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Frontiers of Physics

Spin-orbit coupling in Bose-Einstein condensate and degenerate Fermi gases

Pengjun Wang, Jing Zhang

Published Oct 1, 2014• 10 citations
Publisher

Abstract

We review our recent experimental realization and investigation of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) and quantum degenerate Fermi gas. By using two counter-propagating Raman lasers and controlling the different frequency of two Raman lasers to engineer the atom-light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as hallmarks of SO coupling in a Fermi gas. To clearly reveal the property of SO coupling Fermi gas, we also study the momentum-resolved radio-frequency spectroscopy which characterizes the energy-momentum dispersion and spin composition of the quantum states. We observe the change of fermion surfaces in different helicity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracold Fermi gas.

DOI
10.1007/s11467-013-0377-x

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We review our recent experimental realization and investigation of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) and quantum degenerate Fermi gas. By using two counter-propagating Raman lasers and controlling the different frequency of two Raman lasers to engineer the atom-light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as hallmarks of SO coupling in a Fermi gas. To clearly reveal the property of SO coupling Fermi gas, we also study the momentum-resolved radio-frequency spectroscopy which characterizes the energy-momentum dispersion and spin composition of the quantum states. We observe the change of fermion surfaces in different helicity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracold Fermi gas.
In this Letter, we report the first experimental realization and investigation of a spin-orbit coupled Fermi gas. Both spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state are observed as hallmarks of spin-orbit coupling in a Fermi gas. The single particle dispersion is mapped out by using momentum-resolved radio-frequency spectroscopy. From momentum distribution and momentum-resolved radio-frequency spectroscopy, we observe the change of fermion population in different helicity branches consistent with a finite temperature calculation, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system.
We briefly review recent progress on ultracold atomic Fermi gases with different types of synthetic spin-orbit coupling, including the one-dimensional (1D) equal weight Rashba-Dresselhaus and two-dimensional (2D) Rasbha spin-orbit couplings. Theoretically, we show how the single-body, two-body and many-body properties of Fermi gases are dramatically changed by spin-orbit coupling. In particular, the interplay between spin-orbit coupling and interatomic interaction may lead to several long-sought exotic superfluid phases at low temperatures, such as anisotropic superfluid, topological superfluid and inhomogeneous superfluid. Experimentally, only the first type - equal weight combination of Rasbha and Dresselhaus spin-orbit couplings - has been realized very recently using a two-photon Raman process. We show how to characterize a normal spin-orbit coupled atomic Fermi gas in both non-interacting and strongly-interacting limits, using particularly momentum-resolved radio-frequency spectroscopy. The experimental demonstration of a strongly-interacting spin-orbit coupled Fermi gas opens a promising way to observe various exotic superfluid phases in the near future.
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.
In this letter we propose a method to realize a kind of spin-orbit coupling in ultracold Bose and Fermi gases that depends on the density of atoms. Our method combines two-photon Raman transition and periodical modulation of spin-dependent interaction, which gives rise to both the direct Raman process and the interaction-assisted Raman process. The interaction-assisted Raman process depends on the density of atoms. These two processes have opposite effects in terms of spin-momentum locking and compete with each other. As the interaction modulation increases, the system undergoes a crossover from the direct Raman process dominated regime to the interaction-assisted Raman process dominated regime. During this crossover, for bosons, both the condensate momentum and the chirality of condensate wave function change sign, and for fermions, the Fermi surface distortion is inverted. We highlight that there exists an emergent spatial reflectional symmetry in the crossover regime, which can manifest itself universally in both Bose and Fermi gases. Our method may pave a way to novel phenomena in the density-dependent spin-orbit coupling gauge field with intrinsic dynamics.
Cold atoms with laser-induced spin-orbit (SO) interactions provide a platform to explore quantum physics beyond natural conditions of solids. Here we propose and experimentally realize two-dimensional (2D) SO coupling and topological bands for a rubidium-87 degenerate gas through an optical Raman lattice, without phase-locking or fine-tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including topological superfluids.
In this paper we investigate the properties of Bose gases with Raman-induced spin-orbit(SO) coupling. It is found that the SO coupling can greatly modify the single particle density-of-state, and thus lead to non-monotonic behavior of the condensate depletion, the Lee-Huang-Yang correction of ground-state energy and the transition temperature of a non-interacting Bose-Einstein condensate. The presence of the SO coupling also breaks the Galilean invariance, and this gives two different critical velocities, corresponding to the movement of the condensate and the impurity respectively. Finally, we show that with SO coupling, the interactions modify the BEC transition temperature even at Hartree-Fock level, in contrast to the ordinary Bose gas without SO coupling. All results presented here can be directly verified in the current cold atom experiments using Raman laser-induced gauge field.