Violation of Cauchy-Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures

Abstract

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic horizon is produced by a space-dependent contact interaction. In some cases, CS violation can be observed by direct atom counting in a time-of-flight experiment. We show that near the conventional zero-frequency peak, the decisive CS violation cannot occur.

Quantum Transport in the Black‐Hole Configuration of an Atom Condensate Outcoupled Through an Optical Lattice

“…In particular, near the top of the conduction band strong resonant peaks appear (see Fig. 8), which are expected to provide a good signal for the characterization of the spontaneous emission of Hawking radiation [16,26,53,57]. Regarding a possible experimental implementation, it is worth noting that the quasi-stationary configuration here considered is much closer to actual stationarity than the experimental setup of Ref.…”

“…3], the BdG spectrum presents a plateau in the transmission band instead of having a peaked behavior as in the ideal case. The Hawking spectrum displays strong resonant peaks near the top of the conduction band when this falls below ω max ; this regime is of special interest as it is well known that near resonant peaks one can expect a strong spontaneous Hawking signal standing above the stimulated Hawking signal [16,26,53,57]. This behavior contrasts with the case where the top of the conduction band is above ω max , in which the plateau of the transmission band only goes to zero at the end of Hawking spectrum limit without showing any remarkable structure.…”

“…However, due to the non-perfect stationarity of the GP wave function, the corresponding relative quasi-particle current for the quasi-stationary BdG modes is also inhomogeneous, which implies that the corresponding S-matrix is not pseudo-unitary. Nevertheless, since the region near ω = 0 is not interesting for the observation of the spontaneous Hawking effect [16,18,53], for practical purposes we can restrict the computations to the range ω > ω Λ , ω Λ being a numerically enforced cut-off of order ω Λ ∼ 10 −2 µ 0 ≫ σ(t) so condition (19) is fulfilled and the stationary BdG approximation (20) is expected to be valid.…”

“…The role of the particle-antiparticle pair emitted at the horizon is here played by the spontaneous entangled emission of phonons into the subsonic and supersonic regions [9][10][11][12][13][14][15][16][17][18][19]. Indeed, sonic event horizons have already been experimentally produced by accelerating a condensate [20].…”

Non-Linear Stationary Solutions in Realistic Models for Analog Black-Hole Lasers

“…This configuration was studied in [39] in order to look for resonant BH configurations, which enhance the spontaneous Hawking signal [17]. Here, we focus only on looking for stationary BHL solutions, as in the previous section.…”