Coupling Nanomechanical Cantilevers to Dipolar Molecules

We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems.

Figure 1

Arrangement considered for coupling a nanomechanical oscillator to a dipolar “crystal.” In setup A, a single molecule is coupled to the oscillator. In setup B, the oscillator is again at a distance $R$ from the linear chain of molecules. A weakly confining harmonic trap for the dipoles is shown along the $x$ axis.

Figure 2

Variance in the quadrature component $x_1$ [Eq. (12)], vs squeezing parameter $u$, for a SrO molecule interacting with a cantilever. The two curves are for the cantilever damping rates linewidth $D=1\mathrm{Hz}$ (solid curve) and 0 Hz (dashed curve). Squeezing occurs when the variance in $x_1$ is below $\frac{1}{4}$, and is eventually destroyed due to phase noise in the cantilever.

Figure 3

Sum of variances of $s_1$ and $s_2$, vs squeezing parameter $u$, for a SrO dipolar crystal interacting with a cantilever. The two curves are for cantilever damping rates of $D=1\mathrm{Hz}$ (solid curve) and 0 Hz (dashed curve). Phase fluctuations of the cantilever eventually increase the sum of variances to a value larger than 2, indicative of the loss of entanglement between the two phonon modes.