Dynamical effects induced by synthetic SU(1,1) gauge fields

Abstract

Compact gauge fields are powerful tools for controlling quantum dynamics and topological phases of matter. Non-compact gauge fields are particularly relevant for open systems, where particles or energy are exchanged with the environment. Here, we investigate the wavepacket and entanglement dynamics induced by an $\mathrm{SU}(1,1)$ gauge field. The wavepacket undergoes non-Abelian non-compact Bloch oscillations, in which the spectrum of an auxiliary one-dimensional quantum problem determines the transition between stable oscillations and unstable amplification. In the unstable adiabatic regime, the wavepacket probes an $\mathrm{SU}(1,1)$ topological defect, and its amplification is determined solely by a hyperbolic solid angle in Minkowski space. Threading an $\mathrm{SU}(1,1)$ gauge field through a bosonic tight-binding model yields the bosonic Kitaev model, whose volume or super-volume entanglement scaling is governed by the stability of the gauge field. We further propose an experimental realization of an $\mathrm{SU}(1,1)$ gauge field in a spinor condensate. Our results can be generalized to other non-compact groups and higher dimensions, providing a geometric framework for entanglement control, selective amplification, and engineering energy transfer.