Abstract
We investigate the spontaneous emission (SE) spectrum of a qubit in a lossy resonant cavity. We use neither the rotating-wave approximation nor the Markov approximation. For the weak-coupling case, the SE spectrum of the qubit is a single peak, with its location depending on the spectral density of the qubit environment. Then, the asymmetry (of the location and heights of the two peaks) of the two SE peaks (which are related to the vacuum Rabi splitting) changes as the qubit–cavity coupling increases. Explicitly, for a qubit in a low-frequency intrinsic bath, the height asymmetry of the splitting peaks is enhanced as the qubit–cavity coupling strength increases. However, for a qubit in an Ohmic bath, the height asymmetry of the spectral peaks is inverted compared to the low-frequency bath case. With further increasing the qubit–cavity coupling to the ultra-strong regime, the height asymmetry of the left and right peaks is slightly inverted, which is consistent with the corresponding case of a low-frequency bath. This inversion of the asymmetry arises from the competition between the Ohmic bath and the cavity bath. Therefore, after considering the anti-rotating terms, our results explicitly show how the height asymmetry in the SE spectrum peaks depends on the qubit–cavity coupling and the type of intrinsic noise experienced by the qubit.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Strong and ultra-strong qubit–cavity interactions have been achieved in both cavity quantum electrodynamics (QED) and circuit QED systems. As the qubit–cavity coupling increases to the ultra-strong coupling case, the previously negligible anti-rotating interaction terms in the weak coupling limit become more relevant and lead to a modification of the nature of the quantum state of the qubit system.
Main results. In this paper, we study the spontaneous emission (SE) spectrum of a qubit in a cavity. Our calculations include two kinds of anti-rotating term: one from the intrinsic qubit bath and another from the cavity bath. We compare the case of a qubit in an Ohmic bath to the case of a qubit in a low-frequency bath. We find that for strong qubit–cavity coupling, the combination of the anti-rotating terms and the properties of the baths can cause the various asymmetries of the splitting peaks in the SE spectrum.
Wider implications. The different asymmetric behaviors of the SE spectrum of the qubit in the low-frequency and Ohmic baths may be used to distinguish the intrinsic noise of the qubit. Our results clarify fundamental issues in the growing field of strong qubit–cavity interactions; for example, the cavity works as a quantum bus that couples widely separated qubits in a quantum processor, as quantum memory to store quantum information and as a generator and detector of single microwave photons for quantum communication.
Figure. The SE spectra of the qubit in resonance with the central frequency of the cavity for weak, strong and ultra-strong qubit–cavity interactions. The quality factor of the cavity is Q = 104. (a) Coupling strength to the low-frequency intrinsic bath of the qubit αlow = 10−4; (b) coupling strength to the Ohmic intrinsic bath of the qubit αOhm = 10−4. To see the height asymmetry of the peaks clearly, the horizontal grid lines are plotted as a reference. Note that panel (a) demonstrates an obvious height asymmetry in the case of strong and ultra-strong qubit–cavity coupling and the asymmetry increases as the qubit–cavity coupling grows. Panel (b) shows the very small inverted height asymmetry of two peaks from panel (a) in the strong qubit–cavity coupling case, but as the qubit–cavity coupling increases to the ultra-strong regime, the height asymmetry of the right and left spectral peaks becomes inverted.