Journal
PHYSICAL REVIEW B
Volume 77, Issue 7, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.77.075325
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We consider an electrostatic qubit, interacting with fluctuating charge of a single-electron transistor (SET) in the framework of an exactly solvable model. The SET plays role of an environment affecting the qubits' parameters in a controllable way. We derive the rate equations describing the dynamics of the entire system for an arbitrary qubit-SET coupling. Solving these equations we obtain decoherence and relaxation rates of the qubit, as well as the spectral density of qubit parameters' fluctuations. We found that in a weak-coupling regime decoherence and relaxation rates are directly related to the spectral density taken at either zero or Rabi frequency, depending on which qubit parameter is fluctuating. In the latter case our result coincides with that of the spin-boson model in the weak-coupling limit, despite different origin of the fluctuations. We show that this relation holds also in the presence of weak backaction of the qubit on the environment. In case of strong backaction such a simple relationship no longer holds, even if qubit-SET coupling is small. It does not hold also in the strong-coupling regime, even in the absence of the backaction. In addition, we found that our model predicts localization of the qubit in the strong-coupling regime, resembling that in the spin-boson model.
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