Emergence of volume-law scaling for entanglement negativity from the Hawking radiation of analogue black holes

Abstract

The quantum information content of Hawking radiation holds the key to understanding black-hole evaporation and the fate of unitarity. Motivated by recent advances in cold-atom experiments, we develop a lattice-regularization approach aimed at simulating the coarse-grained entanglement scaling of a quantum field in a 1+1D analogue black-hole background. We provide the first concrete demonstration that logarithmic negativity -- an entanglement monotone that typically exhibits a UV-divergent log-scaling for the conformal vacuum -- acquires a UV-finite volume term from the nonlocal correlations seeded by Hawking radiation. We show that this volume term encodes both the number density and spatial distribution of entangled Hawking pairs along the black-hole interior and exterior. We highlight its prospective detection in currently realizable experiments as well as its implications beyond the analogue paradigm, in particular for black-hole thermodynamics.

Figures (9)

• Figure 1: (a) Sound speed profile $c(x)$ that generates an analogue black-hole horizon at $x=0$. (b) Bipartition scheme for $N$ lattice points sampled along $x\in\left[- \frac{L}{2},\frac{L}{2}\right]$.
• Figure 2: Vacuum scaling of logarithmic negativity $\mathcal{E}_N$ corresponding to Nyquist and harmonic lattices of size $N=10^3$, which differ by an an additive constant.
• Figure 3: Logarithmic negativity scaling with subsystem size $n_A$ for $N=10^3$, $c_L/c_R=1/2$, and various values of (a) the surface gravity $\kappa$ and (b) flow velocity $v_0$. The dashed gray line corresponds to the PG vacuum scaling, and the dashed black line locates the analogue horizon.
• Figure 4: Prefactor of negativity volume-term ($\propto n_A$): Dependence on surface gravity $\kappa$ for (a) the black-hole interior and (b) exterior. Here, $N=600$ and $\tilde{c}_R=1/2$.
• Figure S1: Equal-time (T) correlators for the PG conformal vacuum in the absence of a horizon (a-c), and for the Unruh state in the presence of a horizon (d-l). For the latter, we have chosen $\tilde{\kappa}=0.1$ and $\tilde{c}_L=0.5$.