Squeezer-based pulsed optomechanical interface

We prove feasibility of high-fidelity pulsed optomechanical interface based on all-optical presqueezing of non-Gaussian quantum states of light before they enter the optomechanical system. We demonstrate that feasible presqueezing of optical states effectively increases the low noise transfer of them to mechanical oscillator. It allows one to surpass the limit necessary to transfer highly nonclassical states with negative Wigner function. In particular, we verify that with this help single photon states of light can be efficiently turned to single phonon states of mechanical oscillator, keeping the negativity of the Wigner function. It opens the possibility to merge quantum optomechanics with the recent methods of quantum optics.

Figure 1

(a) Simplified scheme of the interface. The optical mode (O) is prepared in the desired state, passes the squeezing operation ($S$), and is coupled via the QND interaction with the mechanical mode (M). The optical mode is then detected (D) and the outcome of the measurement is used to displace M. (b) A sketch of optomechanical implementation; C—circulator. (c) Principal scheme of squeezing operation (see Sec. 3); OPO—optical parametric oscillator.

Figure 2

Added noise variance $V_N$ (6),(7) in shot noise units as a function of the transfer coefficient $T$ in case of increase of squeezing $S$, coupling $g$, or pulse duration $\tau$. (a) Solution without the mechanical bath (Sec. 4); (b) solution accounting for the mechanical bath but with adiabatically eliminated cavity mode; (c) full solution (Sec. 6). The point ($O$) corresponds to the initial set of parameters (10) with no presqueezing ($S=1$). Markers denote points corresponding to sequential increase of squeezing with the step 3 dB. Dashed line marks the perfect excess-noise-free transfer $V_N=1$. Dotted curve indicates the maximum $V_N$ allowing transfer of the negativity of the Wigner function of a single-photon state for a given transmittivity $T [V_N^2<T/(1-T)]$.

Figure 3

Wigner function of a Fock state $|1\rangle$ transmitted to the mechanical system using the proposed protocol working in the regimes, denoted by corresponding named points at Fig. 2. $O$, without the presqueezing; $A$ with 12 dB of presqueezing with intracavity mode formally eliminated; $B$ with 12 dB of presqueezing, full solution; $C$, same transmittivity as in $A$ and $B$, but no excess noise ($V_N=1$). The negativity at the origin is presented at the framed insets.