Spontaneous parametric down conversion with a depleted pump as an analogue for black hole evaporation/particle production

In this work we argue that black hole evaporation/particle production has a very close analogy to the laboratory process of spontaneous parametric down conversion, when the pump is allowed to deplete. We present an analytical formulation of the recent one-shot decoupling model that was numerically analyzed in Bradler and Adami Phys. Rev. Lett. 116, 101301 (2016) [arXiv:1505.0284]. We compute the resulting "Page Information" curves, which describe the rate at which information escapes form the black hole as it evaporates, for the reduced density matrices for the evaporating black hole internal degrees of freedom, and emitted Hawking radiation pairs entangled across the horizon. The present work reviews and attempts to elucidate the trilinear Hamiltonian models for black hole evaporation/particle production recently investigated by the authors in Class. Quant. Grav 32, 075010 (2015) [arXiv:1408.4491] and Class. Quant. Grav 33, 015005 (2016) [arXiv:1507.00429].