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Journal of Physics B Atomic Molecular and Optical Physics

Collective excitations of a repulsive 2D ultracold Fermi gas with spin–orbit coupling

Lorenzo Gigli, Flavio Toigo

Published Oct 28, 2015• 2 citations
Publisher

Abstract

Abstract We describe the effects of spin–orbit (SO) coupling on the collective properties of a two-dimensional (2D) ultracold Fermi gas with Rashba and Dresselhaus SO couplings of equal strength. We first analyse the thermodynamics of the Fermi gas in the absence of repulsive interaction between the atoms (non-interacting system) showing that SO coupling determines one or more second-order phase transitions in the equation of state of the system; we subsequently suggest an experimental strategy that can make these transitions visible. We then study the interacting system using Feynman’s path integral formulation. The aim of this analysis is to describe the collective properties of the system in the paramagnetic phase and in weak non-equilibrium conditions. Particular emphasis is given to the numerical analysis of the collective modes of the system, in particular to the zero sound mode and to the spin modes.

DOI
10.1088/0953-4075/48/24/245302

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Abstract We describe the effects of spin–orbit (SO) coupling on the collective properties of a two-dimensional (2D) ultracold Fermi gas with Rashba and Dresselhaus SO couplings of equal strength. We first analyse the thermodynamics of the Fermi gas in the absence of repulsive interaction between the atoms (non-interacting system) showing that SO coupling determines one or more second-order phase transitions in the equation of state of the system; we subsequently suggest an experimental strategy that can make these transitions visible. We then study the interacting system using Feynman’s path integral formulation. The aim of this analysis is to describe the collective properties of the system in the paramagnetic phase and in weak non-equilibrium conditions. Particular emphasis is given to the numerical analysis of the collective modes of the system, in particular to the zero sound mode and to the spin modes.
We briefly review recent progress on ultracold atomic Fermi gases with different types of synthetic spin-orbit coupling, including the one-dimensional (1D) equal weight Rashba-Dresselhaus and two-dimensional (2D) Rasbha spin-orbit couplings. Theoretically, we show how the single-body, two-body and many-body properties of Fermi gases are dramatically changed by spin-orbit coupling. In particular, the interplay between spin-orbit coupling and interatomic interaction may lead to several long-sought exotic superfluid phases at low temperatures, such as anisotropic superfluid, topological superfluid and inhomogeneous superfluid. Experimentally, only the first type - equal weight combination of Rasbha and Dresselhaus spin-orbit couplings - has been realized very recently using a two-photon Raman process. We show how to characterize a normal spin-orbit coupled atomic Fermi gas in both non-interacting and strongly-interacting limits, using particularly momentum-resolved radio-frequency spectroscopy. The experimental demonstration of a strongly-interacting spin-orbit coupled Fermi gas opens a promising way to observe various exotic superfluid phases in the near future.
We investigate the collective modes in the spin-orbit-coupled Fermi gas with repulsive sss-wave interaction. The interplay between spin-orbit coupling and atom-atom interactions plays the crucial role in the collective behaviors of Fermi gas. In contrast with ordinary Fermi liquid, spin-orbit-coupled Fermi gas has strongly correlated spin and density excitations. Within the scheme of random-phase approximation, we classify collective modes based on the symmetry group and determine their properties via the poles of corresponding correlation functions. Besides, the particle-hole continuum is obtained, where the imaginary part of these correlation functions becomes nonvanishing. We also propose an experimental protocol for detecting these collective modes and discuss corresponding experimental signatures in the ultracold Fermi gases experiment.
We study the effect of spin-orbit coupling on both the zero-temperature and nonzero-temperature behavior of a two-dimensional Fermi gas. We include a generic combination of Rashba and Dresselhaus terms into the system Hamiltonian, which allows us to study both the experimentally relevant equal-Rashba-Dresselhaus (ERD) limit and the Rashba-only (RO) limit. At zero temperature, we derive the phase diagram as a function of the two-body binding energy and Zeeman field. In the ERD case, this phase diagram reveals several topologically distinct uniform superfluid phases, classified according to the nodal structure of the quasiparticle excitation energies. Furthermore, we use a momentum-dependent SU(2) rotation to transform the system into a generalized helicity basis, revealing that spin-orbit coupling induces a triplet pairing component of the order parameter. At nonzero temperature, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition by including phase fluctuations of the order parameter up to second order. We show that the superfluid density becomes anisotropic due to the presence of spin-orbit coupling (except in the RO case). This leads both to elliptic vortices and antivortices, and to anisotropic sound velocities. The latter prove to be sensitive to quantum phase transitions between topologically distinct phases. We show further that at a fixed nonzero Zeeman field, the BKT critical temperature is increased by the presence of ERD spin-orbit coupling. Subsequently, we demonstrate that the Clogston limit becomes infinite: TBKT{T}_{\mathrm{BKT}}TBKT​ remains nonzero at all finite values of the Zeeman field. We conclude by extending the quantum phase transition lines to nonzero temperature, using the nodal structure of the quasiparticle spectrum, thus connecting the BKT critical temperature with the zero-temperature results.
Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.
We study the ground-state properties of a two-component ultracold superfluid Fermi gas with Rashba spin-orbit coupling at zero temperature in two-dimensional.The gap-order parameter and number densities are found analytically throught the thermodynamic potential at saddle point by using the functional and integral method.We obtain the phase diagram by solve the self-consistent equations.Under the influence of spin orbit couping,and we construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states.The balance of pairing will be broken due to the unequal chemical potentials in the two-component ultracold Fermi gas in two-dimensional with spin orbit coupling.
We investigate the Zeeman field effects on the bulk superfluid properties and the collective modes in two-dimensional (2D) attractive atomic Fermi gases with Rashba-type spin-orbit coupling. In the presence of a large spin-orbit coupling, the system undergoes a quantum phase transition to a topological superfluid state at a critical Zeeman field. We show that the nonanalyticities of the thermodynamic functions as well as other physical quantities at the quantum phase transition originate from the infrared singularities caused by the gapless fermionic spectrum. The same argument applies also to the BCS-BEC evolution in 2D fermionic superfluids with ppp- or ddd-wave pairing. The superfluid density ns{n}_{s}ns​ and the velocity of the Goldstone sound mode cs{c}_{s}cs​ behave oppositely in the normal and the topological superfluid phases: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The velocity of the Goldstone sound mode also shows nonanalyticity at the quantum phase transition. For large Zeeman field, we find ${n}_{s}\ensuremath{\rightarrow}n$ and ${c}_{s}\ensuremath{\rightarrow}{\ensuremath{\upsilon}}_{\mathrm{F}}$, where nnn is the total fermion density and ${\ensuremath{\upsilon}}_{\mathrm{F}}$ is the Fermi velocity of noninteracting system. The unusual behavior of the superfluid density and the collective modes can be understood by the fact that the spin-orbit-coupled superfluid state at large Zeeman field can be mapped to the px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid state of spinless fermions.