Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1508.00932 · Physical Review A

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

Qingze Guan, D. Blume

Published Aug 28, 2015• 18 citations
arXivHTMLPDF

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 ${k}_{\mathrm{so}}$ 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 ${k}_{\mathrm{so}}$ 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 ${k}_{\mathrm{so}}$ as a competition between independent spin dynamics and nearest-neighbor spin interactions.

DOI
10.1103/physreva.92.023641

Related papers

Energy spectrum of a harmonically trapped two-atom system with spin–orbit coupling

Qingze Guan, Xiangyu Yin, Seyed Ebrahim Gharashi +1 more

Ultracold atomic gases provide a novel platform with which to study spin–orbit coupling, a mechanism that plays a central role in the nuclear shell model, atomic fine structure and two-dimensional electron gases. This paper introduces a theoretical framework that allows for the efficient determination of the eigenenergies and eigenstates of a harmonically trapped two-atom system with short-range interaction subject to an equal mixture of Rashba and Dresselhaus spin–orbit coupling created through Raman coupling of atomic hyperfine states. Energy spectra for experimentally relevant parameter combinations are presented and future extensions of the approach are discussed.

arXiv:1406.7177•Journal of Physics B Atomic Molecular and Optical Physics•Aug 6, 2014•18 citations

Harmonically trapped atoms with spin–orbit coupling

Chuanzhou Zhu, Lin Dong, Han Pu

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.

arXiv:1601.01335•Journal of Physics B Atomic Molecular and Optical Physics•Jun 23, 2016•24 citations

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

Xiangyu Yin, Sarang Gopalakrishnan, D. Blume

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. 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 ${k}_{\text{so}}^{2}$ or ${k}_{\text{so}}^{4}$ for the ground state and leads to a shift of the energy of either sign. While the absence of a term proportional to ${k}_{\text{so}}$ follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to ${k}_{\text{so}}^{2}$ 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 ${k}_{\text{so}}$. 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.

arXiv:1402.6734•Physical Review A•Mar 6, 2014•22 citations

Momentum-resolved radio-frequency spectroscopy of a spin-orbit-coupled atomic Fermi gas near a Feshbach resonance in harmonic traps

Shi-Guo Peng, Xia-Ji Liu, Hui Hu +1 more

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 ${}^{40}$K atoms at Shanxi University and ${}^{6}$Li atoms at the Massachusetts Institute of Technology.

arXiv:1210.2160•Physical Review A•Dec 10, 2012•15 citations

Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap

Cory D. Schillaci, Thomas Luu

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.

arXiv:1412.5634•Physical Review A•Apr 7, 2015•9 citations

Spin-orbit-coupled bosons interacting in a two-dimensional harmonic trap

Pere Mujal, A. Polls, Bruno Juliá-Díaz

A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{z}$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. In the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different ${J}_{z}$, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.

arXiv:1907.13355•Physical Review A•Apr 24, 2020•9 citations
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 ggg is calculated. Taking advantage of the fact that the NNN-boson and NNN-fermion systems with infinitely large coupling strength ggg are analytically solvable for vanishing spin-orbit coupling strength kso{k}_{\mathrm{so}}kso​ and vanishing Raman coupling strength \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ, we develop an effective spin model that is accurate to second order in \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ for any kso{k}_{\mathrm{so}}kso​ and infinite ggg. 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{k}_{\mathrm{so}}kso​ as a competition between independent spin dynamics and nearest-neighbor spin interactions.
Ultracold atomic gases provide a novel platform with which to study spin–orbit coupling, a mechanism that plays a central role in the nuclear shell model, atomic fine structure and two-dimensional electron gases. This paper introduces a theoretical framework that allows for the efficient determination of the eigenenergies and eigenstates of a harmonically trapped two-atom system with short-range interaction subject to an equal mixture of Rashba and Dresselhaus spin–orbit coupling created through Raman coupling of atomic hyperfine states. Energy spectra for experimentally relevant parameter combinations are presented and future extensions of the approach are discussed.
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.
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{k}_{\text{so}}kso​. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body sss-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 sss-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 sss-wave interaction generically enters, depending on the exact parameter combinations of the sss-wave scattering lengths, at order kso2{k}_{\text{so}}^{2}kso2​ or kso4{k}_{\text{so}}^{4}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{k}_{\text{so}}kso​ follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to kso2{k}_{\text{so}}^{2}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{k}_{\text{so}}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 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 40{}^{40}40K atoms at Shanxi University and 6{}^{6}6Li atoms at the Massachusetts Institute of Technology.
We explore the two-body spectra of spin-1/21/21/2 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.
A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{z}$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. In the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different Jz{J}_{z}Jz​, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.