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:1405.4048 · Physical Review Letters

Spin-Orbit-Coupled Bose-Einstein Condensates in a One-Dimensional Optical Lattice

Chris Hamner, Yongping Zhang, M. A. Khamehchi, Matthew J. Davis, Peter Engels

Published Feb 17, 2015• 162 citations
arXivHTMLPDF

Abstract

We investigate a spin-orbit-coupled Bose-Einstein condensate loaded into a translating optical lattice. We experimentally demonstrate the lack of Galilean invariance in the spin-orbit-coupled system, which leads to anisotropic behavior of the condensate depending on the direction of translation of the lattice. The anisotropy is theoretically understood by an effective dispersion relation. We experimentally confirm this theoretical picture by probing the dynamical instability of the system.

DOI
10.1103/physrevlett.114.070401

Related papers

Nonlinear energy band structure of spin-orbit coupled Bose-Einstein condensates in optical lattice

Ai‐Xia Zhang, Yan-Fang Jiang, Ju-Kui Xue

In a recent experiment [Hamner C, et al. 2015 Phys. Rev. Lett. 114 070401 ], spin-orbit coupled Bose-Einstein condensates in a translating optical lattice have been successfully prepared into any Bloch band, and directly proved to be the lack of Galilean invariance in the presence of the spin-orbit coupling. The energy band structure of the system becomes complicated because of the lack of Galilean invariance. At present, the energy band structure of the spin-orbit coupled Bose-Einstein condensates in optical lattice is still an open issue, especially the theoretical evidence for the in-depth understanding of the competition mechanism among the spin-orbit coupling, the Raman coupling, the optical lattice and the atomic interactions of the nonlinear energy band structure has not been clear yet. In this paper, based on the two-mode approximation and variational analysis, the nonlinear energy band structure and current density of the spin-orbit coupled Bose-Einstein condensates in the one-dimensional optical lattice are investigated. We find that when the spin-orbit coupling, the Raman coupling, the optical lattice, and the atomic interactions satisfy certain conditions, a loop structure in the Brillouin zone edge will emerge. The critical condition for the loop structure emerging in the Brillouin zone edge is obtained in a parameter space. The Raman coupling and the optical lattice suppress the emergence of the loop structure, while the spin-orbit coupling and the atomic interactions promote the emerging of the loop structure and make the energy band structure more complex. Interestingly, the atomic interactions can make the loop structure occur at both the higher-lying bands and the lowest energy band. The energy band structure is closely related to the current density of the system. The spin-orbit coupling causes the current density to be strongly asymmetric and leads the current density distributions of different spin states to be separated from each other in the momentum space near the boundary of the Brillouin zone. The optical lattice strength and the Raman coupling can weaken the asymmetry. The appearance of loop structure breaks the Bloch oscillation and gives rise to the Landau-Zener tunneling. The separation of the current density distributions of different spin states in the momentum space means the emergence of the spin exchange dynamics. Our results are beneficial to the in-depth understanding of the nonlinear dynamics of the spin-orbit coupled Bose-Einstein condensates in optical lattice.

Acta Physica Sinica•Jan 1, 2021•1 citation

Ground-state phases of a rotating spin-orbit–coupled Bose-Einstein condensate in an optical lattice

Ji-Guo Wang, Liang-Liang Xu, Shi-Jie Yang

We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x -direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.

Europhysics Letters (EPL)•Oct 1, 2017•6 citations

Bose-Einstein condensates in spin-orbit-coupled optical lattices: Flat bands and superfluidity

Yongping Zhang, Chuanwei Zhang

Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.

arXiv:1203.2389•Physical Review A•Feb 13, 2013•90 citations

Negative-Mass Hydrodynamics in a Spin-Orbit–coupled Bose-Einstein Condensate

M. A. Khamehchi, Khalid Hossain, Maren Mossman +4 more

A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features-shock waves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.

arXiv:1612.04055•Physical Review Letters•Apr 10, 2017•145 citations

Experiments with Bose-Einstein Condensates in a Spin-Orbit Coupled Optical Lattice

Peter Engels

Ultracold quantum gases dressed by laser light are a powerful tool to investigate the dynamics of quantum mechanical Hamiltonians. When a Bose-Einstein condensate is placed in appropriately tailored laser fields, spin-orbit coupling as well as periodic band structures can be generated. We have developed an effective band structure picture to describe such Bose-Einstein condensates in a spin-orbit coupled lattice. Our model predicts the location of the resulting band edges. By performing atom loss measurements, we experimentally probe the predicted band structures and find excellent agreement between our experiment and our theoretical predictions.

Frontiers in Optics•Jan 1, 2014•0 citations

Helical supersolid phases in spin-orbit-coupled bosons

Ji-Guo Wang, Shi-Jie Yang

We study the ground-state phases of a spin-orbit-coupled Bose-Einstein condensate loaded in a two-dimensional optical lattice. We find three types of helical supersolid phases, which are dependent on the anisotropy of the spin-orbit coupling with respect to the relative strength of the $y$ and $x$ directions. The period of density modulation increases with the strength of the spin-orbit coupling.

Physical Review A•Apr 28, 2016•6 citations
We investigate a spin-orbit-coupled Bose-Einstein condensate loaded into a translating optical lattice. We experimentally demonstrate the lack of Galilean invariance in the spin-orbit-coupled system, which leads to anisotropic behavior of the condensate depending on the direction of translation of the lattice. The anisotropy is theoretically understood by an effective dispersion relation. We experimentally confirm this theoretical picture by probing the dynamical instability of the system.
In a recent experiment [Hamner C, et al. 2015 Phys. Rev. Lett. 114 070401 ], spin-orbit coupled Bose-Einstein condensates in a translating optical lattice have been successfully prepared into any Bloch band, and directly proved to be the lack of Galilean invariance in the presence of the spin-orbit coupling. The energy band structure of the system becomes complicated because of the lack of Galilean invariance. At present, the energy band structure of the spin-orbit coupled Bose-Einstein condensates in optical lattice is still an open issue, especially the theoretical evidence for the in-depth understanding of the competition mechanism among the spin-orbit coupling, the Raman coupling, the optical lattice and the atomic interactions of the nonlinear energy band structure has not been clear yet. In this paper, based on the two-mode approximation and variational analysis, the nonlinear energy band structure and current density of the spin-orbit coupled Bose-Einstein condensates in the one-dimensional optical lattice are investigated. We find that when the spin-orbit coupling, the Raman coupling, the optical lattice, and the atomic interactions satisfy certain conditions, a loop structure in the Brillouin zone edge will emerge. The critical condition for the loop structure emerging in the Brillouin zone edge is obtained in a parameter space. The Raman coupling and the optical lattice suppress the emergence of the loop structure, while the spin-orbit coupling and the atomic interactions promote the emerging of the loop structure and make the energy band structure more complex. Interestingly, the atomic interactions can make the loop structure occur at both the higher-lying bands and the lowest energy band. The energy band structure is closely related to the current density of the system. The spin-orbit coupling causes the current density to be strongly asymmetric and leads the current density distributions of different spin states to be separated from each other in the momentum space near the boundary of the Brillouin zone. The optical lattice strength and the Raman coupling can weaken the asymmetry. The appearance of loop structure breaks the Bloch oscillation and gives rise to the Landau-Zener tunneling. The separation of the current density distributions of different spin states in the momentum space means the emergence of the spin exchange dynamics. Our results are beneficial to the in-depth understanding of the nonlinear dynamics of the spin-orbit coupled Bose-Einstein condensates in optical lattice.
We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x -direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.
Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.
A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features-shock waves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.
Ultracold quantum gases dressed by laser light are a powerful tool to investigate the dynamics of quantum mechanical Hamiltonians. When a Bose-Einstein condensate is placed in appropriately tailored laser fields, spin-orbit coupling as well as periodic band structures can be generated. We have developed an effective band structure picture to describe such Bose-Einstein condensates in a spin-orbit coupled lattice. Our model predicts the location of the resulting band edges. By performing atom loss measurements, we experimentally probe the predicted band structures and find excellent agreement between our experiment and our theoretical predictions.
We study the ground-state phases of a spin-orbit-coupled Bose-Einstein condensate loaded in a two-dimensional optical lattice. We find three types of helical supersolid phases, which are dependent on the anisotropy of the spin-orbit coupling with respect to the relative strength of the yyy and xxx directions. The period of density modulation increases with the strength of the spin-orbit coupling.