Population Dynamics of Schrödinger Cats

Many modern quantum devices, perhaps most notably the qubits in modern quantum computing platforms, cannot be perfectly isolated from their environment and thus must be understood as open quantum systems. Environmental effects in such systems such as dissipation and noise can be described by the Markovian Lindblad quantum master equation. Lindbladian dynamics may admit dark states, which are pure stationary states for which no outgoing transitions are allowed, thus rendering them protected from decoherence. We discuss the relationship between classical population dynamics and quantum Lindbladian dynamics with dark states and show that there is an exact mapping between the two when the quantum dynamics respects certain weak local symmetries. Relaxing the symmetry condition provides us with a definition of quantum population dynamics, in which animals can enter into superpositions of life and death. Analogous to their classical counterparts, quantum population models can undergo continuous phase transitions between an extinct dark phase and active phases with stable quantum populations. Using a nonequilibrium field theory approach, we discuss a prototypical quantum population dynamics of a single species, which we find demonstrates a dark state phase transition with critical scaling distinct from that observed in both classical population dynamics and usual quantum phase transitions.