Establishing Einstein-Poldosky-Rosen Channels between Nanomechanics and Atomic Ensembles

We suggest interfacing nanomechanical systems via an optical quantum bus to atomic ensembles, for which means of high precision state preparation, manipulation, and measurement are available. This allows, in particular, for a quantum nondemolition Bell measurement, projecting the coupled system, atomic-ensemble–nanomechanical resonator, into an entangled EPR state. The entanglement is observable even for nanoresonators initially well above their ground states and can be utilized for teleportation of states from an atomic ensemble to the mechanical system.

Figure 1

(a) Schematic of setup: A pulse of light described by canonical operators ($x_{\mathrm{in}}$, $p_{\mathrm{in}}$) interacts first with a micromechanical oscillator ($X_m$, $P_m$), realized by, e.g., a membrane coupled to a Fabry-Perot cavity mode ($x_c$, $p_c$). Light leaving the cavity ($x_{\mathrm{out}}$, $p_{\mathrm{out}}$) is phase modulated by the membrane. A filter turns these phases into polarization modulation. Subsequently the pulse ($x_{\mathrm{in}}^{\prime }$, $p_{\mathrm{in}}^{\prime }$) interacts with the collective spin of an atomic ensemble, effectively described by canonical operators $X_a$, $P_a$, and Larmor precessing in a magnetic field $B$. Light ($x_{\mathrm{out}}^{\prime }$, $p_{\mathrm{out}}^{\prime }$) leaving the ensemble is subject to homodyne detection. (b) Atomic level scheme with quantization axis along $z$: Atoms are prepared in the state $+1/2$ of a spin $j=1/2$ ground state, Zeeman split by $\Omega$. Light propagates along $x$ with a classical field polarized along $z$ driving the $\pm 1/2\leftrightarrow \pm 1/2$ transitions (double arrows) and the $y$-polarized quantum sidebands entangled with the nanosystem coupling to the $\pm 1/2\leftrightarrow \mp 1/2$ transitions (single arrows).