Unruh effect and quantum entanglement for the non-uniform Rindler spacetime

TL;DR

Problem: how does the Unruh effect extend to observers with non-uniform acceleration? Approach: develop a framework for a non-uniform Rindler spacetime and an Unruh-DeWitt detector, deriving Bogolyubov relations and particle densities that show a time-dependent Unruh spectrum. Findings: the detector perceives a particle density that contains a time-dependent factor $(\sinh χ(τ))/(1 + \cosh aτ)$ and tends to the standard Unruh density $1/(e^{2π Ω/a}-1)$ in the asymptotic limits; the Minkowski vacuum is deformed into squeezed states, expressible as two-mode squeezed in the uniform case and one-mode squeezed in the non-uniform case. Significance: this clarifies observer-dependent vacuum structure in non-inertial frames and suggests experimental routes to detect Unruh physics under realistic, time-dependent acceleration.

Abstract

While the Unruh effect has traditionally been studied under the assumption of uniform acceleration, a simplification motivated by experimental considerations, it is not necessarily true for all non-inertial motions. We propose a novel approach for the indirect detection of the Unruh effect without relying on the former restriction. Previous studies have shown that probing the decoherence of an Unruh-DeWitt detector can significantly reduce the acceleration required for observing the effect by several orders of magnitude compared to earlier proposals. Building on this idea, we develop a theoretical framework describing a non-inertial observer equipped with a detector undergoing non-uniform, time-dependent acceleration. We show that, in a non-uniformly accelerated Rindler spacetime, the particle distribution perceived in the Minkowski vacuum acquires a time-dependent modification of the standard Unruh spectrum. Furthermore, we demonstrate that the inclusion of quantum entanglement leads to a deformation of the Minkowski vacuum into squeezed states.

Figures (3)

• Figure 1: The non-uniform Rindler spacetime $\mathbf{nuR}$ is a non-inertial construction for an observer moving with non-uniform acceleration in the z-direction. In this $\rm{z}$-$\rm{t}$ plane, the red lines are the event horizons; the blue lines are the Rindler trajectories; and the green lines denote the Rindler-generalized trajectories.
• Figure 2: The entanglement entropy, $S_E$, as a function of $\tau$ and $p$. The red surface corresponds to $\eta = 10$. The green surface corresponds to $\eta = 1$. The cyan surface corresponds to $\eta = 0$.
• Figure 3: The ratio, $W$, as a function of $\tau$ and $\eta$, indicates that decoherence occurs for the accelerated observer compared to its inertial counterpart.