Dissipation-facilitated molecules in a Fermi gas with non-Hermitian spin-orbit coupling

We study the impact of non-Hermiticity on the molecule formation in a two-component spin-orbit-coupled Fermi gas near a wide Feshbach resonance. Under an experimentally feasible configuration where the two-photon Raman process is dissipative, the Raman-induced synthetic spin-orbit coupling acquires a complex strength. Remarkably, dissipation of the system facilitates the formation and binding of molecules, which, despite their dissipative nature and finite lifetime, exist over a wider parameter regime than in the corresponding Hermitian system. These dissipation-facilitated molecules can be probed by the inverse radio-frequency (rf) spectroscopy, provided the Raman lasers are blue detuned to the excited state. The effects of dissipation manifest in the rf spectra as shifted peaks with broadened widths, which serve as a clear experimental signature. Our results, readily observable in current cold-atom experiments, shed light on the fascinating interplay of non-Hermiticity and interaction in few- and many-body open quantum systems.

Figure 1

Schematics of the experimental setup. A two-component Fermi gas with hyperfine spin states $|\uparrow \rangle$ and $|\downarrow \rangle$ are subject to a non-Hermitian SOC through a dissipative Raman process. The parameters $q$, $\eta$, and $\delta$, respectively, represent the transferred momentum, single-photon Rabi frequency, and detuning. The tunable effective decay rate $\mathrm{\Gamma }$ of the intermediate excited state ($|e\rangle$) contains contribution from both spontaneous decay and laser-induced decay. Here we show only Raman lasers with red detuning as an example.

Figure 2

Single-particle physics modified by dissipation. (a) $\text{Re}\left({\xi }_{\mathbf{k}\pm }\right)$ (shifted by ${\xi }_{\mathrm{th}}$) along $k_x$ for different $\tilde{\mathrm{\Gamma }}$ at a fixed $|{\mathrm{\Omega }}_0|=1$. The arrows mark the locations ($k_{\min }$) of the energy minimum. (b1) and (b2) $\text{Im}\left({\xi }_{\mathbf{k}\pm }\right)$ for red-tuned (b1) and blue-detuned (b2) Raman lasers at $|{\mathrm{\Omega }}_0|=1$ and $\tilde{\mathrm{\Gamma }}=0.5$. The helicity indices ($+/-$) are marked on the curves accordingly. (c1) Contour plot of $k_{\min }$ (encoded by the color bar) in the $\left(\right|{\mathrm{\Omega }}_0|,\tilde{\mathrm{\Gamma }})$ plane. (c2) $k_{\min }$ as a function of $\tilde{\mathrm{\Gamma }}$ for given $|{\mathrm{\Omega }}_0|$. (d) Coupling constant $C$ for two lower-helicity fermions at ${\mathbf{k}}_m$ and $-{\mathbf{k}}_m$ as a function of $\tilde{\mathrm{\Gamma }}$. Here ${\mathbf{k}}_m=(k_{\min },0,0)$. (e) Real energy gap $G$ at $\mathbf{k}=(0,0,0)$. In all figures we take $q$ and $E_q$ as the units of momentum and energy, respectively.

Figure 3

Dissipation-facilitated molecules. (a) Critical coupling ${(1/a_s)}_c$ of two-body bound state as a function of $\tilde{\mathrm{\Gamma }}$ for fixed $|{\mathrm{\Omega }}_0|$. (Inset) An enlarged view of the regime where ${(1/a_s)}_c$ turns negative. (b) $\text{Im}\left(E_b\right)$ at the critical coupling as a function of $\tilde{\mathrm{\Gamma }}$ for the red-tuned (${\mathrm{\Omega }}_0=-2$) and blue-detuned (${\mathrm{\Omega }}_0=2$) Raman processes. (c) $\text{Re}\left(E_b\right)$ as functions of $\tilde{\mathrm{\Gamma }}$ for several fixed couplings $1/a_s=0.2,0.5,1$, with $|{\mathrm{\Omega }}_0|=2$. (d) $\text{Im}\left(E_b\right)$ at a fixed coupling strength $1/a_s=1$ for the red-detuned (${\mathrm{\Omega }}_0=-2$) and blue-detuned (${\mathrm{\Omega }}_0=2$) Raman processes. We have taken $q$ and $E_q$ as the units of momentum and energy, respectively.

Figure 4

Molecule spectrum via the inverse rf spectroscopy under blue-detuned Raman lasers. (a1) and (a2) Transition rate $R_i$ at different $\tilde{\mathrm{\Gamma }}$. We use the shifted frequency $\overline{\omega }$ (see main text) as the $x$ axis, and mark the locations of $\text{Re}\left(E_b\right)$ for each case with arrows of the same color. (b) and (c) The peak position ${\overline{\omega }}_p$ and the FWHM of the rf spectrum as functions of $\tilde{\mathrm{\Gamma }}$. In (b) we also show $\text{Re}\left(E_b\right)$ to guide the eye. In all plots we take ${\mathrm{\Omega }}_0=2$ and $1/a_s=1$. We have taken $q$ and $E_q$ as the units of momentum and energy, respectively.