Conditional Entanglement Amplification via Non-Hermitian Superradiant Dynamics.

Because of the inherently probabilistic nature of quantum mechanics, each experimental realization of a dynamical quantum system can produce distinct measurement outcomes, particularly when coupled to a dissipative environment. Although quantum trajectories that lead to exotic, highly entangled states are possible in principle, their observation is typically hindered by extremely low probabilities. In this Letter, we present a method to significantly enhance the probability of generating highly entangled states in an ensemble of atoms undergoing collective superradiant decay on timescales much shorter than the individual atomic spontaneous emission rate. By analyzing an effective non-Hermitian Hamiltonian governing the dynamics between photon emission events, we identify the conditions necessary for these rare no-click trajectories to occur with higher likelihood. Crucially, our method relies on initializing the system in a nonclassical state, whose entanglement is amplified via the non-Hermitian superradiant dynamics. This approach provides a new route to creating highly entangled macroscopic states such as atomic Schrödinger cat states, paving the way for advancements in quantum metrology and other quantum technologies.