Comment on “Questioning the Recent Observation of Quantum Hawking Radiation” [Ann. Phys. (Berlin) 2018, 530, 1700114]

Abstract

The observation of quantum Hawking radiation and its entanglement in an analogue black hole was recently reported. A subsequent article presented critical comments of the study. The article suffers from technical difficulties which invalidate its claims. These include the misunderstanding of a simple Fourier transform, the unnecessary modification of experimental data, and the assertion that the experiment measured a strictly-zero population.

Analytical description of quantum emission in optical analogues to gravity

“…This corresponds to a frequency ω with 8 propagating modes on either side of the RIF interface. We use (38) to obtain all σ in 's (or (39) for σ out 's) from a single matrix…”

“…Combining (38) and (B1) we relate the σ in 's on either side of the RIF. Each column of σ in contains the coefficients of individual local modes to one of the global modes on that side of the RIF.…”

“…We use the construction of GMs described above eq. (B1), with the modes ordered as u, uo, mo, lo, l, nl, nol, nu, and hence (38) writes:…”

“…This leaves us with 64 unknowns in either (38) or (39). The W 's are known, so we can obtain all σ's (we calculate an example in Appendix B).…”

“…As in the astrophysical case [4], the paired spontaneous emission in analogues results from mixing of field modes of positive and negative Klein-Gordon norm at the horizon [2]. Thus, pairs from horizons have been extensively studied for fluid systems, in which their entanglement in various dispersive regimes has been investigated [29][30][31][32][33][34], and are considered an unmistakable signature of the Hawking effect [35][36][37][38][39][40][41].…”