Macroscopic Atom-Molecule Dark State and Its Collective Excitations in Fermionic Systems

We show that a robust macroscopic atom-molecule dark state can exist in fermionic systems, which represents a coherent superposition between the ground molecular Bose-Einstein condensates and the atomic BCS paired state. We take advantage of the tunability offered by external laser fields, and explore this superposition for demonstrating coherent oscillations between ground molecules and atom pairs. We interpret the oscillation frequencies in terms of the collective excitations of the dark state.

Figure 1

(a) $|c_g^s{|}^2/n$, $\mu$, and ${\Delta }^s$ as functions of ${\Omega }_0$. The dark-state solution at ${\Omega }_0=4.1E_F$ is indicated by the vertical line where $|c_g^s{|}^2/n=0.067$, $\mu =0.87E_F$, and ${\Delta }^s=0.17E_F$. (b)–(d) The ground population dynamics where (b) ${\nu }_0=-4.32E_F$, (c) ${\nu }_0=-2.88E_F$, and (d) ${\nu }_0=0.00E_F$. The insets are the Fourier spectra of the corresponding population dynamics after $t=t_s=126.65\hslash /E_F$. We have used the following parameters: $U_0=-28.39E_F/k_F^3$, $g_0=-15.68E_F/k_F^{3/2}$, $n=0.034k_F^3$, and $K_c=14.4k_F$, where $E_F$ and $k_F$ are the Fermi energy and momentum, respectively.

Figure 2

The sections of $f(\omega )$ containing the low-frequency root (left column) and the high-frequency root (right column). (a) and (d) are for ${\nu }_0=-4.32E_F$, (b) and (e) are for ${\nu }_0=-2.88E_F$, and (c) and (f) are for ${\nu }_0=0.00E_F$. Other parameters are the same as in Fig. 1.