We study trajectories of collective spin states of an ensemble of spinors. The spinors considered here are either trapped ions in free space or atoms confined in a cavity, both systems of which are engineered through their interactions with light fields to obey an effective Dicke model. In an appropriate limit of the Dicke model, one obtains one-axis twisting dynamics of the collective spin and evolution after a finite time to a spin cat state or, in the long-time limit, the Dicke state ${|S,0\rangle }_x$, conditioned upon there being no photon emissions from the system (i.e., no quantum jumps). If there is a jump, however, the system evolves probabilistically into one of a finite number of entangled-state cycles, where the system then undergoes a persistent sequence of jumps between two Dicke-state superpositions in a rotated basis. The different cycles can be distinguished by the frequency at which jumps occur.

• Received 16 August 2021
• Accepted 15 November 2021

DOI:https://doi.org/10.1103/PhysRevA.104.053721