Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics

TL;DR

This paper demonstrates how quantum systems with $SU(1,1)$ symmetry naturally produce emergent Anti-de Sitter spacetimes, unifying various phenomena and enabling new quantum control and engineering strategies.

Contribution

It reveals that $SU(1,1)$ symmetric quantum dynamics generate emergent AdS$_{2+1}$ spacetimes, providing a geometric framework for understanding diverse quantum phenomena.

Findings

Quantum dynamics with $SU(1,1)$ symmetry give rise to AdS$_{2+1}$ spacetimes.

Geodesics in AdS$_{2+1}$ correspond to quench dynamics.

Emergent spacetimes can be engineered and used to optimize quantum controls.

Abstract

We show that quantum dynamics of any systems with $SU(1,1)$ symmetry give rise to emergent Anti-de Sitter spacetimes in 2+1 dimensions (AdS$_{2+1}$). Using the continuous circuit depth, a quantum evolution is mapped to a trajectory in AdS$_{2+1}$. Whereas the time measured in laboratories becomes either the proper time or the proper distance, quench dynamics follow geodesics of AdS$_{2+1}$. Such a geometric approach provides a unified interpretation of a wide range of prototypical phenomena that appear disconnected. For instance, the light cone of AdS$_{2+1}$ underlies expansions of unitary fermions released from harmonic traps, the onsite of parametric amplifications, and the exceptional points that represent the $PT$ symmetry breaking in non-Hermitian systems. Our work provides a transparent means to optimize quantum controls by exploiting shortest paths in the emergent spacetimes. It also allows experimentalists to engineer emergent spacetimes and induce tunnelings between different AdS$_{2+1}$.