Harmonically trapped two-atom systems: Interplay of short-range s-wave interaction and spin-orbit coupling

Abstract

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" $k_{\text{so}}$. 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. 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.

15 figures (several subfigures), 23 pages

References in corpus (13)

• Spin-orbit coupling in quantum gases
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Spin-Orbit Coupled Spinor Bose-Einstein Condensates
• Spin-orbit coupled Bose-Einstein condensates
• Molecules of Fermionic Atoms in an Optical Lattice
• Virial expansion for a strongly correlated Fermi gas
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Gate-controlled spin-orbit interaction in a parabolic GaAs/AlGaAs quantum well
• Effective Theory for Trapped Few-Fermion Systems
• BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Modified Bethe-Peierls boundary condition for ultracold atoms with Spin-Orbit coupling
• Occupation numbers of the harmonically trapped few-boson system

Cited by in corpus (15)

• Degenerate Quantum Gases with Spin-Orbit Coupling
• One-dimensional mixtures of several ultracold atoms: a review
• General ultracold scattering formalism with isotropic spin orbit coupling
• Spin structure of harmonically trapped one-dimensional atoms with spin-orbit coupling
• Two interacting ultracold molecules in a one-dimensional harmonic trap
• Energy spectrum of a harmonically trapped two-atom system with spin-orbit coupling
• Spin-orbit coupled bosons interacting in a two-dimensional harmonic trap
• Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap
• Quantum collision theory in flat bands
• Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling
• Are smooth pseudopotentials a good choice for representing short-range interactions?
• Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling
• Spin Hall mode in a trapped thermal Rashba gas
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting