All-optical pump-and-probe detection of two-time correlations in a Fermi gas

We propose an all-optical scheme to probe the dynamical correlations of a strongly interacting gas of ultracold atoms in an optical lattice potential. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the two-time one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasiparticle dispersions are discussed.

Figure 1

Diagram of the internal atomic levels involved in the proposed detection scheme.

Figure 2

Snapshots of the measurement procedure. From left to right: adiabatic storage of coherence from incident beams, free many-body evolution, light re-emission, and detection.

Figure 3

Time dependence of the emission amplitude in the normal ($\mathbf{k}=0$) direction for a normal state N (blue solid line) and a BCS superfluid with gap $\Delta /4J_g=0.2$ (red dashed line). Hopping ratio, $r=0.1$. Temperature, $k_{B}T=J_g/50$.

Figure 4

Frequency dependence of the emission amplitude in the normal ($\mathbf{k}=0$) direction for a normal state N (blue solid line) and a BCS superfluid with gap $\Delta /4J_g=0.2$ (red dashed line). Hopping ratio, $r=0.1$. Temperature, $k_{B}T=J_g/50$.

Figure 5

Frequency dependence of the emission amplitude from a BCS superfluid with $\Delta /4J_g=0.2$ at different angles, $k=k_x=k_y=0,\pi /4a,\pi /2a$, with hopping ratio $r=1$. Inset: magnified view of the $\mathbf{k}=0$ curve. The arrows indicate the corresponding spectral minimum ${\omega }_{min}$. Temperature $k_{B}T=J_g/50$.

Figure 6

Frequency dependence of the emission amplitude from a BCS superfluid with $\Delta /4J_g=0.2$ at different angles, $k=k_x=k_y=0,\pi /4a,\pi /2a$. Hopping ratio $r=3$. The arrows indicate the corresponding spectral minimum ${\omega }_{min}$. Temperature $k_{B}T=J_g/50$.

Figure 7

$\mathbf{k}$ dependence of the lower edge of the spectrum compared to the quasiparticle dispersion $E_{\mathbf{k}}^{-}$ of the BCS superfluid with $\Delta /4J_g=0.2$. From top to bottom, hopping ratio $r=1,1.5,3$. Curves for different $r$ are offset by $0.5$ for better visibility.