Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: an effective bath approach

Abstract

We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the composite qubit-nonlinear oscillator system.

11 pagws, 9 figures

References in corpus (11)

• Single-shot qubit readout in circuit Quantum Electrodynamics
• Single-shot qubit readout in circuit Quantum Electrodynamics
• High-contrast dispersive readout of a superconducting flux qubit using a nonlinear resonator
• Sideband Transitions and Two-Tone Spectroscopy of a Superconducting Qubit Strongly Coupled to an On-Chip Cavity
• Role of relaxation in the quantum measurement of a superconducting qubit using a nonlinear oscillator
• Dissipative dynamics of a biased qubit coupled to a harmonic oscillator: Analytical results beyond the rotating wave approximation
• Dynamics of a qubit coupled to a broadened harmonic mode at finite detuning
• Nonlinear resonant behavior of the dispersive readout scheme for a superconducting flux qubit
• Dissipative dynamics of a two - level system resonantly coupled to a harmonic mode
• Dissipative dynamics of a qubit coupled to a nonlinear oscillator
• The dissipative quantum Duffing oscillator: a comparison of Floquet-based approaches

Cited by in corpus (2)

• Quantifying the nonlinearity of a quantum oscillator
• Qubit-nonlinear-oscillator systems: from the moderate-coupling limit to the ultrastrong-coupling regime