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

The outcoupling of a Bose‐Einstein condensate through an optical lattice provides an interesting scenario to study quantum transport phenomena or the analog Hawking effect as the system can reach a quasi‐stationary black‐hole configuration. We devote this work to characterize the quantum transport properties of quasi‐particles on top of this black‐hole configuration by computing the corresponding scattering matrix. We find that most of the features can be understood in terms of the usual Schrödinger scattering. In particular, a transmission band appears in the spectrum, with the normal‐normal transmission dominating over the anomalous‐normal one. We show that this picture still holds in a realistic experimental situation where the actual Gaussian envelope of the optical lattice is considered. A peaked resonant structure is displayed near the upper end of the transmission band, which suggests that the proposed setup is a good candidate to provide a clear signal of spontaneous Hawking radiation.