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arXiv:2405.20255

Beyond spin-charge separation: Helical modes and topological quantum phase transitions in one-dimensional Fermi gases with spin-orbit and Rabi couplings

Xiaoyong Zhang, Carlos A. R. Sá de Melo

Published May 30, 2024• 1 citation
arXivHTMLPDF

Abstract

Motivated by the experimental observation of spin-charge separation in one-dimensional interacting Fermi gases, we investigate these systems in the presence of spin-orbit coupling and Rabi fields. We demonstrate that spin-charge-separated modes evolve into helical collective modes due to the special mixing of spin and charge induced by spin-orbit coupling and Rabi fields. We obtain the phase diagram of chemical potential versus Rabi fields for given spin-orbit coupling and interactions, and find several topological quantum phase transitions of the Lifshitz type. We show that the velocities of the collective modes are nonanalytic at the boundaries between different phases. Lastly, we analyze the charge-charge, spin-charge and spin-spin dynamical structure factors to show that the dispersions, spectral weights and helicities of the collective modes can be experimentally extracted in systems such as $^{6}{\rm Li}$, $^{40}{\rm K}$ and $^{173}{\rm Yb}$.

DOI
10.48550/arxiv.2405.20255

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Motivated by the experimental observation of spin-charge separation in one-dimensional interacting Fermi gases, we investigate these systems in the presence of spin-orbit coupling and Rabi fields. We demonstrate that spin-charge-separated modes evolve into helical collective modes due to the special mixing of spin and charge induced by spin-orbit coupling and Rabi fields. We obtain the phase diagram of chemical potential versus Rabi fields for given spin-orbit coupling and interactions, and find several topological quantum phase transitions of the Lifshitz type. We show that the velocities of the collective modes are nonanalytic at the boundaries between different phases. Lastly, we analyze the charge-charge, spin-charge and spin-spin dynamical structure factors to show that the dispersions, spectral weights and helicities of the collective modes can be experimentally extracted in systems such as 6Li^{6}{\rm Li}6Li, 40K^{40}{\rm K}40K and 173Yb^{173}{\rm Yb}173Yb.
We study the emergence of finite-temperature topological phase transitions of the Berezinskii-Kosterlitz-Thouless type and the collective mode spectrum of two-dimensional Fermi gases in the presence of attractive sss-wave interactions, spin-orbit coupling, and Zeeman fields. We show that neglecting the spin-dependent phase shift on the fermionic wave function misses an important point. Including this spin-dependent shift, we derive the effective low-energy and long-wavelength quantum action for independent (unlocked) phase fluctuations in the U(1) (charge) and SU(2) (spin) sectors and show that at least two phase transitions occur because charge and spin degrees of freedom are coupled due to the presence of spin-orbit and Zeeman fields. Furthermore, we demonstrate that vortex and antivortex excitations are characterized by two topological quantum numbers, corresponding to the quantized circulation of charge and spin velocities. Finally, we show that there are two collective modes in the superfluid phase at low temperatures which arise due to the coupling between sound and transverse-spin waves.
We discuss the effects of spin–orbit coupling and Rabi fields in Tomonaga–Luttinger liquids for SU(2) and SU(3) Fermi systems. In the SU(2) case, we show that spin–orbit coupling and Rabi fields mix separated spin and charge excitations producing helical massless bosons, which we call Weyl bosons in analogy to their cousins, the Weyl fermions. We discuss the phase diagram and the velocities of bosonic modes, showing where different flavors of Weyl bosons emerge. We suggest that the dispersion and helicity of Weyl bosons can be detected through measurements of the the dynamical structure factor tensor. In the SU(3) case, we preliminarily discuss the effects of spin–orbit coupling and Rabi fields, and conjecture that the emergent collective modes have a scalar (charge), vector (spin) and tensor (quadrupolar) components, suggesting that these modes are more complex than Weyl bosons. To describe spin–orbit coupling, we use the terminology color-orbit coupling, where the three internal states are labeled as colors Red, Green and Blue. We discuss the phase diagram and velocities of boson modes in the non-interacting regime and ponder over several open questions that need to be addressed for SU(3) systems. Lastly, we make some concluding remarks and suggest potential experimental candidates, with two and three internal states, where spin–orbit or color-orbit coupling and Rabi fields could be used to investigate the emergence of unusual collective modes with scalar, vector and tensor properties.
We discuss topological phase transitions in ultracold Fermi superfluids induced by interactions and artificial spin-orbit fields. We construct the phase diagram for population-imbalanced systems at zero and finite temperatures, and analyze spectroscopic and thermodynamic properties to characterize various phase transitions. For balanced systems, the evolution from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superfluids in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges in the helicity basis. However, for imbalanced populations, spin-orbit fields induce a triplet component for the order parameter in the helicity basis, and may produce nodes in the quasiparticle excitation spectrum leading to bulk topological phase transitions of the Lifshitz type. Additionally a fully gapped phase exists, where a crossover from indirect to direct gap occurs, but a topological transition to a gapped phase possessing Majorana fermion edge states does not occur.
We theoretically investigate one-dimensional three-component spin-orbit-coupled Fermi gases in the presence of the Zeeman field. By solving the Bogoliubov-de Gennes equations, we obtain the phase diagram at a given chemical potential and order parameter. We show that, with increasing the intensity of the Zeeman field, in addition to undergoing a phase transition from Bardeen-Cooper-Schrieffer (BCS) superfluid to topological superfluid, similar to the two-component system, the three-component system may exhibit some other interesting topological phase transitions. For example, by appropriately adjusting the chemical potential $\ensuremath{\mu}$, the system can be in a nontrivial topological superfluid in the whole region of the Zeeman field hhh. It also may initially be a topological superfluid and then translate to a topologically trivial BCS superfluid with increasing the field hhh. Even more exotically, the system may exhibit a re-entrance behavior, being a topological superfluid at small and large fields but a topologically trivial BCS superfluid in between at a mediate Zeeman field. It can therefore have two regions with zero-energy Majorana fermions. As a consequence of these interesting topological phase transitions, the system of the three-component spin-orbit-coupled Fermi gases in a certain parameter range is more optimizing for the experimental realization of the topological phase due to the smaller magnetic field needed. Thus, a promising candidate for the realization of the topological phase is proposed.
Magnetic phenomena in itinerant electron systems have been at the forefront of materials science. Here we show that the Weyl spin-orbit coupling (SOC) in three-dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations, and phase transitions. A putative ferromagnetic state (FM) is always unstable against a stripe spiral spin density wave (S-SDW) or a stripe longitudinal SDW (LSDW) at small or large SOC strengths, respectively. The stripe-ordering wave vector is given by the nesting momentum of the two SOC-split Fermi surfaces with the same or opposite helicities at small or large SOC strengths, respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz-type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and Fermi surface reconstructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold-atom experiments are briefly discussed. In view of recent ground-breaking experimental advances in generating two-dimensional SOC in cold atoms, these phenomena can be observed in current or near-future cold-atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.
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.