Qubits on the horizon: decoherence and thermalization near black holes

Abstract

We examine the late-time evolution of a qubit (or Unruh-De Witt detector) that hovers very near to the event horizon of a Schwarzschild black hole, while interacting with a free quantum scalar field. The calculation is carried out perturbatively in the dimensionless qubit/field coupling g, but rather than computing the qubit excitation rate due to field interactions (as is often done), we instead use Open EFT techniques to compute the late-time evolution to all orders in g2t/rs (while neglecting order g4t/rs effects) where rs = 2GM is the Schwarzschild radius. We show that for qubits sufficiently close to the horizon the late-time evolution takes a simple universal form that depends only on the near-horizon geometry, assuming only that the quantum field is prepared in a Hadamard-type state (such as the Hartle-Hawking or Unruh vacua). When the redshifted energy difference, ω, between the two qubit states (as measured by a distant observer looking at the detector) satisfies ωrs ≪ 1 this universal evolution becomes Markovian and describes an exponential approach to equilibrium with the Hawking radiation, with the off-diagonal and diagonal components of the qubit density matrix relaxing to equilibrium with different characteristic times, both of order rs/g2.

A preprint version of the article is available at ArXiv.

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Kaplanek, G., Burgess, C.P. Qubits on the horizon: decoherence and thermalization near black holes. J. High Energ. Phys. 2021, 98 (2021). https://doi.org/10.1007/JHEP01(2021)098

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Keywords

  • Effective Field Theories
  • Black Holes
  • Renormalization Group
  • Renormalization Regularization and Renormalons