Analog spacetimes from nonrelativistic Goldstone modes in spinor condensates

Abstract

It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert 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 Bose-Einstein 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 Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 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 Newton-Cartan 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 spin-1 condensates such as ${}^{87}$Rb, ${}^7$Li, ${}^{41}$K (Newton-Cartan), and ${}^{23}$Na (Einstein-Hilbert).

24 pages, 2 tables, 6 figures

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Cited by in corpus (5)

• Local Ward identities for collective excitations in fermionic systems with spontaneously broken symmetries
• Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
• Quantum black holes as classical space factories
• Mechanical cosmology: simulating scalar fluctuations in expanding Universes using synthetic mechanical lattices
• Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: from scalar to Proca fields