Pairing Dynamics of Polar States in a Quenched $p$-Wave Superfluid Fermi Gas

We study the pairing dynamics of polar states in a single species $p$-wave superfluid Fermi gas following a sudden change of the interaction strength. The anisotropy of pair interaction together with the presence of the centrifugal barrier results in profoundly different pairing dynamics compared to the $s$-wave case. Depending on the direction of quenches, quench to the BCS regime results in large oscillatory depletion of momentum occupation inside the Fermi sea or large oscillatory filling of momentum occupation. A crucial role of the resonant state supported by the centrifugal barrier in the pairing dynamics is elucidated.

Figure 1

Dynamics of $|{\mathrm{\Delta }}_0|$ and the momentum occupation $|v_{\mathbf{k}}{|}^2$ at the designated time. Inverse scattering volume $1/k_F^3{a}_p$ is quenched (a) from $-20$ to $-10$ and (b) from $-20$ to 10.

Figure 2

Momentum occupations $|v_{\mathbf{k}}{|}^2$ at $t{ϵ}_F=25$ (left) and 60 (right). $1/k_F^3{a}_p$ is quenched from $-20$ to $-10$.

Figure 3

Dynamics of $|{\mathrm{\Delta }}_0|$ and the momentum occupation $|v_{\mathbf{k}}{|}^2$ at the designated time. Inverse scattering volume $1/k_F^3{a}_p$ is quenched (a) from $-10$ to $-20$ and (b) from $+10$ to $-15$.

Figure 4

The snapshots of the momentum occupation $|v_{\mathbf{k}}{|}^2$. $1/k_F^3{a}_p$ is quenched (a) from $-10$ to $-20$ (left) and (b) from $+10$ to $-15$ (right).

Figure 5

The snapshots of the magnitude (left column) and the phase (right column) of the pair amplitude $u_{\mathbf{k}}^{*}{v}_{\mathbf{k}}$ in momentum space. The red circles in right panels highlight the position of the phase rotation of $2\pi .1/k_F^3{a}_p$ is quenched (a) from $-20$ to $-10$ (top), (b) from $-10$ to $-20$ (middle), and (c) from $+10$ to $-15$ (bottom). The snapshots are taken at $t{ϵ}_F=60$, 22, and 11.5, respectively.