Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics

Chenwei Lv; Qi Zhou

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arXiv · 2205.07429

Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics

Chenwei Lv·Qi Zhou

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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$_{2+1}$.

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Chenwei Lv, Qi Zhou. 2022-05-16. Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics. https://arxiv.org/abs/2205.07429

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