  We investigate the spontaneous emission spectrum of a qubit in a lossy
resonant cavity. We use neither the rotating-wave approximation nor the Markov
approximation. The qubit-cavity coupling strength is varied from weak, to
strong, even to lower bound of the ultra-strong. For the weak-coupling case,
the spontaneous emission spectrum of the qubit is a single peak, with its
location depending on the spectral density of the qubit environment. Increasing
the qubit-cavity coupling increases the asymmetry (the positions about the
qubit energy spacing and heights of the two peaks) of the two spontaneous
emission peaks (which are related to the vacuum Rabi splitting) more.
Explicitly, for a qubit in a low-frequency intrinsic bath, the height asymmetry
of the splitting peaks becomes larger, when the qubit-cavity coupling strength
is increased. However, for a qubit in an Ohmic bath, the height asymmetry of
the spectral peaks is inverted from the same case of the low-frequency bath,
when the qubit is strongly coupled to the cavity. Increasing the qubit-cavity
coupling to the lower bound of the ultra-strong regime, the height asymmetry of
the left and right peak heights are inverted, which is consistent with the same
case of low-frequency bath, only relatively weak. Therefore, our results
explicitly show how the height asymmetry in the spontaneous emission spectrum
peaks depends not only on the qubit-cavity coupling, but also on the type of
intrinsic noise experienced by the qubit.
