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For some cavity-quantum-electrodynamics systems, such as a single electronspin coupled to a passive cavity, it is challenging to reach thestrong-coupling regime. In such a weak-coupling regime, the conventionaldispersive readout technique cannot be used to resolve the quantum states ofthe spin. Here we propose an improved dispersive readout method to measure thequantum states of a weakly coupled qubit by harnessing either one or twoauxiliary cavities linearly coupled to the passive cavity containing the qubit.With appropriate parameters in both cases, the system excluding the qubit canexhibit a parity-time-symmetric phase transition at the exceptional point (EP).Because the EP can amplify the perturbation induced by the qubit and theparity-time symmetry can narrow the linewidths of the peaks in the transmissionspectrum of the passive cavity, we can measure the quantum states of the weaklycoupled qubit via this transmission spectrum. Owing to the weak couplingbetween the qubit and the passive cavity, the backaction due to the measurementof the qubit can also be reduced in comparison with the conventional dispersivereadout technique in the strong-coupling regime.

Dispersive readout of a weakly coupled qubit via the parity-time-symmetric phase transition