Kerr nonlinearities and nonclassical states with superconducting qubits and nanomechanical resonators

Abstract

We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e. quantum superpositions of pairs of distinguishable coherent states 180${}^{\circ }$ out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented, and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement a Kerr nonlinearity in this system may be used for high precision measurements in nanomechanical resonators.

5 pages, 2 figures, fixed typos

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• Exploiting Kerr Cross Non-linearity in Circuit Quantum Electrodynamics for Non-demolition Measurements
• Mechanical cat states in graphene resonators
• Quantum State Synthesis of Superconducting Resonators
• Two proposals for testing quantum contextuality of continuous-variable states
• Quantum phase measurement and Gauss sum factorization of large integers in a superconducting circuit
• Motional Entanglement with Trapped Ions and a Nanomechanical Resonator
• Nonlinear-dissipation-induced Entanglement of Coupled Nonlinear Oscillators
• A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation
• Controlling properties of a hybrid Cooper pair box interacting with a nanomechanical resonator in the presence of Kerr nonlinearities and losses
• Quantum Decoherence of Charge Qubit coupled to Nonlinear Nanomechanical Resonator
• Transmission losses in optical qubits for controlled teleportation