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arXiv:1111.2340 · Physical Review A

Low-density molecular gas of tightly bound Rashba-Dresselhaus fermions

So Takei, Chien-Hung Lin, Brandon Anderson, Victor M. Galitski

Published Feb 21, 2012• 30 citations
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Abstract

We study interacting Rashba-Dresselhaus fermions in two spatial dimensions. First, we present an exact solution to the two-particle bound-state problem of spin-orbit (SO)-coupled fermions for arbitrary Rashba and Dresselhaus SO interactions. An exact molecular-wave function and the Green's function are derived explicitly along with the binding energy and the spectrum of the molecular state. In the second part, we consider a thermal Boltzmann gas of fermionic molecules and compute the time-of-flight (TOF) velocity and spin distributions for a single fermion in the gas. We show that the signatures of the bound state can be observed already in the first-moment expectation values, such as TOF density and spin profiles.

DOI
10.1103/physreva.85.023626

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We study interacting Rashba-Dresselhaus fermions in two spatial dimensions. First, we present an exact solution to the two-particle bound-state problem of spin-orbit (SO)-coupled fermions for arbitrary Rashba and Dresselhaus SO interactions. An exact molecular-wave function and the Green's function are derived explicitly along with the binding energy and the spectrum of the molecular state. In the second part, we consider a thermal Boltzmann gas of fermionic molecules and compute the time-of-flight (TOF) velocity and spin distributions for a single fermion in the gas. We show that the signatures of the bound state can be observed already in the first-moment expectation values, such as TOF density and spin profiles.
We derive general conditions for the emergence of singlet Feshbach molecules in the presence of artificial Zeeman fields for arbitrary mixtures of Rashba and Dresselhaus spin-orbit coupling in two or three dimensions. We focus on the formation of two-particle bound states resulting from interactions between ultracold spin-1/2\text{spin-}1/2spin-1/2 fermions, under the assumption that interactions are short ranged and occur only in the s-waves\text{-wave}s-wave channel. In this case, we calculate explicitly binding energies of Feshbach molecules and bound-state energy thresholds and analyze their dependence on spin-orbit couplings, Zeeman fields, interactions, and center-of-mass momentum, paying particular attention to the experimentally relevant case of spin-orbit couplings with equal Rashba and Dresselhaus (ERD) amplitudes.
In this Thesis we discussed ultracold Fermi gas with an s-wave interaction and synthetic spin-orbit coupling under a variety of conditions. We considered the system in both three and two spatial dimensions, with equal-Rashba-Dresselhaus type or Rashba-only type of spin-orbit-coupling, and with or without an artificial Zeeman field. We found competing effects on Fermionic superfluidity from spin-orbit coupling and Zeeman fields, and topologically non-trivial states in the presence of both fields. We gave an outlook on the many-body physics in the last.
We investigate normal-state properties of spin-orbit-coupled Fermi gases with repulsive sss-wave interaction, in the absence of molecule formation, i.e., in the so-called ``upper branch.'' Within the framework of random-phase approximation, we derive analytical expressions for the quasiparticle lifetime ${\ensuremath{\tau}}_{s}$, the effective mass ms∗{m}_{s}^{*}ms∗​, and the Green's function renormalization factor Zs{Z}_{s}Zs​ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit-coupled electron gas with Coulomb interaction, we show that the modifications are dependent on the Rashba band index sss and occur in the first order of the spin-orbit-coupling strength. We also calculate experimental observables such as spectral weight, density of state, and specific heat, which exhibit significant differences from their counterparts without spin-orbit coupling. We expect our microscopic calculations of these Fermi-liquid parameters would have immediate applications to the spin-orbit-coupled Fermi gases in the upper branch of the energy spectrum.
We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable sss-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.
We present a theoretical approach to the problem of two-dimensional fermion pairing under spin-orbit (SO) coupling and Zeeman interaction with an external magnetic field. We introduce a generic pairing Hamiltonian operating in the Hilbert space spanning free pairs and bare two-body bound states. The SO coupling of Rashba or Dresselhaus type provides ppp-wave dressing of an sss-wave spin-singlet bound state by continua in the triplet scattering channels. In the strong-coupling (Bose-Einstein condensate) limit of the many-body fermion system at zero temperature our theory maps onto the two-channel Fano-Anderson model of a spinless resonant ppp-wave superfluid.
We investigate theoretically radio-frequency spectroscopy of weakly bound molecules in an ultracold spin-orbit-coupled atomic Fermi gas. We consider two cases with either equal Rashba and Dresselhaus coupling or pure Rashba coupling. The former system has been realized very recently at Shanxi University [Wang et al., Phys. Rev. Lett. 109, 095301 (2012)] and MIT [Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)]. We predict realistic radio-frequency signals for revealing the unique properties of anisotropic molecules formed by spin-orbit coupling.