Geometric phase outside a Schwarzschild black hole and the Hawking effect

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 ω∞rs ≪ 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.

Section: Jhep01(2021)098mentioning

confidence: 99%

Qubits on the horizon: decoherence and thermalization near black holes

Kaplanek

Burgess

2021

“…Qubit behaviour in the hotspot model is nevertheless both very rich and yet amenable to explicit calculation, and as such provides a useful test of tools that are applied in these other more complicated gravitational settings. (For other examples of qubits used to probe black-hole systems see [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. )…”

Section: Introduction and Discussion Of Resultsmentioning

confidence: 99%

Qubit heating near a hotspot

Kaplanek

Burgess

Holman³

2021

Effective theories describing black hole exteriors contain many open-system features due to the large number of gapless degrees of freedom that lie beyond reach across the horizon. A simple solvable Caldeira-Leggett type model of a quantum field interacting within a small area with many unmeasured thermal degrees of freedom was recently proposed in ref. [23] to provide a toy model of this kind of dynamics against which more complete black hole calculations might be compared. We here compute the response of a simple Unruh-DeWitt detector (or qubit) interacting with a massless quantum field ϕ coupled to such a hotspot. Our treatment differs from traditional treatments of Unruh-DeWitt detectors by using Open-EFT tools to reliably calculate the qubit’s late-time behaviour. We use these tools to determine the efficiency with which the qubit thermalizes as a function of its proximity to the hotspot. We identify a Markovian regime in which thermalization does occur, though only for qubits closer to the hotspot than a characteristic distance scale set by the ϕ-hotspot coupling. We compute the thermalization time, and find that it varies inversely with the ϕ-qubit coupling strength in the standard way.

“…[13], D. M. Tong et al, from kinematic approach, gave an expression of the mixed-state geometric phase in the nonunitary evolution, this phase is manifestly gauge invariant and can be experimentally tested in interferometry. After that, the study of geometric phase in open quantum system became more extensive [7,8,14,15].…”

Section: Introductionmentioning

confidence: 99%

“…J. Hu et al [14], by using open quantum system approach, analysed geometric phase for an accelerated two-level atom. Not only that, since any systems, in quantum sense, will be subject to vacuum fluctuations, they also generalized the geometric phase, which is acquired by a twolevel atom coupling to vacuum fluctuations, to the background of Schwarzschild black hole [15]. Because of this coupling, one naturally expect that some physical properties of vacuum will be reflected in the observable phenomena of quantum system, such as Lamb shift [17,18,19] and geometric phase, when this system evolves in the vacuum.…”

Section: Introductionmentioning

confidence: 99%

Geometric phase of two-level atoms and thermal nature of de Sitter spacetime

Tian

Jing

2013

Abstract:In the framework of open quantum systems, we study the geometric phase acquired by freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We find that, for the freely falling atom, the geometric phase gets a correction resulting from a thermal bath with the Gibbons-Hawking temperature, thus it clearly reveals the intrinsic thermal nature of de Sitter spacetime from a different physical context. For the static atom, there is a correction to the geometric phase coming from both the intrinsic thermal nature of de Sitter spacetime and the Unruh effect associated with the proper acceleration of the atom. Furthermore, in a gedanken experiment, we estimate the magnitude of the correction to the geometric phase as opposed to that in a flat spacetime. We find that the correction for the freely falling atom is too tiny to be measured, and that for the static atom achieves an observable magnitude only when the atom almost locates at the horizon.