Decoherence by black holes via holography

TL;DR

This work investigates decoherence in quantum systems coupled to strongly interacting environments using holographic duality with Lifshitz scaling. By computing the holographic influence functional from on-shell bulk actions in Lifshitz spacetimes and Lifshitz black holes, it shows that zero temperature environments yield supraohmic dissipation with vanishing decoherence at long flight times, while finite-temperature environments produce a constant, ohmic decoherence rate that scales with temperature. The study further uncovers a stringy (finite $\alpha'$) correction and analyzes Unruh-effect-driven decoherence, including holographic EPR pairs, where causal contact can suppress decoherence of one partner. Overall, the results provide a quantum-gravitationally consistent picture linking flat-space coherence, Lifshitz dynamics, and black-hole decoherence, hinting at how finite-$N$ effects might refine our understanding of information retention in holographic black holes.

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 $τ_0$ 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 $τ_0 \to \infty$. Remarkably, in the zero-temperature regime, the decoherence exhibits a power-law decay at large $τ_0$ 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.

Figures (2)

• Figure 1: The spacetime paths of the wavepackets for an interference experiment.
• Figure 2: The causal diagrams for the induced metrics on the static string worldsheet in (\ref{['zeroT']}) (parameterized by $t$ and the conformal coordinate $\tilde{x}$) and the accelerating string worldsheet in (\ref{['ws']}) (parameterized by $t$ and $x$), respectively. In both diagrams, $q_1$ and $q_2$ are the trajectories of the string endpoints. Two large arrows are light rays emitted from $q_1$ at the times $t=0$ and $t=t_0$, respectively. The shaded regions include those points in the future that are causally connected to the events when the light rays were emitted. Thus, in the static case, the interference experiment on $q_2$ can be affected by $q_1$ after $t\sim\frac{1}{r_0}$. In the accelerating case, the two endpoints are causally separated by the bifurcate horizons (the dashed lines), so there is no effect from $q_1$ on the interference experiment performed on $q_2$.