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:1301.0800 · Physical Review A

Emergence of topological and strongly correlated ground states in trapped Rashba spin-orbit-coupled Bose gases

B. Ramachandhran, Hui Hu, Han Pu

Published Mar 26, 2013• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.033627

Related papers

Half-quantum vortex state in a spin-orbit-coupled Bose-Einstein condensate

B. Ramachandhran, Bogdan Opanchuk, Xia-Ji Liu +3 more

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 ${g}_{c}$, 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 $g>{g}_{c}$ 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.

arXiv:1201.1471•Physical Review A•Feb 6, 2012•163 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

Zero-momentum coupling induced transitions of ground states in Rashba spin–orbit coupled Bose–Einstein condensates

Jingjing Jin, Suying Zhang, Wei Han

We investigate the transitions of ground states induced by zero momentum (ZM) coupling in pseudospin-1/2 Rashba spin-orbit coupled Bose-Einstein condensates confined in a harmonic trap. In a weak harmonic trap, the condensate presents a plane wave (PW) state, a stripe state or a spin polarized ZM state, and the particle distribution of the stripe state is weighted equally at two points in the momentum space without ZM coupling. The presence of ZM coupling induces an imbalanced particle distribution in the momentum space, and leads to the decrease of the amplitude of the stripe state. When its strength exceeds a critical value, the system experiences the transition from stripe phase to PW phase. The boundary of these two phases is shifted and a new phase diagram spanned by the ZM coupling and the interatomic interactions is obtained. The presence of ZM coupling can also achieve the transition from ZM phase to PW phase. In a strong harmonic trap, the condensate exhibits a vortex lattice state without ZM coupling. For the positive effective Rabi frequency of ZM coupling, the condensate is driven from a vortex lattice state to a vortex-free lattice state and finally to a PW state with the increase of coupling strength. In addition, for the negative effective Rabi frequency, the condensate is driven from a vortex lattice state to a stripe state, and finally to a PW state. The stripe state found in the strong harmonic trap is different from that in previous works because of its nonzero superfluid velocity along the stripes. We also discuss the influences of the ZM coupling on the spin textures, and indicate that the spin textures are squeezed transversely by the ZM coupling.

Journal of Physics B Atomic Molecular and Optical Physics•May 13, 2014•7 citations

Rashba Spin-Orbit Coupled Quantum Gases

B. Ramachandhran

Spin-orbit (SO) coupling leads to many fundamental phenomena in a wide range of quantum systems from nuclear physics, condensed matter physics to atomic physics. For instance, in electronic condensed matter systems, SO coupling can lead to quantum spin Hall states or topological insulators, which have potential applications in quantum devices. Recently, SO coupling has been artificially induced in quantum liquids - ultracold dilute atomic Bose and Fermi gases - by the so-called synthetic gauge fields. Combined with unprecedented controllability of interactions and geometry in ultracold atoms, this manipulation of SO coupling opens an entirely new paradigm for studying strong correlations of quantum many-body systems under Abelian and non-Abelian gauge fields. In the major portion of this thesis, we theoretically investigate the ground state and collective excitations of a two-component Bose gas in a two-dimensional harmonic trap, subject to Rashba SO coupling. Our work represents an important extension into the regime of non-Abelian gauge field in which the spin degrees of freedom play an essential role. -- Abstract and Thesis are based on our publications in: (1) 10.1103/PhysRevLett.108.010402 (2) 10.1103/PhysRevA.85.023606 (3) 10.1103/PhysRevA.87.033627 (4) 10.1103/PhysRevA.83.033607 (5) 10.1103/PhysRevLett.110.123201

•Apr 4, 2014•0 citations

Ground states of spin-orbit-coupled Bose-Einstein condensates in a spin-dependent asymmetric potential

Jingjing Jin, Congying Ma, Ziyu Chen +1 more

Abstract We investigate the ground-state properties of spin–orbit (SO)-coupled Bose–Einstein condensates confined in a spin-dependent asymmetric potential composed of harmonic and quartic contributions. The combined effect of the two potentials gives rise to an effective spatially inhomogeneous Zeeman field along the z -direction, and the complex competition among SO coupling, interatomic interactions, and this effective field leads to the emergence of nontrivial topological phases and complex spin textures in the system. For weak interatomic interactions, as the SO coupling strength increases, the system undergoes a series of transitions between ground-state phases: from a spin-polarized state, to an Anderson–Toulouse (AT) vortex state, a high-order radial dark soliton state, and finally to a domain structure. For strong interatomic interactions, the condensate evolves from a spin-polarized state to an AT vortex state, and then to a spatially coexisting state of AT and Mermin–Ho vortices, which corresponds to a novel topological excitation in pseudospin space: a skyrmion-dominated texture embedded with circular-hyperbolic antimeron pairs, realizing the coexistence and nesting of multiple topological defects. For sufficiently strong SO coupling, both components eventually evolve into similar multiring-shaped higher-order radial dark soliton states, with the number of soliton rings increasing as the SO coupling strength increases. Our results enrich the ground-state phases and topological excitations of cold atomic systems and provide new insights for exploring and manipulating nontrivial topological excitations in such systems.

Journal of Physics B Atomic Molecular and Optical Physics•May 27, 2026•0 citations

Meron Ground State of Rashba Spin-Orbit-Coupled Dipolar Bosons

Ryan Wilson, Brandon Anderson, Charles W. Clark

We study the effects of dipolar interactions on a Bose-Einstein condensate with synthetically generated Rashba spin-orbit coupling. The dipolar interaction we consider includes terms that couple spin and orbital angular momentum in a way perfectly congruent with the single-particle Rashba coupling. We show that this internal spin-orbit coupling plays a crucial role in the rich ground-state phase diagram of the trapped condensate. In particular, we predict the emergence of a thermodynamically stable ground state with a meron spin configuration.

arXiv:1306.6610•Physical Review Letters•Oct 30, 2013•86 citations
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+1/2n+1/2n+1/2 quantum angular momentum vortex configurations, where n=0,1,2,3,...n=0,1,2,3,...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.
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{g}_{c}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>gcg>{g}_{c}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.
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.
We investigate the transitions of ground states induced by zero momentum (ZM) coupling in pseudospin-1/2 Rashba spin-orbit coupled Bose-Einstein condensates confined in a harmonic trap. In a weak harmonic trap, the condensate presents a plane wave (PW) state, a stripe state or a spin polarized ZM state, and the particle distribution of the stripe state is weighted equally at two points in the momentum space without ZM coupling. The presence of ZM coupling induces an imbalanced particle distribution in the momentum space, and leads to the decrease of the amplitude of the stripe state. When its strength exceeds a critical value, the system experiences the transition from stripe phase to PW phase. The boundary of these two phases is shifted and a new phase diagram spanned by the ZM coupling and the interatomic interactions is obtained. The presence of ZM coupling can also achieve the transition from ZM phase to PW phase. In a strong harmonic trap, the condensate exhibits a vortex lattice state without ZM coupling. For the positive effective Rabi frequency of ZM coupling, the condensate is driven from a vortex lattice state to a vortex-free lattice state and finally to a PW state with the increase of coupling strength. In addition, for the negative effective Rabi frequency, the condensate is driven from a vortex lattice state to a stripe state, and finally to a PW state. The stripe state found in the strong harmonic trap is different from that in previous works because of its nonzero superfluid velocity along the stripes. We also discuss the influences of the ZM coupling on the spin textures, and indicate that the spin textures are squeezed transversely by the ZM coupling.
Spin-orbit (SO) coupling leads to many fundamental phenomena in a wide range of quantum systems from nuclear physics, condensed matter physics to atomic physics. For instance, in electronic condensed matter systems, SO coupling can lead to quantum spin Hall states or topological insulators, which have potential applications in quantum devices. Recently, SO coupling has been artificially induced in quantum liquids - ultracold dilute atomic Bose and Fermi gases - by the so-called synthetic gauge fields. Combined with unprecedented controllability of interactions and geometry in ultracold atoms, this manipulation of SO coupling opens an entirely new paradigm for studying strong correlations of quantum many-body systems under Abelian and non-Abelian gauge fields. In the major portion of this thesis, we theoretically investigate the ground state and collective excitations of a two-component Bose gas in a two-dimensional harmonic trap, subject to Rashba SO coupling. Our work represents an important extension into the regime of non-Abelian gauge field in which the spin degrees of freedom play an essential role. -- Abstract and Thesis are based on our publications in: (1) 10.1103/PhysRevLett.108.010402 (2) 10.1103/PhysRevA.85.023606 (3) 10.1103/PhysRevA.87.033627 (4) 10.1103/PhysRevA.83.033607 (5) 10.1103/PhysRevLett.110.123201
Abstract We investigate the ground-state properties of spin–orbit (SO)-coupled Bose–Einstein condensates confined in a spin-dependent asymmetric potential composed of harmonic and quartic contributions. The combined effect of the two potentials gives rise to an effective spatially inhomogeneous Zeeman field along the z -direction, and the complex competition among SO coupling, interatomic interactions, and this effective field leads to the emergence of nontrivial topological phases and complex spin textures in the system. For weak interatomic interactions, as the SO coupling strength increases, the system undergoes a series of transitions between ground-state phases: from a spin-polarized state, to an Anderson–Toulouse (AT) vortex state, a high-order radial dark soliton state, and finally to a domain structure. For strong interatomic interactions, the condensate evolves from a spin-polarized state to an AT vortex state, and then to a spatially coexisting state of AT and Mermin–Ho vortices, which corresponds to a novel topological excitation in pseudospin space: a skyrmion-dominated texture embedded with circular-hyperbolic antimeron pairs, realizing the coexistence and nesting of multiple topological defects. For sufficiently strong SO coupling, both components eventually evolve into similar multiring-shaped higher-order radial dark soliton states, with the number of soliton rings increasing as the SO coupling strength increases. Our results enrich the ground-state phases and topological excitations of cold atomic systems and provide new insights for exploring and manipulating nontrivial topological excitations in such systems.
We study the effects of dipolar interactions on a Bose-Einstein condensate with synthetically generated Rashba spin-orbit coupling. The dipolar interaction we consider includes terms that couple spin and orbital angular momentum in a way perfectly congruent with the single-particle Rashba coupling. We show that this internal spin-orbit coupling plays a crucial role in the rich ground-state phase diagram of the trapped condensate. In particular, we predict the emergence of a thermodynamically stable ground state with a meron spin configuration.