HeNe ring-laser gyros are standard sensors in inertial guidance; mirror reflectances now reach 99.9999%. Present research instruments have an area of ∼ 1 m 2 , a passive quality factor of 10 11 , and a resolution of the frequency difference of counter-rotating optical beams approaching microhertz. In the Sagnac effect, this difference is proportional to the angular velocity. Present resolution is limited by thermal drifts in frequency pulling, itself reflecting mirror backscatter. The capability of ring lasers for measurements of geodesic interest, including seismometry and earth tides, and for detection of other sources of nonreciprocal refractive indices, including axions and CP violation, are discussed. In standard polarization geometries the observable is necessarily time-reversal odd. Scaling rules for dimensions, finesse etc summarizing past progress and suggesting future potential are given.

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The earliest prediction of the Sagnac effect, and of the possibility of detecting the Earth’s rotation with an interferometer of square kilometer area, is by Lodge (1893, 1897). We illustrate the extraordinary range of theoretical motivations for the experimental study of the Sagnac effect, starting with previously unpublished correspondence between Lodge and Larmor, and ending with present (and planned) ring interferometer experiments whose sensitivity to the Earth’s rotation is of the order of parts per million (billion, respectively).

The phase perturbation arising from spin-rotation coupling is developed as a natural extension of the celebrated Sagnac effect. Experimental evidence in support of this phase shift, however, has yet to be realized due to the exceptional sensitivity required. We draw attention to the relevance of a series of experiments establishing that circularly polarized light, upon passing through a rotating half-wave plate, is changed in frequency by twice the rotation rate. These experiments may be interpreted as demonstrating the role of spin-rotation coupling in inducing this frequency shift, thus providing direct empirical verification of the coupling of the photon helicity to rotation. A neutron interferometry experiment is proposed which would be sensitive to an analogous frequency shift for fermions. In this arrangement, polarized neutrons enter an interferometer containing two spin flippers, one of which is rotating while the other is held stationary. An observable beating in the transmitted neutron beam intensity is predicted. 1Theoretical interest in the influence of rotation on the phase of light passing through an optical interferometer already dates over a century [1]. Sagnac's observation of a phase shift proportional to the scalar product of the rotation frequency and the area of his interferometer [2] provided an empirical basis for a rich field of both fundamental and applied research into the influence of rotation on the phase of a quantum mechanical wave function [3].The Sagnac effect may be regarded as a manifestation of the coupling of orbital angular momentum of a particle, L = r × p, to rotation. Suppose any radiation propagates in vacuum around a rotating interferometer and has frequency ω 0 and wave vector k 0 when measured in the corotating frame. An inertial observer O will observe that the wave vector of the radiation along the ith arm of the interferometer is (at first order in Ω) k i = k 0 +ω 0 Ω×r i /c 2 such that a phase shift arises:where we have used ∆r i = ∆t i v i , for any particle in vacuum v i = c 2 k i /ω i = c 2 p i /ω i , and A ≡ 1/2 i r i × ∆r i is the area of the interferometer [4]. The Sagnac phase shift (1) is a scalar quantity that is independent of the motion of the observer. The same result therefore applies for an observer O ′ at rest in the corotating frame. An interpretation of this expression for O ′ is that the coupling of orbital angular momentum to rotation induces a frequency perturbation (relative to that measured by O) proportional to Ω·L. Summing this frequency perturbation over the time of flight of a particle around the interferometer in effect recovers the Sagnac phase shift. From the standpoint of our rotating observer, Eq. (1) may naturally be extended to include the intrinsic spin of a quantum mechanical particle through replacing the orbital angular momentum L with the total angular momentum J = L + S. This formalism consequently predicts that in the rotating frame, in addition to the Sagnac phase shift, a displacement of the interference fringes due...

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