Decoherence and noise control in strongly driven superconducting quantum bits
by
Anatoly Yu. Smirnov
D-Wave Systems Inc.

We have examined fluctuations and dissipation in a quantum bit interacting with a heat bath and driven by a strong resonant field. This model is of immediate relevance for three Josephson junctions (3JJ) flux qubits, which have been experimentally studied by Chiorescu et al. [1] and by Il'ichev et al. [2]. The setup of the experiment [2] consists of a qubit loop inductively coupled to a high-quality LC-circuit (tank) having a resonant frequency, that is much lower than the frequency of quantum beating in the qubit. Measurements of the average and spectral characteristics of the tank voltage give information about low-frequency parts of a qubit's magnetic susceptibility and a spectrum of fluctuations. The resonant driving force induces Rabi oscillations, which modify the damping rates and noise characteristics of the quantum bit.

With non-Markovian stochastic equations [3, 4] we have calculated effects of the Rabi oscillations on the dissipative evolution of the 3JJ qubits and have shown that experimental results [1] are indicative of significant decoherence suppression by the strong resonant field. Besides that, the nonequilibrium spectrum of current fluctuations in the qubit loop has been obtained analytically. The low-frequency component of this spectrum has a peak at the Rabi frequency with a linewidth, which determines a decay of the Rabi oscillations. Changing the amplitude of the driving force allows to control the decoherence rate and the noise level in the qubit. This control has been demonstrated in the experiment [2]. A comparison with theoretical predictions [4] lets us to extract a long enough decoherence time, near 2.5 microsec, for a decay of Rabi oscilations in the 3JJ quantum bit coupled to a linear detector (the tank). We have analyzed a back-action of the detector on the quantum system and have found a signal-to-noise ratio. It has been shown that the noise spectroscopy performed in Ref.[2] can be considered as an example of quantum weak continuous measurements.

[1] I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science, v.299, 1869 (2003).

[2] E. Il'ichev, N. Oukhanski, A. Izmalkov, Th. Wagner, M. Grajcar, H.-G. Meyer, A.Yu. Smirnov, A. Maassen van den Brink, M.H.S. Amin, and A.M. Zagoskin, Phys.Rev.Lett., v.91, 097906 (2003).

[3] A.Yu. Smirnov, Phys.Rev.B, v.67, 155104 (2003).

[4] A.Yu. Smirnov, Phys.Rev.B, v.68, 134514 (2003).

Date received: February 19, 2004