Decoherence by black holes via holography

TL;DR

This paper explores how black holes influence quantum decoherence using holographic duality, revealing temperature-dependent decoherence rates and the impact of causality on entanglement in quantum systems with Lifshitz geometries.

Contribution

It demonstrates the effects of Lifshitz black holes on decoherence rates and the role of causality in entanglement, extending holographic decoherence analysis to Lifshitz spacetimes.

Findings

Finite temperature causes constant decoherence rate.

Zero temperature leads to vanishing decoherence at large times.

Decoherence exhibits power-law decay as $z \to \infty$.

Abstract

In this note, we reexamine decoherence effects in quantum field theories with gravity duals. The thought experiment proposed in \cite{DSW_22, DSW_23}, which reveals novel decoherence patterns associated with black holes, also manifests itself from the perspective of the boundary theory. In particular, we consider a moving mirror coupled to quantum critical theories characterized by a dynamical exponent $z$ that are dual to asymptotically Lifshitz geometries. The interference experiment occurs on the boundary, where a superposition of two spatially separated quantum states of a mirror is maintained for a finite time $\tau_0$ before recombination. We find that the interaction with a quantum field at finite temperature, arising from the presence of a Lifshitz black hole, leads to a constant decoherence rate. In contrast, for the zero-temperature case corresponding to pure Lifshitz spacetime, the decoherence rate vanishes in the large-time limit $\tau_0 \to \infty$. Remarkably, in the zero-temperature regime, the decoherence exhibits a power-law decay at large $\tau_0$ as $z \rightarrow \infty$, a behavior reminiscent of the decoherence patterns seen in extremal black hole geometries. In addition, we investigate the decoherence of one particle in an EPR pair constructed holographically. Our results indicate that causality plays a crucial role in determining whether the entanglement leads to the suppression of decoherence in the other particle.