  Noise affects the coherence of qubits and thereby places a bound on the
performance of quantum computers. We theoretically study a generic two-level
system with fluctuating control parameters in a photonic cavity and find that
basic features of the noise spectral density are imprinted in the transient
transmission through the cavity. We obtain analytical expressions for generic
noise and proceed to study the cases of quasistatic, white and $1/f^{\alpha}$
noise in more detail. Additionally, we propose a way of extracting the spectral
density for arbitrary noise in a frequency band only bounded by the range of
the qubit-cavity detuning and with an exponentially decaying error due to
finite measurement times. Our results suggest that measurements of the
time-dependent transmission probability represent a novel way of extracting
noise characteristics.
