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 theoretically study an interacting few-body system of Rashba spin-orbit-coupled two-component Bose gases confined in a harmonic trapping potential. We solve the interacting Hamiltonian at large Rashba coupling strengths using an exact-diagonalization scheme, and obtain the ground-state phase diagram for a range of interatomic interactions and particle numbers. At small particle numbers, we observe that the bosons condense to an array of topological states with
n+1/2 quantum angular momentum vortex configurations, where
n=0,1,2,3,.... At large particle numbers, we observe two distinct regimes: at weaker-interaction strengths, we obtain ground states with topological and symmetry properties that are consistent with mean-field theory computations; at stronger-interaction strengths, we report the emergence of strongly correlated ground states.
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.
We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy. Published by the American Physical Society 2024
We study a class of interacting, harmonically trapped boson systems at angular momentum L. The Hamiltonian leaves a L-dimensional subspace invariant, and this permits an explicit solution of several eigenstates and energies for a wide class of two-body interactions. PACS numbers: 05.30.Jp, 03.75.Fi, 03.65.Fd, 67.40.Db Typeset using REVTEX 1 The study of vortices in Bose-Einstein condensates of trapped atomic vapors is of considerable experimental [1,2] and theoretical [3–13] interest. Present experiments and much theoretical work [3–7] focus on the Thomas-Fermi regime of short coherence length [14]. The opposite limit of perturbatively weak contact interactions is not yet realized experimentally but is of theoretical interest as well [8–13]. The case of attractive interactions was studied by Wilkin et al. [9]. Mottelson developed a theory for repulsive interactions [10], and Kavoulakis et al. [12] and Jackson et al. [13] compared mean field and exact numerical results. Exact diagonalization techniques by us showed that the ground state energy depends linearly on angular momentum and led to an analytical expression for the ground state wave function [11]. Recently, the form of this wave function and its eigenenergy were confirmed in analytic calculations [15–17]. However, we still lack insight about why certain eigenstates turn out to be simple analytical functions. We show in this paper that there is a subspace structure that explains these findings. Interestingly, this structure is not limited to the two-body contact interaction considered in previous investigations but present in a rather large class of Hamiltonians. Let us consider a system of N harmonically trapped bosons in two spatial dimensions 1 at angular momentum
We theoretically investigate the condensate state and collective excitations of a two-component Bose gas in a two-dimensional harmonic trap subject to isotropic Rashba spin-orbit coupling. In the weakly interacting regime when the interspecies interaction is larger than the intraspecies interaction (${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}>g$), we find that the condensate ground state has a half-quantum angular momentum vortex configuration with spatial rotational symmetry and skyrmion-type spin texture. Upon increasing the interatomic interaction beyond a threshold
gc, the ground state starts to involve higher-order angular momentum components and thus breaks rotational symmetry. In the case of ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}<g$, the condensate becomes unstable toward the superposition of two degenerate half-quantum vortex states. Both instabilities (at
g>gc and ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}<g$) can be determined by solving the Bogoliubov equations for collective density oscillations of the half-quantum vortex state and by analyzing the softening of mode frequencies. We obtain the phase diagram as a function of the interatomic interactions and the spin-orbit coupling. In addition, we directly simulate the time-dependent Gross-Pitaevskii equation to examine the dynamical properties of the system. Finally, we investigate the stability of the half-quantum vortex state against both trap anisotropy and anisotropy in the spin-orbit coupling.