We introduce a theoretical approach to determine the spin structure of harmonically trapped atoms with two-body zero-range interactions subject to an equal mixture of Rashba and Dresselhaus spin-orbit coupling created through Raman coupling of atomic hyperfine states. The spin structure of bosonic and fermionic two-particle systems with finite and infinite two-body interaction strength
g is calculated. Taking advantage of the fact that the
N-boson and
N-fermion systems with infinitely large coupling strength
g are analytically solvable for vanishing spin-orbit coupling strength
kso and vanishing Raman coupling strength $\mathrm{\ensuremath{\Omega}}$, we develop an effective spin model that is accurate to second order in $\mathrm{\ensuremath{\Omega}}$ for any
kso and infinite
g. The three- and four-particle systems are considered explicitly. It is shown that the effective spin Hamiltonian, which contains a Heisenberg exchange term and an anisotropic Dzyaloshinskii-Moriya exchange term, describes the transitions that these systems undergo with the change of
kso as a competition between independent spin dynamics and nearest-neighbor spin interactions.
Abstract We study harmonically trapped one-dimensional atoms subjected to an equal combination of Rashba and Dresselhaus spin–orbit coupling induced by Raman transition. We first examine the wave function and the degeneracy of the single-particle ground state, followed by a study of two weakly interacting bosons or fermions. For the two-particle ground state, we focus on the effects of the interaction on the degeneracy, the spin density profiles, and the density–density correlation functions. Finally we show how these studies help us to understand the many-body properties of the system.
We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wave function, binding energy, and effective mass, are determined from the two-particle solution of two interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Fermi golden rule and take into account the effect of harmonic traps within local density approximation. The total radio-frequency spectroscopy is discussed as functions of temperature and spin-orbit coupling strength. Our results give a qualitative picture of radio-frequency spectroscopy of a resonantly interacting spin-orbit-coupled Fermi gas and can be directly tested in atomic Fermi gases of
40K atoms at Shanxi University and
6Li atoms at the Massachusetts Institute of Technology.
We explore the two-body spectra of spin-
1/2 fermions in isotropic harmonic traps with external spin-orbit potentials and short-range two-body interactions. Using a truncated basis of total angular momentum eigenstates, nonperturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.
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.
The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms, and condensed-matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold-atom systems, giving rise to a spin-orbit coupling term with ``strength''
kso. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body
s-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground-state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small
s-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly interacting unitary regime. We find that the interplay between the spin-orbit coupling term and the
s-wave interaction generically enters, depending on the exact parameter combinations of the
s-wave scattering lengths, at order
kso2 or
kso4 for the ground state and leads to a shift of the energy of either sign. While the absence of a term proportional to
kso follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to
kso2 for certain parameter combinations is unexpected. The well-known fact that the spin-orbit coupling term couples the relative and center-of-mass degrees of freedom has interesting consequences for the trapped two-particle systems. For example, we find that, for certain parameter combinations, the spin-orbit coupling term turns sharp crossings into avoided crossings with an energy splitting proportional to
kso. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.