Non-Hermitian topological superfluidity in a three-dimensional fermi gas with spin-orbit coupling

TL;DR

The paper addresses non-Hermitian many-body physics in a three-dimensional Fermi gas with Rashba spin-orbit coupling (SOC), Zeeman splitting, and two-body loss in a cubic lattice. It adopts a non-Hermitian mean-field approach to derive the Bogoliubov spectrum $E_{\mathbf{k}\pm}$ and a zero-temperature gap equation, enabling a phase diagram in the interaction–dissipation plane and in the dissipation–Zeeman field plane. Key findings include dissipation-induced phase transitions from superfluid to normal to metastable superfluid, with a reentrant MSF region at weak coupling due to the quantum Zeno effect; SOC broadens the normal and metastable regions and suppresses conventional SF, while SOC plus Zeeman field yields a topological superfluid (TSF) characterized by a nonzero Chern number $C$ in a finite $h$ window. The work reveals how non-Hermiticity, SOC, and topology intertwine to control pairing and offers signatures in momentum-space densities that could guide experiments in ultracold atoms.

Abstract

The experimental advances in realizing artificial spin-orbit coupling (SOC) and non-Hermitian potentials in ultracold atomic system open a new avenue for exploring their significant roles in quantum many-body physics. Here, we investigate a non-Hermitian, two-component Fermi system in a cubic lattice with Rashba SOC and complex-valued interaction arising from two-body loss. We adopt the non-Hermitian mean field theory and map out the phase diagram at zero temperature. The interplay of dissipation and on-site interaction drives a dissipation-induced phase transition from superfluid (SF) to normal phase (N). Notably, for weak interaction strengths, this leads to a reentrance of the superfluid state. The presence of SOC significantly expands the parameter regime for both the normal phase and the metastable superfluid phase(MSF). Whereas, the Zeeman field can drive the system from a conventional superfluid into a topological superfluid phase(TSF), characterized by a nontrivial topological invariant. These results enrich our knowledge of pairing superfluidity in Fermi systems.

Figures (4)

• Figure 1: Zero-temperature phase diagram in the parameter space of the interaction strength $U_1$ and the dissipation $\gamma$ with the spin-orbit coupling strength: (a) $\alpha/t=0$, (b) $\alpha/t=0.4$, and (c) $\alpha/t=0.8$. The blue, light blue, and yellow regions denote stable superfluid, metastable superfluid, and normal states, respectively. In all figures we take $\mu/t=0$, $h/t=0$. Due to numerical constraints, the region with small $U_1$ is not shown.
• Figure 2: The real parts of (a) order parameter $\Delta_0/t$ and (b) condensate energy $\Delta E/t$ as functions of the dissipation $\gamma$ for SOC strength $\alpha/t=(0,0.4,0.8)$. The inset in (b) provides a magnified view at low dissipation strengths. (c) The real parts of order parameter $\Delta_0/t$ as a function of SOC strength $\alpha$ with $\gamma/t=(0.2,0.6,1)$. (d) The energy gap of the single-particle spectrum as a function of the spin-orbit coupling strength $\alpha$. In all figures we take $\mu/t=0$, $U_1/t=1.8$ and $h/t=0$.
• Figure 3: Zero-temperature phase diagram in the plane of the dissipation $\gamma$ and Zeeman field $h$ with the SOC strength: (a) $\alpha/t=0.6$, (b) $\alpha/t=1$. The green region shows the topological superfluid phase. In all figures we take $U_1/t=4$ and $\mu/t=0$.
• Figure 4: The momentum space density distribution in $k_z=0$ plane for three phase marked in Fig. 3(b). The order parameters are (a) $\Delta_0/t=0.855+0.127i$ (superfluid phase), (b) $\Delta_0/t=0.755+1.087i$ (metastable superfluid phase), (c) $\Delta_0/t=0.016+0.008i$ (topological superfluid phase), other parameters are the same as Fig. 3(b).