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We propose a method to create superpositions of two macroscopic quantumstates of a single-mode microwave cavity field interacting with asuperconducting charge qubit. The decoherence of such superpositions can bedetermined by measuring either the Wigner function of the cavity field or thecharge qubit states. Then the quality factor Q of the cavity can be inferredfrom the decoherence of the superposed states. The proposed method isexperimentally realizable within current technology even when the $Q$ value isrelatively low, and the interaction between the qubit and the cavity field isweak.Comment: 8 page

Measuring the quality factor of a microwave cavity using superconducting qubit devices