Fidelity susceptibility and topological phase transition of a two-dimensional spin-orbit-coupled Fermi superfluid

We investigate the fidelity susceptibility (FS) of a two-dimensional spin-orbit-coupled (SOC) Fermi superfluid and the topological phase transition driven by a Zeeman field in the perspective of its ground state wave function. Without Zeeman coupling, FS shows additional features characterizing the BCS-BEC crossover induced by SOC. In the presence of a Zeeman field, the topological phase transition is explored using both FS and the topological invariant. In particular, we obtain the analytical result of the topological invariant which explicitly demonstrates that the topological phase transition corresponds to a sudden change of the ground state wave function. Consequently, FS diverges at the phase transition point with its critical behavior being $\chi \propto \text{ln}|h-h_c|$ . Based on this observation, we conclude that the topological phase transition can be detected by measuring the momentum distribution in cold atom experiments.

Figure 1

Fidelity susceptibility (in arbitrary dimension) as functions of interaction parameters and strength of SOC in (a) and (b) three dimensions and (c) and (d) two dimensions. In (a) and (c), $\tilde{\lambda }$ are given as 0, 1, and 2 for the solid blue line, black dotted line, and red dashed line, respectively. The interaction parameters are set to be $\eta =1/\left(k_{F}a\right)=-1.2,-1,-0.6$ in (b) and $\eta =E_b/E_F=0.2,0.8,2.2$ in (d) for lines from above.

Figure 2

Fidelity susceptibility (in arbitrary dimension) as functions of Zeeman field with $E_b/E_F=0.5$ and $m\lambda /k_F=1$. The vertical red dashed line denotes the critical Zeeman field $h_c=0.792$. The two inserted figures correspond to the momentum distribution of the total particle numbers shown in Eq. (3) as a function of $p_x$ with $p_y=0$.