Unconventional spin Hall effect in PT symmetric spin-orbit coupled quantum gases (2501.08860v2)

Abstract: 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.

• The paper investigates the intrinsic spin Hall effect in R P T symmetric quantum gases using theoretical models and numerical simulations.
• In Fermi gases, the study finds geometrical contributions largely dominate spin Hall conductivity in insulating states, unlike metallic states.
• Bose gases exhibit an unconventional spin Hall effect with anisotropic conductivity, proposing experimental detection using dipole oscillations.

Overview of the Unconventional Spin Hall Effect in $\mathcal{PT}$ Symmetric Spin-Orbit Coupled Quantum Gases

This paper investigates the intrinsic spin Hall effect (SHE) in $\mathcal{PT}$ symmetric quantum gases with spin-orbit coupling (SOC), confined to optical lattices. The authors leverage both a theoretical framework and numerical simulations to delve into this complex phenomenon, with the major focus on contrasting the effects in Fermi and Bose gases. Key insights arise from the interplay between $\mathcal{PT}$ symmetry, SOC, and the populated characteristics of quantum gases, giving rise to unique spin transport phenomena.

Spin Hall Effect in Quantum Gases

In electronic systems, the SHE leads to a transverse spin current from an applied electric field, a principle applicable in spintronics and the development of advanced electronic devices. The interest in extending this concept to neutral quantum gases comes from the opportunity to simulate and explore solid-state phenomena in cleaner systems, devoid of impurities, and thus potentially revealing intrinsic mechanisms more clearly.

Distinctive Features of $\mathcal{PT}$ Symmetric Quantum Gases

• Degenerate Fermi Gas:
  • The paper models how a two-component Fermi gas within a $\mathcal{PT}$ symmetric SOC framework can present an analogous intrinsic SHE to that observed in electronic materials. The presence of doubly degenerate non-interacting bands is key, where the Berry curvature and spin polarization are opposite for degenerate states. This property cultivates a transverse spin current when subjected to external perturbations.
  • Analytical and numerical results indicate that the geometrical contribution to spin Hall conductivity largely dominates in insulating states, a finding that contrasts with metallic states where spin dynamics take precedence.
• Bose Gas:
  • The investigation into Bose gases reveals an unconventional SHE characterized by coplanar spin polarization and currents, deviating from traditional models. This setup provides a broader angle on spin transport mechanics, showcasing a unique anisotropic spin Hall conductivity that stems from the system's in-plane magnetization.
  • The intrinsic spin Hall conductivity demonstrates a distinct angular dependence based on the symmetry of the Bose-Einstein condensate's ground state, offering novel experimental validation possibilities by observing dipole oscillations in harmonically trapped systems.

Theoretical and Experimental Implications

• Theoretical Foundation:
  • This work adds a robust theoretical underpinning to the understanding of SOC effects in quantum gases, emphasizing the role of $\mathcal{PT}$ symmetry in creating novel quantum states and transport phenomena.
  • The adaptation and understanding of intrinsic SHE in such gases elevate their potential to simulate complex condensed matter systems and perhaps guide the development of spintronic devices leveraging ultracold atomic gases.
• Experimental Proposals:
  • The authors propose methods to detect the unconventional SHE through dipole oscillations in a harmonically trapped system. These techniques can serve as a blueprint for experimental validation of their theoretical predictions, potentially leading to the observation of new quantum behaviors in laboratory settings.

Future Directions

The investigation opens pathways for further research to explore and quantify spin transport properties across varying conditions and quantum phases of matter. The clarity of $\mathcal{PT}$ symmetric systems in eliminating extrinsic factors makes them a promising avenue for probing deeper into the quantum characteristics of SHE. Additionally, exploring the inverse SHE within such models or examining systems beyond harmonically trapped configurations may provide fresh perspectives on the quantum phases and symmetries influencing spin dynamics. As quantum technology advances, the amalgamation of these intricate spin phenomena with practical applications in spintronics and beyond seems an inevitable horizon to explore.