Mechanical Squeezing via Fast Continuous Measurement

We revisit quantum state preparation of an oscillator by continuous linear position measurement. Quite general analytical expressions are derived for the conditioned state of the oscillator. Remarkably, we predict that quantum squeezing is possible outside of both the backaction dominated and quantum coherent oscillation regimes, relaxing experimental requirements even compared to ground-state cooling. This provides a new way to generate nonclassical states of macroscopic mechanical oscillators, and opens the door to quantum sensing and tests of quantum macroscopicity at room temperature.

Figure 1

Wiener filter for cavity optomechanical systems. (a) Schematic of proposed experiment. Mechanical motion (blue) is detected by homodyne measurement of the optical phase quadrature $y_{\mathrm{out}}$ (red). The Wiener filter ($H$) filters the homodyne photocurrent ($Y$) providing the estimated position $q^{\mathrm{est}}$ (orange). (b) Power spectral densities of the signals and the filter response function (green solid line) in the frequency domain. Position estimate, orange solid line; normalized optical readout, red solid line; normalized shot noise, purple dashed line.

Figure 2

(a) Characterization of the optimal variance $V_{\delta q^{\theta }\delta q^{\theta }}$ of the conditional state as a function of $n_{\mathrm{th}}$ (at fixed temperature; $n_{\mathrm{th}}\propto {\mathrm{\Omega }}^{-1}$) and $C$ with $\eta =1$. Black dashed lines show thresholds for different measurement regimes. Colored dots I–IV show the parameters used to generate the Wigner functions $W(q,p)$ in Fig. 2; white vertical dashed line separates the QCO regime (left) and non-QCO regime (right). (b) (I–IV) Wigner distribution of conditional states. Blue dashed ellipses, contour line of $W=e^{-1}\times W_{\max }$; white dashed circles, ground state.

Figure 3

Optimum variance of the conditional state for different measurement efficiencies ($\eta$) at fixed temperature $T=300\mathrm{K}$ and cooperativity $C=5\times {10}^3$ as a function of $n_{\mathrm{th}}$ (or, equivalently, ${\mathrm{\Omega }}^{-1}$), with and without the RWA.