We study qubit decoherence under generalized dispersive readout, i.e., we
investigate a qubit coupled to a resonantly driven dissipative harmonic
oscillator. We provide a complete pictureby allowing for arbitrarily large
qubit-oscillator detuning and by considering also a coupling to the square of
the oscillator coordinate, which is relevant for flux qubits. Analytical
results for the decoherence time are obtained by a transformation of the
qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master
equation treatment beyond the Markov limit. We predict a crossover from
Markovian decay to a decay with Gaussian shape. Our results are corroborated by
the numerical solution of the full qubit-oscillator master equation in the
original frame.
We propose a startling hybrid quantum architecture for simulating a
localization-delocalization transition. The concept is based on an array of
superconducting flux qubits which arecoupled to a diamond crystal containing
nitrogen-vacancy (NV) centers. The underlying description is a
Jaynes-Cummings-lattice in the strong-coupling regime. However, in contrast to
well-studied coupled cavity arrays the interaction between lattice sites is
mediated here by the qubit rather than by the oscillator degrees of freedom.
Nevertheless, we point out that a transition between a localized and a
delocalized phase occurs in this system as well. We demonstrate the possibility
of monitoring this transition in a non-equilibrium scenario, including
decoherence effects. The proposed scheme allows the monitoring of
localization-delocalization transitions in Jaynes-Cummings-lattices by use of
currently available experimental technology. Contrary to cavity-coupled
lattices, our proposed recourse to stylized qubit networks facilitates (i) to
investigate localization-delocalization transitions in arbitrary dimensions and
(ii) to tune the inter-site coupling in-situ.