Jaynes-Cummings model under continuous measurement: Weak chaos in a quantum system induced by unitarity collapse

Abstract

We show that a system managed by quantum theory bears chaotic behavior induced by unitarity collapse in its time development. Nonunitary time evolution of the Jaynes-Cummings (JC) model, the interacting system consisting of two subsystems (a two-level atom and a quantized photon field), under a continuous quantum-nondemolition (QND) measurement of the photon number is investigated. In the regime of weak coupling between the subsystems, the measured system shows the Rabi oscillation and the decrease of the photon number variance, which mimic the unmeasured JC system and the photon field under the continuous QND photodetection, respectively. In the strong-coupling regime, the quantum system shows a nonintegrable nature, that is, it yields weak chaos characterized by both the broad continuous power spectrum and the decaying correlation function due to the lack of quantum recurrence.