Role Reversal in a Bose-Condensed Optomechanical System

We analyze the optomechanicslike properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits the nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter-wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nature Phys. 4, 561 (2008)]. We demonstrate that this system can lead to the creation of a variety of nonclassical matter-wave fields, in particular, cat states, and discuss several possible protocols to measure their Wigner function.

Figure 1

Schematic of the BEC-optical fields system and simplified level diagram of the condensed atoms, driven by a classical field of Rabi frequency ${\Omega }_p$ and a quantized field of vacuum Rabi frequency $g_c$.

Figure 2

Normalized absolute value of the transition moments $|G_{0,m}|$ between the trap ground state and its excited states as a function of the recoil momentum $\Delta \mathbf{k}$ (in units of $L^{-1}$).

Figure 3

Atom number distribution $P_a(n)$ for the displaced cat state (8), with $|\alpha |=2$ and $|\beta |=4$. (a) $\alpha$ and $\beta$ are in phase. (b) $\alpha$ and $\beta$ are $\pi /2$ out of phase.