Decoherence by black holes via holography

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, is also manifest in 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 takes place 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 this 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.