Spontaneous Beliaev-Landau scattering out of equilibrium
The convenient assumption of detailed balance, valid for a quantum many-body system at thermal equilibrium, ensures that any microscopic process is balanced by its reverse process, thus making the exact underlying dynamics largely irrelevant for the equilibrium ensemble. In a cold-atom system, for example, the Bogoliubov method provides an approximate solution to a system with sufficiently small interactions and large density. The guarantee of a thermal equilibrium with detailed balance motivates one to put forward a Bose-Einstein distribution for the quasiparticles, regardless of the exact underlying kinetics.
For an open quantum system no such claims can be made. Consequently, physical observables in the steady state may be much more sensitive to the specific dynamics of underlying microscopic processes. In this context, we will illustrate how the dynamics of photons inside an array of coupled nonlinear cavities can be fundamentally different from equilibrium. Due to the continuous pumping and dissipation of photons in the chain, this system is inherently open and connected with its environment. Remarkably, the spontaneous occurrence of third-order scattering pro- cesses (traditionally called Beliaev-Landau scatterings) in the steady state leaves a distinguishable imprint upon the momentum distribution of the photons in the array. We therefore conclude that these scatterings, which are neglected in the Bogoliubov approximation, have to be explicitly taken into account when evaluating steady-state properties of photons inside the cavity array.
We will outline how the truncated Wigner approach, when naively applied, dramatically overestimates the effects of Beliaev-Landau scatterings inside the chain of cavities. Instead, we will present a consistent method, based on the construction of a hierarchy of correlations, to provide a viable way for evaluating the expected corrections beyond Bogoliubov.
Reference article: Phys. Rev. A 96, 053854 (2017)
Host: Mohammad Hafezi