Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency

We investigate a hybrid optomechanical system composed of a micromechanical oscillator as a movable membrane and an atomic three-level ensemble within an optical cavity. We show that a suitably tailored cavity field response via electromagnetically induced transparency (EIT) in the atomic medium allows for strong coupling of the membrane's mechanical oscillations to the collective atomic ground-state spin. This facilitates ground-state cooling of the membrane motion, quantum state mapping, and robust atom-membrane entanglement even for cavity widths larger than the mechanical resonance frequency.

Figure 1

(a) Hybrid optomechanical system composed of an atomic ensemble and a mechanical oscillator enclosed in an optical cavity. (c) Cavity field transmission frequency profile for (un)resolved sideband cooling of the membrane motion in the bad cavity limit (upper) and cavity EIT-resolved sideband cooling (lower).

Figure 2

Cavity EIT cooling: (a) Logarithmic plot (of base 10) of $n_f$ as a function of normalized two-photon detuning $\delta /{\omega }_m$. (b) Variation of $n_f$ with $\Omega$ for $\delta ={\omega }_m$. (c) Variation of $n_f$ with $G$ for standard self-cooling with no atoms (${\Delta }_c=\kappa /2$, dashed line) and cavity EIT cooling [$\delta ={\omega }_m$, $\Omega =\left(2\pi \right)300$ MHz, solid line]. The insets show the case of $N={10}^6$ atoms (see text). State mapping: (d) Time evolution of Wigner functions for an initially squeezed ground-state atomic spin. See text for parameters.

Figure 3

Atom-membrane steady-state entanglement: (a) Logarithmic negativity $E_N$ as a function of $\delta$ for the parameters given in the text. (b) Variation of $E_N$ with $G$ for $\delta =-{\omega }_m$. (c) Variation of $E_N$ with $n_i$, showing robustness of entanglement with respect to temperature.