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Within the capacity of current experiments, we design a composite atom-cavitysystem with a common bath, in which the decay channels of the atom and thecavity mode interfere with each other. When the direct atom-cavity coupling isabsent, the system can be trapped in a quasi-dark state (the coherentsuperposition of excited states for the atom and the cavity mode) without decayeven in the presence of the bath. When the atom directly couples with thecavity, the largest decay rate of the composite system will surpass the sum ofthe two subsystems while the smallest decay rate may achieve 0. This ismanifested in the transmission spectrum, where the vacuum Rabi splitting showsan obvious asymmetric character.

The quasi-dark state and quantum interference in Jaynes-Cummings model with a common bath