Dephasing of a flux-qubit coupled to a harmonic oscillator

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Decoherence in superconducting qubits is known to arise because of a variety of environmental degrees of freedom. In this article, we focus on the influence of thermal fluctuations in a weakly damped circuit resonance coupled to the qubit. Because of the coupling, the qubit frequency is shifted by an amount n δν₀ if the resonator contains n energy quanta. Thermal fluctuations induce temporal variations n(t) and thus dephasing. We give an approximate formula for the qubit dephasing time as a function of δν₀. We discuss the specific case of a flux-qubit coupled to the plasma mode of its DC-SQUID detector. We first derive a plasma mode-qubit interaction hamiltonian which, in addition to the usual Jaynes-Cummings term, has a coupling term quadratic in the oscillator variables coming from the flux-dependence of the SQUID Josephson inductance. Our model predicts that δν₀ cancels in certain non-trivial bias conditions for which dephasing due to thermal fluctuations should be suppressed.