Engineering Nonclassicality in a Mechanical System through Photon Subtraction

Nonclassical states of a mechanical mode at nonzero temperature are achieved in a scheme that combines radiation-pressure coupling to a light field and photon subtraction. The scheme embodies an original and experimentally realistic way to obtain mesoscopic quantumness by putting together two mature technologies for quantum control. The protocol is quasi-insensitive to mechanical damping.

Figure 1

Sketch of the thought experiment. A laser field (with a set polarization) enters a cavity and drives the oscillations of an end mirror embodying a mechanical mode. The field is then photon subtracted by a high-transmittivity beam splitter (BS) and a Geiger-like photodetector. A click at the latter triggers a shutter (such as an electrically driven half-wave-plate) that blocks the pumping process. We show the symbols for a polarizing beam splitter (PBS) and a quarter-wave-plate (QWP) used to direct the field to the cavity or the photosubtraction unit.

Figure 2

WF of $m$ for $\Delta /{\omega }_m=0.05$, $T=0.4\mathrm{K}$, and $\mu =5\times {10}^{-12}\mathrm{kg}$. We have taken a cavity of length $L=1\mathrm{mm}$, frequency ${\omega }_c/2\pi \simeq 4\times {10}^{14}\mathrm{Hz}$, and finesse ${10}^4$, pumped with $20\mathrm{mW}$. The mechanical damping rate is as small as $\sim 10\mathrm{Hz}$ [2].

Figure 3

(a) Conditional Wigner function of mode $m$ after photon subtraction for $T=4\times {10}^{-3}\mathrm{K}$ and $\mu =5\times {10}^{-12}\mathrm{kg}$. (b) Same as panel (a) but assuming that modes $m$ and $f$ are initially in a pure two-mode squeezed-vacuum state of squeezing factor $\zeta =0.4$. (c)–(f) Snapshot of the Wigner function of the mechanical mode for $T=0.1$, 0.2, 0.3, 0.4 K [in going from panel (c) to (f)]. (g) Negativity of $W(0,0)$ against temperature $T$ for $\Delta /{\omega }_m=0.05$. Other parameters as in Fig. 2.