Quantum jumps in amplitude bistability: Tracking a coherent and invertible state localization

TL;DR

This paper explores the detailed quantum dynamics of amplitude bistability in the Jaynes-Cummings model, revealing a two-stage coherent localization process during quantum jumps and how spontaneous emission affects this mechanism.

Contribution

It introduces a novel two-stage coherent localization process for quantum jumps in amplitude bistability, extending understanding of quantum trajectories and metastable states.

Findings

Quantum jumps involve a coherent localization stage.

Unstable states mediate the transition between metastable states.

Spontaneous emission prolongs and degrades the coherence of jumps.

Abstract

We investigate the nature of quantum jumps occurring between macroscopic metastable states of light in the open driven Jaynes-Cummings model. We find that, in the limit of zero spontaneous emission considered in [H. J. Carmichael, Phys. Rev. X 5, 031028 (2015)], the jumps from a high-photon state to the vacuum state entail two stages. The first part is coherent and modelled by the localization of a state superposition, in the example of a null-measurement record predicted by quantum trajectory theory. The underlying evolution is mediated by an unstable state (which often splits to a complex of states), identified by the conditioned density matrix and the corresponding quasiprobability distribution of the cavity field. The unstable state subsequently decays to the vacuum to complete the jump. Coherence in the localization allows for inverting the null-measurement photon average about its initial value, to account for the full switch which typically lasts a small fraction of the cavity lifetime; an asymptotic law for the jump time is established in high-amplitude bistability. This mechanism is contrasted to the jumps leading from the vacuum to the high-photon state in the bistable signal. Spontaneous emission degrades coherence in the localization, and prolongs the jumps.