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TT: Fachverband Tiefe Temperaturen

TT 35: Postersession Transport: Nanoelectronics, Quantum Coherence and Quantum Information, Fluctuations and Noise

TT 35.30: Poster

Mittwoch, 25. März 2009, 14:00–18:00, P1A

The dissipative quantum Duffing oscillator — •Carmen Frammelsberger and Milena Grifoni — Institute for Theoretical Physics, University of Regensburg

The knowledge about relaxation and dephasing properties of solid state qubits is essential for quantum computation. In this contribution we consider a qubit interacting with an intermediate driven quantum Duffing oscillator which is itself coupled to an Ohmic bath. This resembles the case of a flux qubit read out by a DC-SQUID acting as a nonlinear oscillator. We consider the oscillator to be part of the environment seen by the qubit. We generalize the concept of an effective spectral density introduced by [1] to the case, that the intermediate oscillator is nonlinear. This is done by mapping the whole system onto a spin-boson problem with an effective spectral density using linear response theory. Within this approach we relate the effective spectral density with the imaginary part of the susceptibility of the quantum Duffing oscillator.

We derive the nonlinear effective spectral density in the rotating wave approximation (RWA) and observe both Ohmic low frequency behaviour and for high damping the response of a linear oscillator with shifted eigenfrequency. Within the RWA the possible parameters are restricted to finite nonlinearity and weak driving amplitudes. We elaborate a time-dependent perturbation theory to consider both the exact Floquet states of the linear oscillator as well as the result for the undriven quantum Duffing oscillator.

[1] A. Garg et al., J. Chem. Phys. 83, 9 (1985).