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Spin-Orbit Coupled Ultracold Gases in Optical Lattices:Single-Particle Physics and Superfluid-Insulator Transition

Lihong Zhou, Xiaoling Cui

Published Jul 6, 2015• 0 citations
OpenAlex

Abstract

We study the interplay effect of spin-orbit coupling(SOC) and optical lattice to the single-particle physics and superfluid-insulator transition in ultracold Fermi gases. We consider the type of SOC that has been realized in cold atoms experiments via two-photon Raman processes. Our analyses are based on the knowledge of full single-particle spectrum in lattices, without relying on any tightbinding approximation. We point out that the tight-binding models used in literature are either very limited or completely inapplicable in predicting the correct single-particle physics. Moreover, we show that the Raman field (creating SOC) can induce band-gap closing in a two-dimensional optical lattice, leading to the intriguing phenomenon of superfluidity-reentrance for interacting fermions at integer filling. We present the superfluid-insulator phase diagram in a wide parameter regime of chemical potentials and Raman fields. All these results are far beyond any tight-binding model can predict, and can be directly probed in current cold atoms experiments

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Spin-orbit coupled ultracold gases in optical lattices: High-band physics and insufficiency of tight-binding models

Lihong Zhou, Xiaoling Cui

We study the interplay effect of spin-orbit coupling (SOC) and an optical lattice on the single-particle physics and superfluid-insulator transition in ultracold Fermi gases. We consider the type of SOC that has been realized in cold atom experiments via two-photon Raman processes. Our analyses are based on the knowledge of a full single-particle spectrum in lattices without relying on any tight-binding approximation. We evaluate existing tight-binding models and point out their limitations in predicting the correct single-particle physics due to the missed high-band contributions. Moreover, we show that the Raman field (creating SOC) can induce band-gap closing in a two-dimensional optical lattice, leading to the intriguing phenomenon of superfluidity reentrance for interacting fermions at integer filling. We present the superfluid-insulator phase diagram in a wide parameter regime of chemical potentials and Raman fields. All these results are far beyond any that a tight-binding model can predict and can be directly probed in current cold atoms experiments.

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Spin-orbit coupling (SOC) in ultracold atoms is engineered by light-atom interaction, such as two-photon Raman transitions between two Zeeman spin states. In this paper, we propose and experimentally realize chiral Raman coupling to generate SOC in ultracold atomic gases, which exhibits high quantization axis direction dependence. Chiral Raman coupling for SOC is created by chiral light-atom interaction, in which a circularly polarized electromagnetic field generated by two Raman lasers interacts with two Zeeman spin states $\ensuremath{\delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ (chiral transition). We present a simple scheme of chiral one-dimensional (1D) Raman coupling by employing two Raman lasers at an intersecting angle ${90}^{\ensuremath{\circ}}$ with the proper polarization configuration. In this case, Raman coupling for SOC exists in one direction of the magnetic quantization axis and disappears in the opposite direction. Then we extend this scheme into a chiral two-dimensional (2D) optical square Raman lattice configuration to generate the 1D SOC. There are two orthogonal 1D SOCs, which exist in the positive and negative directions of the magnetic quantization axis respectively. This case is compared with 2D SOC based on the nonchiral 2D optical Raman lattice scheme for studying the topological energy band. This paper broadens the horizon for understanding chiral physics and simulating topological quantum systems.

arXiv:2502.06259•Physical Review A•Feb 20, 2025•4 citations
We study the interplay effect of spin-orbit coupling(SOC) and optical lattice to the single-particle physics and superfluid-insulator transition in ultracold Fermi gases. We consider the type of SOC that has been realized in cold atoms experiments via two-photon Raman processes. Our analyses are based on the knowledge of full single-particle spectrum in lattices, without relying on any tightbinding approximation. We point out that the tight-binding models used in literature are either very limited or completely inapplicable in predicting the correct single-particle physics. Moreover, we show that the Raman field (creating SOC) can induce band-gap closing in a two-dimensional optical lattice, leading to the intriguing phenomenon of superfluidity-reentrance for interacting fermions at integer filling. We present the superfluid-insulator phase diagram in a wide parameter regime of chemical potentials and Raman fields. All these results are far beyond any tight-binding model can predict, and can be directly probed in current cold atoms experiments
We study the interplay effect of spin-orbit coupling (SOC) and an optical lattice on the single-particle physics and superfluid-insulator transition in ultracold Fermi gases. We consider the type of SOC that has been realized in cold atom experiments via two-photon Raman processes. Our analyses are based on the knowledge of a full single-particle spectrum in lattices without relying on any tight-binding approximation. We evaluate existing tight-binding models and point out their limitations in predicting the correct single-particle physics due to the missed high-band contributions. Moreover, we show that the Raman field (creating SOC) can induce band-gap closing in a two-dimensional optical lattice, leading to the intriguing phenomenon of superfluidity reentrance for interacting fermions at integer filling. We present the superfluid-insulator phase diagram in a wide parameter regime of chemical potentials and Raman fields. All these results are far beyond any that a tight-binding model can predict and can be directly probed in current cold atoms experiments.
Abstract The dynamic structure factors reflecting the excitation spectra were investigated in a one-dimensional (1D) optical lattice with a spin-orbit coupling (SOC) effect. The results reveal that the single-particle excitations of both the density and spin dynamical structure factors are strongly reconstructed and split owing to the SOC effect, and a hat-like excitation band appears in the high-binding-energy region. The hat-like excitation band of the density dynamical structure factor exhibits an arc form, and has a pocket in the spin dynamical structure factor. In particular, only a gapless single-particle excitation point is left for both the density dynamical structure factor and the spin dynamical structure factor when the SOC strength reaches a critical point at half-filling. A stronger SOC strength causes the gapless excitation points to disappear, which indicates that the metal-insulator transition occurs. The metal-insulator transition only appears in half-filling and lightly doped regimes.
This review focuses on recent developments in synthetic spin-orbit (SO) coupling in ultracold atomic gases. Two types of SO coupling are discussed. One is Raman process induced coupling between spin and motion along one of the spatial directions and the other is Rashba SO coupling. We emphasize their common features in both single-particle and two-body physics and the consequences of both in many-body physics. For instance, single particle ground state degeneracy leads to novel features of superfluidity and a richer phase diagram; increased low-energy density-of-state enhances interaction effects; the absence of Galilean invariance and spin-momentum locking gives rise to intriguing behaviours of superfluid critical velocity and novel quantum dynamics; and the mixing of two-body singlet and triplet states yields a novel fermion pairing structure and topological superfluids. With these examples, we show that investigating SO coupling in cold atom systems can, enrich our understanding of basic phenomena such as superfluidity, provide a good platform for simulating condensed matter states such as topological superfluids and more importantly, result in novel quantum systems such as SO coupled unitary Fermi gas and high spin quantum gases. Finally we also point out major challenges and some possible future directions.
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.
Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. The experimental schemes for achieving non-Abelian superfluid phases are given. Finally, we point out the future important issues in this rapidly growing research field.
Spin-orbit coupling (SOC) in ultracold atoms is engineered by light-atom interaction, such as two-photon Raman transitions between two Zeeman spin states. In this paper, we propose and experimentally realize chiral Raman coupling to generate SOC in ultracold atomic gases, which exhibits high quantization axis direction dependence. Chiral Raman coupling for SOC is created by chiral light-atom interaction, in which a circularly polarized electromagnetic field generated by two Raman lasers interacts with two Zeeman spin states $\ensuremath{\delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ (chiral transition). We present a simple scheme of chiral one-dimensional (1D) Raman coupling by employing two Raman lasers at an intersecting angle ${90}^{\ensuremath{\circ}}$ with the proper polarization configuration. In this case, Raman coupling for SOC exists in one direction of the magnetic quantization axis and disappears in the opposite direction. Then we extend this scheme into a chiral two-dimensional (2D) optical square Raman lattice configuration to generate the 1D SOC. There are two orthogonal 1D SOCs, which exist in the positive and negative directions of the magnetic quantization axis respectively. This case is compared with 2D SOC based on the nonchiral 2D optical Raman lattice scheme for studying the topological energy band. This paper broadens the horizon for understanding chiral physics and simulating topological quantum systems.