Superconducting phase qubit coupled to a nanomechanical resonator: Beyond the rotating-wave approximation

Andrew T. Sornborger; Andrew N. Cleland; Michael R. Geller

doi:10.1103/PhysRevA.70.052315

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Superconducting phase qubit coupled to a nanomechanical resonator: Beyond the rotating-wave approximation

Andrew T. Sornborger, Andrew N. Cleland, Michael R. Geller

DOI 10.1103/PhysRevA.70.052315 · Physical Review A

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Abstract

We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems. Here we present a simple theoretical technique, using a basis of dressed states, to perturbatively account for the leading-order corrections to the RWA. By comparison with exact numerical results, we demonstrate that the method is accurate for moderately strong coupling and provides a useful theoretical tool for describing fast quantum information processing. The method applies to any quantum two-level system linearly coupled to a harmonic oscillator or single-mode boson field.