Expansion dynamics of the Fulde-Ferrell-Larkin-Ovchinnikov state

We consider a two-component Fermi gas in the presence of spin imbalance, modeling the system in terms of a one-dimensional attractive Hubbard Hamiltonian initially in the presence of a confining trap potential. With the aid of the time-evolving block decimation method, we investigate the dynamics of the initial state when the trap is switched off. We show that the dynamics of a gas initially in the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is decomposed into the independent expansion of two fluids, namely the paired and the unpaired particles. In particular, the expansion velocity of the unpaired cloud is shown to be directly related to the FFLO momentum. This provides an unambiguous signature of the FFLO state in a remarkably simple way.

Figure 1

Expansion of a spin-density imbalanced Fermi gas in the 1D FFLO state after the confining potential has been switched off. Our exact simulations show an effective two-fluid behavior: pairs and unpaired particles expand with different velocities. Remarkably, the expansion velocity of the unpaired particles is directly related to the FFLO momentum and provides a straightforward way for observing the FFLO state.

Figure 2

(a) The density profiles of up ($n_{\uparrow }$) and down spins ($n_{\downarrow }$) in the ground state when $N_{\uparrow }=10$, $N_{\downarrow }=6$, $U=-10J$, and there is to a good approximation an infinitely strong repulsive potential everywhere except at the lattice sites 66-85. (b) The pair momentum correlation function $n_k$ for the same state. There are peaks at the FFLO momenta $q=\pm (k_{F\uparrow }-k_{F\downarrow })=0.2\pi /L$.

Figure 3

(a) The time development of the doublon density $n_{\uparrow \downarrow }$, corresponding to the ground state shown in Fig. 2. (b) The time development of the unpaired particle density $n_{\uparrow }-n_{\uparrow \downarrow }$.

Figure 4

(a) The FFLO momentum $q$ determined from the edge expansion velocity of the unpaired cloud, compared to the $q$ of the ground state, as a function of $N_{\downarrow }$ describing the imbalance ($N_{\uparrow }=10$). We also show the expansion momentum $k\ne q$ obtained in the case of a noninteracting gas, and a non-FFLO state without pair coherence. (b) Same as in (a), but having initially a shallow harmonic trap ($V_{ho}=0.0003$, $C=75.5$).

Figure 5

(a) The time development of the doublon density $n_{\uparrow \downarrow }$ with the same parameters as in Fig. 2 but the initial trap being harmonic ($V_{ho}=0.0003$, $C=75.5$) instead of a box trap. (b) The time development of the unpaired particle density $n_{\uparrow }-n_{\uparrow \downarrow }$.