Right-eigenstate-based approach to non-Hermitian superfluidity with two-body loss

TL;DR

The paper develops a right-eigenstate-based mean-field framework for non-Hermitian superfluidity with two-body loss, deriving the NH gap equation and showing gauge-invariant, smooth order-parameter solutions. It demonstrates that two-body loss enhances the order parameter magnitude while driving the condensed phase toward metastability, and that backscattering can destabilize and destroy the superfluid, with phase diagrams revealing stable, metastable, and normal regions. The biorthogonal counterpart yields discontinuities and no nontrivial solutions in moderate dissipation, illustrating the advantage of the right-eigenstate formulation for open quantum fluids. The results offer experimentally testable predictions for ultracold-atom platforms with tunable two-body loss and backscattering and provide a robust tool for exploring dissipation-stabilized phenomena in NH systems.

Abstract

We theoretically explore a non-Hermitian superfluid model with complex-valued interaction, inspired by two-body loss stemming from inelastic scattering observed in ultracold atomic experiments. Utilizing both the right-eigenstate-based mean-field theory and its biorthogonal counterpart, we study the properties of the system. Notably, the right-eigenstate-based framework produces smooth and continuous solutions, in stark contrast to the absence of nontrivial solutions and the abrupt discontinuities observed in the biorthogonal-eigenstate-based framework under moderate dissipation. In addition, the lower condensation energy obtained in the former framework suggests its superior suitability for describing this system. Furthermore, we explore the impact of backscattering, a crucial factor in realistic systems. Our analysis reveals that, facilitated by two-body loss, even moderate backscattering destabilizes the superfluid state. Sufficiently strong backscattering completely destroys it, highlighting a key mechanism for the fragility of this non-Hermitian quantum phase.

Figures (5)

• Figure 1: Numerical solutions derived from the NH gap equation [Eq. \ref{['equ:M1:eqgapeq']}]. (a) $\Delta_0$ plotted against $\gamma$ for $U_0=2.8$. The inset shows the complex angle $\theta$ of $\Delta_0$ (grey dot) and $U$ (grey line) as functions of $\gamma$ for $U_0=2.8$, demonstrating exact coincidence. (b) $E_c$ as a function of $\gamma$ for $U_0=2.8$, with the inset presenting results for $E_c$ over a broader range of $\gamma$. (c) The phase diagram of superfluid stability at half-filling, where the blue curve indicates $\text{Re}E_c = 0$.
• Figure 2: Comparison of numerical solutions to the NH gap equation under different definitions of the order parameters. (a) $\Delta_0$ and (b) $\text{Re}E_c$ as functions of $\gamma$ for $U_0=1.8$. The blue lines represent solutions based on the right-eigenstate-based approach (RR), while the red points correspond to solutions based on the biorthogonal approach (LR). The inset in (b) highlights the results for the metastable superfluid phase, whereas the main panel depicts the stable superfluid phase.
• Figure 3: Numerical solutions derived from the NH gap equation with backscattering [Eq. \ref{['equ:M1:eqgapeqBS']}]. $\Delta_0$ (a) and $E_c$ (b) are shown as functions of $\Gamma_{BS}$ for $U_0=6.8$ and $\gamma=10$. The inset in (a) displays $\text{Re}\Delta_0$ (grey line) and $\text{Im}\Delta_0$ (grey dot) normalized to their maximum values.
• Figure 4: Phase diagrams. (a) Phase diagram in the $U_0$-$\Gamma_{BS}$ plane at $\gamma=10$. The grey dashed line corresponds to the phase transition described in Fig. \ref{['fig:fig3']}; (b) Three-dimensional phase diagram in the $U_0$-$\gamma$-$\Gamma_{BS}$ parameter space. Region I: the stable superfluid phase; Region II: the metastable superfluid phase; Region III: the normal phase. The blue curve (or surface) represents the condition $\text{Re}E_c = 0$ with $\Delta_0 \ne 0$, while the red curve (or surface) signifies the onset of $\Delta_0 = 0$.
• Figure S1: Phase diagrams in the $U_0 - \Gamma_{BS}$ plane: (a) $\gamma=0$; (b) $\gamma=3$; (c) $\gamma=6$. These diagrams correspond to cross-sections along the $\gamma$ axis in Fig. \ref{['fig:fig4']}(b). The blue curve denotes the condition $\text{Re}E_c = 0$ with $\Delta_0 \ne 0$, while the red curve marks the onset of $\Delta_0 = 0$. (d) The critical lines representing the transition to the normal phase (corresponding to the red curves in panels (a), (b), and (c)) exhibit complete overlap across various values of $\gamma$.