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European Journal of Physics

Remarks on ring interferometry

G C Scorgie

Published Mar 1, 1991• 5 citations
Publisher

Abstract

Within the domain of flat spacetime a generalized view of ring interferometry leads to a relation that is free from restriction on the geometry and kinematics of the interferometer. The treatment applies also to experiments using a pair of open paths rather than a closed circuit and depending on translational acceleration in the absence of angular velocity.

DOI
10.1088/0143-0807/12/2/002

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Within the domain of flat spacetime a generalized view of ring interferometry leads to a relation that is free from restriction on the geometry and kinematics of the interferometer. The treatment applies also to experiments using a pair of open paths rather than a closed circuit and depending on translational acceleration in the absence of angular velocity.
By emphasizing a common kinematic core at the expense of the specific dynamics appropriate to individual configurations a unified view is obtained of a large part of the field of interferometry whether using photons or material particles. The only restriction on the coordinate system is that the metric tensor is independent of time. Within this framework a comparison is made of the main features of various types of interferometer, and the effect of dispersion is calculated for the type based on the ring laser oscillator. For a ring interferometer using material particles the particle proper time for a complete transit around the ring is shown to be the same for both directions of travel and a paradoxical consequence is noticed.
Atom interferometry is a sensitive tool for measuring relativistic effects, but there are no known non-trivial exact solutions for relativistic atom interferometer phase shifts. Here we derive relativistically exact expressions within the usual semiclassical approximation for a wide range of experimentally interesting atom interferometer pulse sequences in flat spacetime, including Mach-Zehnder, resonant, and large momentum transfer interferometer geometries. As an example, the leading order phase shift ωagT2/cω_a g T^2/cωa​gT2/c for a Mach-Zehnder clock atom interferometer is found to become ωa(1+ωa2m)(e−gT/c−1)2c/gω_a \left(1 + \frac{ω_a}{2m}\right)(e^{-gT/c}-1)^2 c/gωa​(1+2mωa​​)(e−gT/c−1)2c/g when all relativistic kinematics are included. We calculate exact phase shifts for both clock (single-photon) interferometers and Raman or Bragg (two-photon) interferometers.
We describe our progress in the development of an atom based rotation sensor, which employs state-dependent trapping potentials to transport ultracold atoms along a closed path and perform Sagnac interferometry. Whilst guided atom interferometers are sought after to build miniaturized devices that overcome size restrictions from free-falling atoms, fully trapped interferometers also remove free-propagation along an atomic waveguide. This provides additional control of motion, e.g. removing wave-packet dispersion and enabling operation that remains independent of external acceleration. Our experimental scheme relies on radio-frequency and microwave-fields, which are partly generated via atom-chip technology, providing a step towards implementing a small, robust, and eventually portable atomic-gyroscope.