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arXiv:1211.5133

Quantum Degenerate Fermi Gas with Spin-orbit Coupling and Crossed Zeeman Fields

Kangjun Seo, Han Li, C. A. R. Sá de Melo

Published Nov 21, 2012• 0 citations
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Abstract

We study quantum degenerate ultra-cold Fermi gases in the presence of artificial spin-orbit coupling and crossed Zeeman fields. We emphasize the case where parity is violated in the excitation spectrum and compare it with the simpler situation where parity is preserved. We investigate in detail spectroscopic properties such as the excitation spectrum, the spectral function, momentum distribution and density of states for the cases where parity is preserved or violated. Similarly, we show that thermodynamic properties such as pressure, chemical potential, entropy, specific heat, isothermal compressibility and induced spin polarization become anisotropic as a function of Zeeman field components, when parity is violated. Lastly, we discuss the effects of interactions and present results for the pairing temperature as the precursor for the transition to a superfluid state. In particular, we find that the pairing temperature is dramatically reduced in the weak interaction regime as parity violation gets stronger, and that the momentum dependence of the order parameter for superfluidity violates parity when crossed Zeeman fields are present for finite spin-orbit coupling.

DOI
10.48550/arxiv.1211.5133

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Main purpose of this thesis is to present a discussion of the effects \nof artificial spin-orbit coupling and Zeeman fields in fermionic \nultra-cold atoms. Part of the work described here is inspired by \nthe experimental realization of artificial spin-orbit coupling (SOC) in the \nfermionic isotope $^{40}$K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of \ntwo-body bound states of fermions when artificial spin-orbit \ncoupling and artificial Zeeman fields are present. These bound-states \nare analyzed for two-hyperfine-state fermions in free space and \nin a harmonically confining potential. The second aspect explored \nis the study of spectroscopic and thermodynamic properties of \nthree-hyperfine-state fermions. These properties are investigated \nas a function of spin-orbit coupling and Zeeman fields for non-interacting \natoms, but when atom-atom interactions are also included, the many-body \nsystem consisting of three-hyperfine-state fermions \ncan exhibit exotic superfluid phases.

•May 15, 2015•2 citations
We study quantum degenerate ultra-cold Fermi gases in the presence of artificial spin-orbit coupling and crossed Zeeman fields. We emphasize the case where parity is violated in the excitation spectrum and compare it with the simpler situation where parity is preserved. We investigate in detail spectroscopic properties such as the excitation spectrum, the spectral function, momentum distribution and density of states for the cases where parity is preserved or violated. Similarly, we show that thermodynamic properties such as pressure, chemical potential, entropy, specific heat, isothermal compressibility and induced spin polarization become anisotropic as a function of Zeeman field components, when parity is violated. Lastly, we discuss the effects of interactions and present results for the pairing temperature as the precursor for the transition to a superfluid state. In particular, we find that the pairing temperature is dramatically reduced in the weak interaction regime as parity violation gets stronger, and that the momentum dependence of the order parameter for superfluidity violates parity when crossed Zeeman fields are present for finite spin-orbit coupling.
We discuss the creation of parity violating Fermi superfluids in the presence of non-Abelian gauge fields involving spin-orbit coupling and crossed Zeeman fields. We focus on spin-orbit coupling with equal Rashba and Dresselhaus (ERD) strengths which has been realized experimentally in ultra-cold atoms, but we also discuss the case of arbitrary mixing of Rashba and Dresselhaus (RD) and of Rashba-only (RO) spin-orbit coupling. To illustrate the emergence of parity violation in the superfluid, we analyze first the excitation spectrum in the normal state and show that the generalized helicity bands do not have inversion symmetry in momentum space when crossed Zeeman fields are present. This is also reflected in the superfluid phase, where the order parameter tensor in the generalized helicity basis violates parity. However, the pairing fields in singlet and triplet channels of the generalized helicity basis are still parity even and odd, respectively. Parity violation is further reflected on ground state properties such as the spin-resolved momentum distribution, and in excitation properties such as the spin-dependent spectral function and density of states.
We performed a theoretical investigation on the ground state properties of a two dimensional ultra-cold Fermi superfluid with an anisotropic spin-orbit coupling (SOC). In the absence of Zeeman field, the system evolves from weak coupling BCS regime to strongly interacting BEC regime (BCS-BEC crossover) with increasing either the two-particle interaction strength or SOC parameters. We focused on the behaviors of pairing parameter and density of states (DOS) when increasing the anisotropic parameter of the SOC. Surprisingly, we discovered that the gap parameter decreases with increasing the anisotropic parameters, but the DOS at the Fermi surface shows non-monotonic behavior as a function of the anisotropic parameter. In the presence of the Zeeman field, we discussed a particular type of topological phase transition by obtaining the analytical result of the topological invariant and directly related this quantum phase transition with a sudden change of the ground state wave-function. Effects of higher partial wave pairing terms on this topological phase transition were briefly discussed.
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.
We investigate the thermodynamic properties of a superfluid Fermi gas subject to Rashba spin-orbit coupling and effective Zeeman field. We adopt a TTT-matrix scheme that takes beyond-mean-field effects, which are important for strongly interacting systems, into account. We focus on the calculation of two important quantities: the superfluid transition temperature and the isothermal compressibility. Our calculation shows very distinct influences of the out-of-plane and the in-plane Zeeman fields on the Fermi gas. We also confirm that the in-plane Zeeman field induces a Fulde-Ferrell superfluid below the critical temperature and an exotic finite-momentum pseudogap phase above the critical temperature.
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.
Main purpose of this thesis is to present a discussion of the effects \nof artificial spin-orbit coupling and Zeeman fields in fermionic \nultra-cold atoms. Part of the work described here is inspired by \nthe experimental realization of artificial spin-orbit coupling (SOC) in the \nfermionic isotope 40^{40}40K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of \ntwo-body bound states of fermions when artificial spin-orbit \ncoupling and artificial Zeeman fields are present. These bound-states \nare analyzed for two-hyperfine-state fermions in free space and \nin a harmonically confining potential. The second aspect explored \nis the study of spectroscopic and thermodynamic properties of \nthree-hyperfine-state fermions. These properties are investigated \nas a function of spin-orbit coupling and Zeeman fields for non-interacting \natoms, but when atom-atom interactions are also included, the many-body \nsystem consisting of three-hyperfine-state fermions \ncan exhibit exotic superfluid phases.