Qubit decoherence and symmetry restoration through real-time instantons

A parametrically driven quantum oscillator, stabilized by a nonlinear dissipation, exhibits a spontaneous breaking of the parity symmetry. It results in the quantum bistability, corresponding to a Bloch sphere of dark states. This makes such a driven-dissipative system an attractive candidate for a qubit. The parity symmetry breaking is exact both on the classical level and within the quantum mechanical perturbation theory. Here, we show that nonperturbative quantum effects lead to the symmetry restoration and result in an exponentially small but finite qubit decoherence rate. Technically, the symmetry restoration is due to real-time instanton trajectories of the Keldysh path integral, which represents the Lindbladian evolution of the driven-dissipative oscillator.