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

TL;DR

This paper studies how conformal spacetime fluctuations cause dephasing in nonrelativistic quantum particles, deriving a formula for coherence loss and discussing experimental detection prospects.

Contribution

It introduces a model linking conformal spacetime fluctuations to quantum dephasing, providing a quantitative formula for coherence loss based on spectral density.

Findings

Dephasing depends quadratically on particle mass.

Coherence loss scales with the inverse cube of a cutoff scale.

Current experiments are not sensitive enough to detect this effect.

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 Schrodinger 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.