Dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance across the phase transition from BCS to Sarma superfluid

We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation approach at zero temperature, and find their dynamical characters across the phase transition from a balanced conventional Bardeen-Cooper-Schrieffer (BCS) superfluid to a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a Bose-Einstein-condensate-like regime of the Fermi superfluid, dynamic structure factors can help distinguish the in-phase ground state from the out-of-phase metastable state by the relative location of molecular excitation and Leggett mode, or the minimum energy to break a Cooper pair. In the phase transition from BCS to Sarma superfluid, we find the dynamic structure factor of Sarma superfluid has its own specific gapless excitation at a small transferred momentum where the collective phonon excitation acquires a finite width, and also a relatively strong atomic excitation at a large transferred momentum, because of the existence of unpaired Fermi atoms. Our results can be used to differentiate Sarma superfluid from BCS superfluid.

Figure 1

The free energy of both spin-population balanced BCS state (black dashed line) and spin-polarized Sarma state (red solid line) at scattering length $1/k_F{a}_0=-0.5, 1/k_F{a}_1=-0.05$ and Zeeman detuning $\delta \left(B\right)=0.4{\varepsilon }_F$. $F_{\mathrm{IG}}$ is the free energy of ideal Fermi gases with the same particle number.

Figure 2

The total density DSF (blue solid line) and relative one (red dotted line) of BCS superfluid in (a) in-phase ground state and (b) out-of-phase metastable state. Two insets are their own zoom-in figures of the pair-breaking excitation, the left and right arrow mark the initial position of pair-breaking excitation in the open and closed channel, respectively.

Figure 3

The total (top panel) and relative (bottom panel) DSF in BCS superfluid side of phase transition, with scattering length $1/k_F{a}_0=-0.5, 1/k_F{a}_1=-0.05$, Zeeman detuning $\delta \left(B\right)=0.4{\varepsilon }_F$. The result is independent on the value of chemical potential difference when $\delta \mu <\delta {\mu }_{\mathrm{cr}}$. (a) Phonon mode, (b) Leggett mode, (c) $2{\mathrm{\Delta }}_c$, (d) $2{\mathrm{\Delta }}_o$, (e) pair-breaking excitations at a large $q$ in two channels.

Figure 4

The total (top panel) and relative (bottom panel) DSF in Sarma superfluid side of phase transition, with scattering length $1/k_F{a}_0=-0.5, 1/k_F{a}_1=-0.05$, Zeeman detuning $\delta \left(B\right)=0.4{\varepsilon }_F$, and chemical potential difference $\delta \mu =0.5{\varepsilon }_F$. (${\mathrm{a}}^{\prime }$) Phonon mode mixed with single-particle gapless excitation in close channel, (b) Leggett mode, (d) $2{\mathrm{\Delta }}_o$, (e) pair-breaking excitations at a large $q$ in two channels.

Figure 5

The total (top panel) and relative (bottom panel) dynamic structure factors of Sarma superfluid at small transferred momentums, $q=0.3,0.5,0.7,0.9k_F$. An arrow in bottom panel locates the Leggett mode.

Figure 6

The total (top panel) and relative (bottom panel) DSF of Sarma superfluid at big transferred momentums, $q=2,3,4k_F$.

Figure 7

The comparison of total DSF between BCS superfluid state (blue line) and Sarma superfluid state (gray dotted line) at (a) $q=1k_F$ and (b) $q=5k_F$.