Radiation statistics of a degenerate parametric oscillator at threshold

Abstract

As a function of the driving strength, a degenerate parametric oscillator exhibits an instability at which spontaneous oscillations occur. Close to threshold, both the nonlinearity as well as fluctuations are vital to the accurate description of the dynamics. We study the statistics of the adiation that is emitted by the degenerate parametric oscillator at threshold. For a weak nonlinearity, we can employ a quasiclassical description. We identify a universal Liouvillian that captures the relevant long-time dynamics for large photon-numbers. We find that the cumulants obey a universal power-law scaling as a function of the nonlinearity. The Fano factor shows a maximum close, but not coinciding, with the threshold. Moreover, we predict a certain ratio of the first three cumulants to be independent of the microscopic details of the system and connect the results to experimental platforms.

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

“…This means that states with large λ (large n i or λ i ) decay faster than others. This insight makes it possible to adiabatically eliminate the fast modes, see [10] for an example.…”

“…The identification of eigenmodes with a simple exponential time-evolution allows one to separate fast from slow degrees of freedom efficiently. This makes it possible to reduce problems with multiple time-scales to the slow time-dynamics of the relevant mode at long-times, see [10].…”