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arXiv:quant-ph/0605017 · Physical Review Letters

Nonlinear Coupling of Nanomechanical Resonators to Josephson Quantum Circuits

Xingxiang Zhou, Ari Mizel

Published Dec 26, 2006• 80 citations
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Abstract

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.

DOI
10.1103/physrevlett.97.267201

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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.
We propose a scheme for generating squeezed states based on a superconducting hybrid system. Our system consists of a nanomechanical resonator, a superconducting flux qubit, and a superconducting transmission line resonator. Using our proposal, one can easily generate the squeezed states of the nanomechanical resonator. In our scheme, the nonlinear interaction between the nanomechanical resonator and the superconducting transmission line resonator can be implemented by the flux qubit as 'nonlinear media' with a tunable Josephson energy. The realization of the nonlinearity does not need any operations on the flux qubit and just needs to adiabatically keep it at the ground state, which can greatly decrease the effect of the decoherence of the flux qubit on the squeezed efficiency.
We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generalized situations where the superconducting Josephson junction system is a multi-level system. We also address the practical issues concerning experimental realization.
We study a system of two nanomechanical resonators embedded in a dc superconducting quantum interference device (SQUID). We show that the inductively coupled resonators can be treated as two entangled quantum memory elements with states that can be read from, or written on, by employing the SQUID as a displacement detector or switching additional external magnetic fields, respectively. We present a scheme to squeeze the even mode of the state of the resonators and, consequently, reduce the noise in the measurement of the magnetic flux threading the SQUID. We finally analyze the effect of dissipation on the squeezing using the quantum master equation, and show the qualitatively different behavior for the weak and strong damping regimes. Our predictions can be tested using current experimental capabilities.
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