Generalized Glauber theorem for dark-matter axion and graviton detection

Abstract

We revisit the generalized Glauber theorem motivated by recent applications to dark-matter axion searches and graviton production. For Hamiltonian containing up to quadratic terms in annihilation and creation operators coupled to classical sources, the time-evolution operator can be factorized into displacement, squeezing, and rotation operators. We derive the differential equations governing time evolution of their parameters, reducing the quantum dynamics to c-number equations that can be solved analytically or numerically. To compare another form of the time-evolution operator, Dyson series, we demonstrate the essential role of time ordering. This formalism based on generalized Glauber theorem provides a unified description of particle production from classical backgrounds. Axion-photon conversion in microwave haloscopes is recovered as the linear-interaction limit, while squeezed graviton production from black-hole mergers follows naturally from quadratic interactions. Extending the theorem to thermal initial states yields a realistic quantum description of microwave cavities used in axion experiments. We show that higher-order photon statistics exhibit nontrivial behavior, providing a rigorous foundation for Monte Carlo simulations of quantum-enhanced axion searches beyond heuristic noise estimates.