Non-Markovian qubit spectroscopy in cavity QED

The strong-coupling regime of cavity quantum electrodynamics (QED) can be identified spectroscopically from a peak splitting (~qubit-cavity coupling) that is large compared to the qubit decoherence and cavity decay rates. This interpretation normally relies on a Markovian model of qubit dynamics together with input-output theory. A Markovian description may however break down for charge qubits (coupling to ~1/f noise) or spin qubits (coupling to a slow nuclear-spin bath). Motivated by very recent work showing strong coupling of spin/charge qubits coupled to superconducting microwave resonators, we use a generalized input-output theory to account for a generic non-Markovian environment. This allows us to calculate a spectroscopic lineshape that fully accounts for non-Markovian features and which may be relevant to recent experiments.