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, 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.

💡 Research Summary

In this paper the authors revisit the decoherence phenomenon associated with black holes by employing the holographic duality framework, specifically Lifshitz holography, which describes strongly coupled quantum critical systems with a dynamical exponent z. The central setup consists of a “mirror” – either a point particle (n = 0) or an extended object (n ≥ 1) – represented holographically by a string or probe brane propagating in an asymptotically Lifshitz spacetime. The mirror is prepared in a spatial superposition of two well‑separated trajectories C₁ and C₂, and an interference experiment is performed on the boundary theory. The influence of the environmental quantum field on the mirror is captured by the Feynman–Vernon influence functional, which in the holographic context is identified with the on‑shell world‑volume action of the string/brane evaluated on a pair of classical solutions satisfying (i) prescribed boundary values that encode the two trajectories and (ii) infalling boundary conditions at the bulk horizon.

Two distinct bulk backgrounds are considered. At finite temperature the bulk geometry is a Lifshitz black hole; at zero temperature it reduces to pure Lifshitz spacetime. By solving the linearized equations for transverse fluctuations X(t,r) of the string/brane, the authors obtain the retarded Green’s function G_R(ω) and the Hadamard function G_H(ω) of the boundary operator that couples to the mirror. In the finite‑temperature case G_H(ω) possesses a constant low‑frequency component, leading to a decoherence functional

 W = −∫(dω/2π) G_H(ω) |ζ̃(ω)|² ≈ −Γ τ₀,

with Γ∝T³, i.e. the decoherence rate scales with the cube of the Lifshitz black‑hole temperature. This reproduces the “constant decoherence rate” found by Danielson, Satishchandran and Wald (DSW) and shows that the effect can be interpreted as arising from the thermal bath provided by the black‑hole horizon.

In the zero‑temperature limit the retarded Green’s function expands as G_R(ω)=m(iω)²+γ(−iω)^α+…, where α = 1+(n+2)/z>1. The corresponding Hadamard function behaves as G_H(ω)∝|ω|^α, and the decoherence functional becomes

 W ∝ ℓ₀² τ₀^{α−1}.

Thus for any finite z the decoherence decays with the interaction time τ₀ and vanishes as τ₀→∞, reflecting the recovery of coherence in a pure Lifshitz vacuum. Remarkably, as z→∞ (α→1) the decay turns into a power‑law (logarithmic) form, reminiscent of the slow decoherence observed in extremal black‑hole geometries. Hence Lifshitz holography provides a continuous interpolation between flat‑space decoherence (z=1) and black‑hole‑induced decoherence (large z, finite T).

The paper also explores an EPR‑type configuration where two particles are entangled holographically. By accelerating one endpoint of the string (thereby inducing an Unruh temperature) the authors find a constant decoherence rate for the accelerated particle, while the inertial partner experiences suppressed decoherence until causal signals from the accelerated worldline can reach it. This demonstrates that causality governs whether entanglement can protect the partner from decoherence.

Finally, the authors discuss subleading 1/λ corrections (finite ’t Hooft coupling) by expanding the on‑shell action beyond the leading N → ∞ limit. These corrections introduce higher‑order frequency dependence in the influence functional, indicating that even at strong coupling quantum corrections can modify decoherence rates.

Overall, the work shows that holographic Lifshitz duals capture the essential physics of black‑hole‑induced decoherence: a constant rate at finite temperature, a vanishing rate at zero temperature, and a tunable power‑law behavior controlled by the dynamical exponent z. The results bridge semiclassical thermal‑bath pictures with fully quantum holographic descriptions, offering a new avenue to study information loss, decoherence control, and the role of causality in strongly coupled quantum systems.