We have a new paper published in Physical Review A: Analog spacetimes from nonrelativistic Goldstone modes in spinor condensates.

Analog Spacetimes from Nonrelativistic Goldstone Modes in Spinor Condensates
Wilson, Justin H.,
Curtis, Jonathan B.,
and Galitski, Victor M.
Phys. Rev. A
105,
043316
(2022).
It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an EinsteinHilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor BoseEinstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a NewtonCartan geometry. The kind of spacetime (EinsteinHilbert or NewtonCartan) is intimately linked to the meanfield phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudospin1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the NewtonCartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin1 condensates such as Rb87, Li7, K41 (NewtonCartan), and Na23 (EinsteinHilbert).