Title:	Born–Oppenheimer and the geometry of ray space: an application to cold atoms
Authors:	Samuel, J
Issue Date:	6-Dec-2022
Publisher:	IOP Publishing Ltd.
Citation:	Journal of Physics A : Mathematical and Theoretical, 2022, 55, p484002
Abstract:	It is known that, within the Born–Oppenheimer approximation, the slow modes of the nuclear motion are altered by three effects that emerge from integrating out the fast modes of the electronic motion. The first is an effective scalar potential Vdyn coming from the eigenvalue of the electronic state, the second is an effective magnetic field coming from the Berry phase vector potential A. The third term is an additional potential Vgeom originating in the geometry of ray space and the Fubini–Study metric. In this article, we illustrate these effects and their geometric origin in the context of a simple toy model of a slow neutron interacting with a strong, spatially varying magnetic field. Regarding the neutron spin as a fast degree of freedom, we work out the slow dynamics of the motion of the neutron. Our treatment is geometrical and brings out the effects originating in the Kähler geometry of ray space and the Fubini–Study metric. We then give examples of magnetic field configurations which isolate these three separate effects. Finally we apply these ideas to the trapping of cold atoms. Our main result is that the geometric electric potential Vgeom dominates for smaller traps and can be used to confine cold atoms in static traps. This observation could result in better and smaller atomic clocks. This paper is dedicated to Michael Berry on his 80th birthday.
Description:	Restricted Access
URI:	http://hdl.handle.net/2289/8014
ISSN:	1751-8113 1751-8121 (Online)
Alternative Location:	https://arxiv.org/abs/2208.03001 https://inspirehep.net/literature/2132747 https://ui.adsabs.harvard.edu/abs/2022arXiv220803001S/abstract https://doi.org/10.1088/1751-8121/aca63b
Copyright:	2022 IOP Publishing Ltd.
Appears in Collections:	Research Papers (TP)

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