A matter-wave cavity experiment in the ultrastrong driving regime: anomalous fixed points and curved spacetime

We confine a one-dimensional quantum degenerate lithium-7 gas within a cavity potential whose length is periodically modulated. This analog simulation of a driven cavity switches the roles of matter and light in a traditional optical cavity; we excite the quantum gas into an optical lattice Bloch band with nearly linear dispersion to simulate photons and reflect the matter waves with a blue-detuned light sheet potential. The low group velocity of this band dispersion enables the observation of phenomena which in a true photonic system would require otherwise experimentally inaccessible relativistic speeds. For instance, by periodically modulating the position of one of the optical barriers, we realize a discrete Floquet map whose (un)stable stroboscopic fixed points have analogous character to (black)white hole event horizons. Residual lattice band nonlinearities simulate massive photons and give rise to additional, anomalous fixed points. This new platform would expand the capabilities of curved spacetime simulation as well as provide a proof-of-concept for a novel pulsed laser source based on the Floquet map's mode squeezing.