Non-Markovian qubit spectroscopy in cavity QED

Markovian models of qubit dynamics break down for charge qubits coupled to 1/f noise and for spin qubits coupled to slow nuclear-spin baths. For spin/charge qubits also coupled to a cavity, it can be difficult to directly extract time-domain coherence dynamics because the AC control fields used to prepare and measure these qubits have the potential to excite the cavity mode. In this talk, we present a way of extracting the coherence dynamics of a qubit coupled to a cavity purely from frequency-dependent measurements of the cavity response in cavity quantum electrodynamics (QED). In contrast to a more standard equation-of-motion approach, we make neither a Markov approximation nor a weak-coupling approximation for the qubit-bath dynamics. Using this approach, we calculate the spectroscopic response of a spin qubit coupled to nuclear spins. This response shows pronounced non-Lorentzian features, indicative of non-Markovian dynamics, arising from a many-spin collective mode. We also consider the case of a qubit coupled to a single bosonic mode corresponding to, e.g., a mechanical degree of freedom, phonon, or cavity mode. In this instance, strong coupling gives rise to higher harmonics in the qubit coherence spectrum.