Dephasing of a non-relativistic quantum particle due to a conformally fluctuating spacetime

Abstract

Abstract. We investigate the dephasing suffered by a nonrelativistic quantum particle within a conformally fluctuating spacetime geometry. Starting from a minimally coupled massive Klein-Gordon field, the low velocity limit yields an effective Schrödinger equation where the wave function couples to gravity through an effective nonlinear potential induced by the conformal fluctuations. The quantum evolution is studied through a Dyson expansion scheme up to second order. We show that only the nonlinear part of the potential can induce dephasing. This happens through an exponential decay of the off diagonal terms of the particle density matrix. The bath of conformal radiation is modeled in 3-dimensions and its statistical properties are described in general in terms of a power spectral density. The case of a Lorentz invariant spectral density, allowing to model vacuum fluctuations at a low energy domain, is investigated and a general formula describing the loss of coherence derived. This depends quadratically on the particle mass and on the inverse cube of a typical particle dependent cutoff scale. Finally, the possibilities for experimental verification are discussed. It is shown that current interferometry experiments cannot detect such an effect. However this conclusion may improve by using high mass entangled quantum states.

Quantum gravitational decoherence of light and matter

“…Decoherence plays a central role in quantum-to-classical transition, a main question in the foundation of quantum mechanics, through unavoidable entanglements between the quantum system and the environment, leading to the loss of coherence between the system's superposition states and, hence, the appearance of a classical mixture [3,4]. Gravitationally induced decoherence could, therefore, set a limit for precision measurements and astronomical observations providing a strong motivation to investigate its full nature and detailed mechanisms [5][6][7][8][9][10].…”

If detected, would hypothetical gravitational Casimir effects prove gravity quantization?

“…20,21 This is achieved by describing the total metric, g μν = η μν + h μν , by the Minkowski metric, η μν , perturbed by relatively small, classical metric perturbations, h μν , expressed within the transversetraceless (TT) gauge. 22 By writing the equal time correlation relation, < h ij h ij >, with i, j = 1 .…”

Parametric Instability in Scalar Gravitational Fields

“…The strength of a gravitational field at a distance r away from an object of mass M is measured by the parameter ǫ ≡ GM rc 2 (27) which is proportional to the Newtonian gravitational potential and is directly related to the redshift 45 . Infinitesimal gravitational fields correspond to the limit ǫ → 0, leading to the Minkowski spacetime of special relativity.…”

“…In this case the scalar gravitational field may be simulated according to parametric instability ( §5) and therefore provides an initial estimate of the effect that can be extended for further investigation with realistic stars, including the possible energy transfer from a collapsed star core to stalled shock waves in supernova formations and other astrophysical problems 29,30 . A further motivation is to seek a possible source of conformal fluctuations of spacetime as a result of background scalar gradational waves 27 .…”