### Abstract

We investigate the dephasing suffered by a non-relativistic quantum particle within a conformally fluctuating spacetime geometry. Starting from a minimally coupled massive Klein–Gordon field, we derive an effective Schrödinger equation in the non-relativistic limit. The wavefunction 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 three dimensions and its statistical properties are described in terms of a general power spectral density. Vacuum fluctuations at a low energy domain are investigated by introducing an appropriate power spectral density and a general formula describing the loss of coherence is derived. This depends quadratically on the particle mass and on the inverse cube of a particle-dependent typical 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.

Original language | English |
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Article number | 145013 |

Number of pages | 30 |

Journal | Classical and Quantum Gravity |

Volume | 26 |

Issue number | 14 |

Early online date | 26 Jun 2009 |

DOIs | |

Publication status | Published - 21 Jul 2009 |

### Keywords

- general relativity
- conformal geometry
- quantum decoherence

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## Cite this

Bonifacio, P. M., Wang, C. H. T., Mendonca, J. T., & Bingham, R. (2009). Dephasing of a non-relativistic quantum particle due to a conformally fluctuating spacetime.

*Classical and Quantum Gravity*,*26*(14), [145013 ]. https://doi.org/10.1088/0264-9381/26/14/145013