Hybrid phase-space--Fock-space approach to evolution of a driven nonlinear resonator

Abstract

We analyze the quantum evolution of a weakly nonlinear resonator due to a classical near-resonant drive and damping. The resonator nonlinearity leads to squeezing and heating of the resonator state. Using a hybrid phase-space--Fock-space representation for the resonator state within the Gaussian approximation, we derive evolution equations for the four parameters characterizing the Gaussian state. Numerical solution of these four ordinary differential equations is much simpler and faster than simulation of the full density matrix evolution, while providing good accuracy for the system analysis during transients and in the steady state. We show that steady-state squeezing of the resonator state is limited by 3 dB; however, this limit can be exceeded during transients.

24 pages, 10 figures, v2 published version

References in corpus (13)

• Observation of quantum jumps in a superconducting artificial atom
• High-Fidelity Readout in Circuit Quantum Electrodynamics Using the Jaynes-Cummings Nonlinearity
• Generating Entangled Microwave Radiation Over Two Transmission Lines
• Cavity-assisted squeezing of a mechanical oscillator
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Quantifying decoherence in continuous variable systems
• Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities
• Mass Detection with Nonlinear Nanomechanical Resonator
• Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback
• Critical exponents in metastable decay via quantum activation
• Dispersive Qubit Measurement by Interferometry with Parametric Amplifiers
• Quantum Bayesian approach to circuit QED measurement with moderate bandwidth
• Measuring a transmon qubit in circuit QED: dressed squeezed states