A Single Spin Switches the Steady-State Phase of an Open Quantum System

Abstract

Changing a many-body system by one constituent is normally expected to produce only a vanishing correction to an intensive observable. Here we show that, above a critical dissipation imbalance, adding or removing one spin at fixed intensive controls switches the steady state of a dissipative collective spin between a phase-averaged ring and a south-polar fixed point. Unlike previous one-spin sensing through dark-state interference, parity here determines whether the Dicke ladder samples an interior zero of the nonlinear jump amplitude. The integer-spin ladder samples this zero, making Dicke states with m<0 transient, whereas the half-integer ladder misses it and remains a single recurrent class. Exact finite-size steady states show that exponential competition between stationary weights amplifies this microscopic connectivity difference, yielding a first-order dissipative phase transition confined to the odd-N sequence. Multisector one-spin loading and state-unresolved removal confirm the switch, while the exponentially increasing switching time reflects the metastable isolation of the competing macroscopic basins. Our results establish representation-lattice sampling as a route to phase control, suggesting parity-based detection of single-spin addition or removal.