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arXiv:2211.15511 · Physical Review Research

Intrinsic anomalous Hall effect across the magnetic phase transition of a spin-orbit-coupled Bose-Einstein condensate

Canhao Chen, Guan-Hua Huang, Zhigang Wu

Published Apr 28, 2023• 5 citations
arXivHTMLPDF

Abstract

We study theoretically the zero-temperature intrinsic anomalous Hall effect in an experimentally realized two-dimensional spin-orbit-coupled Bose gas. For anisotropic atomic interactions and as the spin-orbit-coupling strength increases, the system undergoes a ground-state phase transition from states exhibiting a total in-plane magnetization to those with a perpendicular magnetization along the $z$ direction. We show that finite frequency, or ac, Hall responses exist in both phases in the absence of an artificial magnetic field, as a result of finite interband transitions. However, the characteristics of the anomalous Hall responses are drastically different in these two phases because of the different symmetries preserved by the corresponding ground states. In particular, we find a finite dc Hall conductivity in one phase, but not the other. The underlying physical reasons for this are analyzed further by exploring relations of the dc Hall conductivity to the system's chirality and Berry curvatures of the Bloch bands. Finally, we discuss an experimental method of probing the anomalous Hall effect in trapped systems.

DOI
10.1103/physrevresearch.5.023070

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We theoretically study the intrinsic spin Hall effect in PT symmetric, spin-orbit coupled quantum gases confined in an optical lattice. The interplay of the PT symmetry and the spin-orbit coupling leads to a doubly degenerate non-interacting band structure in which the spin polarization and the Berry curvature of any Bloch state are opposite to those of its degenerate partner. Using experimentally available systems as examples, we show that such a system with a two-component Fermi gas exhibits an intrinsic spin Hall effect akin to that found in the context of electronic materials. For a two-component Bose gas, however, an unconventional spin Hall effect emerges in which the spin polarization and the currents are coplanar and the spin Hall conductivity displays a characteristic anisotropy. We propose to detect such an unconventional spin Hall effect in harmonically trapped systems using dipole oscillations and perform extensive numerical simulations to validate the proposal. Our work paves the way for quantum simulation of the solid-state intrinsic spin Hall effect and experimental explorations of unconventional spin Hall effects in quantum gases.
Motivated by recent experiments by Lin et al., [Nature (London) 471, 83 (2011)] that engineered spin-orbit coupling in ultracold mixtures of bosonic atoms, we study the dipole oscillation of trapped spin-orbit-coupled noncondensed Bose and Fermi gases. We find that different directions of oscillation are coupled by the spin-orbit interactions. The phase difference between oscillatory motion in orthogonal directions and the trapping frequencies of the modes are shown to be related to the anomalous Hall conductivity. Our results can be used to experimentally determine the anomalous Hall conductivity for cold-atom systems.
We theoretically show that the spin Hall effect arises in a Bose-Einstein condensate (BEC) of neutral atoms interacting via the magnetic dipole-dipole interactions (MDDIs). Since the MDDI couples the total spin angular momentum and the relative orbital angular momentum of two colliding atoms, it works as a spin-orbit coupling. Thus, when we prepare a BEC in a magnetic sublevel m=0m=0m=0, thermally and quantum-mechanically excited atoms in the m=1m=1m=1 and $\ensuremath{-}1$ states feel the Lorentz-like forces in the opposite directions. This is the origin for the emergence of the spin Hall effect. We define the mass-current and spin-current operators from the equations of continuity and calculate the spin Hall conductivity from the off-diagonal current-current correlation function within the Bogoliubov approximation. We find that the correction of the current operators due to the MDDI significantly contributes to the spin Hall conductivity. A possible experimental situation is also discussed.
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We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.