Nonlinear Coupling of Nanomechanical Resonators to Josephson Quantum Circuits

We propose a technique to couple the position operator of a nanomechanical resonator to a SQUID device by modulating its magnetic flux bias. By tuning the magnetic field properly, either linear or quadratic couplings can be realized, with a discretely adjustable coupling strength. This provides a way to realize coherent nonlinear effects in a nanomechanical resonator by coupling it to a Josephson quantum circuit. As an example, we show how squeezing of the nanomechanical resonator state can be realized with this technique. We also propose a simple method to measure the uncertainty in the position of the nanomechanical resonator without quantum state tomography.

Figure 1

(a) A nanomechanical resonator in one arm of a SQUID device threaded by a magnetic field. (b) A more sophisticated design in which a nanomechanical resonator is coupled to a charge qubit. The shaded box is the superconducting island of the charge qubit.

Figure 2

(a) Time dependence of the nanoresonator position uncertainty $\Delta X$ (normalized to the initial uncertainty) under the effect of squeezing and decoherence. See text for experimental parameters and initial conditions. (b) The maximum achievable squeezing (minimum $\Delta X$) as a function of the dephasing rate. All other parameters are the same as in (a).