Probing the Unruh effect with an accelerated extended system

It has been proved in the context of quantum fields in Minkowski spacetime that the vacuum state is a thermal state according to uniformly accelerated observers—a seminal result known as the Unruh effect. Recent claims, however, have challenged the validity of this result for extended systems, thus casting doubts on its physical reality. Here, we study the dynamics of an extended system, uniformly accelerated in the vacuum. We show that its reduced density matrix evolves to a Gibbs thermal state with local temperature given by the Unruh temperature T U = ℏ a ∕ ( 2 π c k B ) , where a is the system’s spatial-dependent proper acceleration— c is the speed of light and k B and ℏ are the Boltzmann’s and the reduced Planck’s constants, respectively. This proves that the vacuum state does induce thermalization of an accelerated extended system—which is all one can expect of a legitimate thermal reservoir. The Unruh effect is a seminal result which illustrates the relative character of the particle concept in QFT, but its validity for extended systems is debated. Here, the authors show how a uniformly accelerated extended system of two coupled spins will evolve to a Gibbs thermal state at the Unruh temperature.