the interaction between the atoms is neglected, the mean-field approximation may be used in the superradiant phase. In this approximation, we analyze the static spin structure factors of the system with different filling numbers and atomic detuning. Then we characterize the cavity photons-assisted magnetic transformation and obtain the phase diagrams which are dependent on the cavity parameters. Finally, the feasible experimental parameters of our results are also discussed.
We investigate fermionic atoms subjected to an optical lattice and coupled to a high finesse optical cavity with photon losses. A transverse pump beam introduces a coupling between the atoms and the cavity field. We explore the steady-state phase diagram taking fluctuations around the mean field of the atoms-cavity coupling into account. Our approach allows us to investigate both one- and higher-dimensional atomic systems. The fluctuations beyond mean field lead to an effective temperature that changes the nature of the self-organization transition. We find a strong dependence of the results on the atomic filling, in particular when contrasting the behavior at low filling and at half filling. At low filling, the transition to a self-organized phase takes place at a critical value of the pump strength. In the self-organized phase, the cavity field takes a finite expectation value and the atoms show a modulation in the density. Surprisingly, at even larger pump strengths a strongly nonmonotonous behavior of the temperature is found and hints toward effects of cavity cooling at many-body resonances. Additionally multiple self-organized stable solutions of the cavity field and the atoms occur, signaling the presence of a fluctuation-induced bistability, with the two solutions having different effective temperatures previously discussed by Tolle . []. In contrast, at half filling a bistable region arises at the self-organization transition already neglecting the fluctuations. The presence of the fluctuations induce an effective temperature, as at lower fillings, and change the behavior of the transition and the steady states drastically. We analyze the properties of the occurring steady states of the coupled atoms-cavity system.
Abstract We discuss the fluid structure in the quantum phases of a 1D spinful Fermi gas of atoms interacting via an infinitely long-range coupling, as it may result from a photon-mediated two-body coupling in optical cavities. The system reveals a rich physics, where the spin/charge-density wave and superfluid-like order compete with each other. Following our previous work based on a combined mean-field, exact diagonalization and bosonization analysis, we provide the phase diagram of the system and discuss the structure of the fluid, addressing the main features in momentum space of the order parameters, momentum distribution and two-body correlations. We highlight that the nesting of the Fermi surface in 1D ultimately drives the formation of periodic structures commensurate with the cavity-induced mean-field potential.
We predict the existence of a topological superradiant state in a two-component degenerate Fermi gas in a cavity. The superradiant light generation in the transversely driven cavity mode induces a cavity-assisted spin-orbit coupling and opens a bulk gap at half filling. This mechanism can simultaneously drive a topological phase transition in the system, yielding a topological superradiant state. We map out the steady-state phase diagram in the presence of an effective Zeeman field, and identify a critical tetracritical point beyond which the topological and the conventional superraidiant phase boundaries separate. The topological phase transition can be detected from its signatures in either the momentum distribution of the atoms or the variation of the cavity photon occupation due to the nontrivial feedback of the atoms on the cavity field.
We numerically study a gas of two-component fermions coupled to a transversely pumped optical cavity and confined to a two-dimensional static square optical lattice. In the dispersive regime, the steady state of the system is described by an extended Hubbard Hamiltonian with cavity-mediated long-range interactions. Using real-space dynamical mean-field theory (RDMFT), we investigate the formation of the (superradiant) checkerboard density-wave phase. Our analysis focuses on paramagnetic phases both at quarter and half filling. At quarter filling, we find a reentrant homogeneous Fermi liquid to density wave phase transition with increasing temperature, which is due to the higher entropy of the ordered phase. At half filling, in addition to the Fermi liquid to Mott insulator phase transition, marked by a vanishing quasiparticle residue at the Fermi level, we identify the transition into a density-wave phase. Due to perfect Fermi surface nesting at half filling, we find that arbitrarily small long-range interactions destabilize the system towards the density-wave phase in the absence of short-range interactions. By varying short- and long-range interactions at a fixed low temperature, we obtain the full phase diagram and identify a region of coexistence between the homogeneous Fermi liquid and Mott insulating phase with the density-wave phase. In this region, we determine the thermodynamic phase transition by comparing the energies of the different RDMFT solutions.