Dissipative dynamics of a qubit coupled to a nonlinear oscillator

Details Dissipative dynamics of a qubit coupled to a nonlinear oscillator Dissipative dynamics of a qubit coupled to a nonlinear oscillator

2009-07-31

arxiv.org/abs/0907.5535v2

Phys. Rev. A 80, 052331 (2009)

Physics

Quantum Physics

24 pages, 7 figures, 1 table; in the text between Eq. (8) and (9) there were misprints in the published version until 3rd Dec

Scientific paper

10.1103/PhysRevA.80.052331

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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