Spin structure of harmonically trapped one-dimensional atoms with spin-orbit coupling

Abstract

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 $k_{so}$ and vanishing Raman coupling strength $\Omega$, we develop an effective spin model that is accurate to second-order in $\Omega$ for any $k_{so}$ 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 $k_{so}$ as a competition between independent spin dynamics and nearest-neighbor spin interactions.

23 pages, 10 figures

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Cited by in corpus (15)

• One-dimensional mixtures of several ultracold atoms: a review
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Probing Ferromagnetic Order in Few-Fermion Correlated Spin-Flip Dynamics
• Harmonically Trapped Atoms with Spin-Orbit Coupling
• Scattering framework for two particles with isotropic spin-orbit coupling applicable to all energies
• Spin-orbit coupled bosons interacting in a two-dimensional harmonic trap
• Generation of spin-dependent coherent states in a quantum wire
• Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling
• Quantum collision theory in flat bands
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Spin-orbit coupling in the presence of strong atomic correlations
• Interaction-induced Bloch Oscillation in a Harmonically Trapped and Fermionized Quantum Gas in One Dimension
• Strongly Repulsive 1D Gases at Higher Branches: Spin-Charge Correlation and Coupled Spin-Chain Model