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arXiv · 0907.5535

Dissipative dynamics of a qubit coupled to a nonlinear oscillator

Carmen Vierheilig·Johannes Hausinger·Milena Grifoni
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Abstract

We consider the dissipative dynamics of a qubit coupled to a nonlinear oscillator (NO) embedded in an Ohmic environment. By treating the nonlinearity up to first order and applying Van Vleck perturbation theory up to second order in the qubit-NO coupling, we derive an analytical expression for the eigenstates and eigenfunctions of the coupled qubit-NO system beyond the rotating wave approximation. In the regime of weak coupling to the thermal bath, analytical expressions for the time evolution of the qubit's populations are derived: they describe a multiplicity of damped oscillations superposed to a complex relaxation part toward thermal equilibrium. The long time dynamics is characterized by a single relaxation rate, which is maximal when the qubit is tuned to one of the resonances with the nonlinear oscillator.

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Carmen Vierheilig, Johannes Hausinger, Milena Grifoni. 2009-07-31. Dissipative dynamics of a qubit coupled to a nonlinear oscillator. https://doi.org/10.1103/physreva.80.052331

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