Black Hole Horizons, Quantum Dam-Breaks, and Effective Optical Lenses in Bose-Einstein Condensates
Liam Farrell, McMaster University
Hawking radiation (HR) is the phenomenon where gravitational black holes emit thermal radiation due to quantum pair-creation near the event horizon. Low energy analogues of HR can occur in flowing ultracold Bose-Einstein condensates (BECs): an event horizon can form if there is a region where the flow speed of the gas exceeds the speed of sound. Such acoustic horizons remarkably produce HR just like their gravitational counterparts, but in the form of sound waves (phonons), which play the role of electromagnetic radiation (photons). The sudden removal of a potential energy wall in a BEC gives rise to a superfluid version of a hydrodynamic dam-breaking problem, leading to rich quantum wave dynamics and the possibility of sonic horizon formation. Denoting ∆ρ as the initial difference in density between two reservoirs on either side of a dam in a BEC, we analytically and numerically model the breaking dynamics in different ∆ρ regimes. We comment on horizon formation and the possibility of detecting sonic HR from such horizons. By making connections to the mathematics of tidal bores, an underlying wave structure is also revealed that mimics the physics of double rainbows. In a separate but related study, we apply similar principles to create an effective Maxwell fish-eye lens (MFEL) in an atomic BEC. A MFEL possess a spatially varying refractive index n(r) with the property that rays emitted from any point within the lens are perfectly focused. Experimentally creating such lenses is challenging in typical optical media, and BECs offer an alternate platform where wave dynamics can be observed in real time. We experimentally, numerically, and analytically demonstrate the focusing behavior of our analogue MFEL, providing both a geometric and physical framework for engineering effective refractive indices using ultracold atoms.
