Geometric phases and the Sagnac effect: Foundational aspects and sensing applications

Abstract

Geometric phase is a key player in many areas of quantum science and technology. In this review article, we outline several foundational aspects of quantum geometric phases and their relations to classical geometric phases. We then discuss how the Aharonov-Bohm and Sagnac effects fit into this context. Moreover, we present a concise overview of technological applications of the latter, with special emphasis on gravitational sensing, like in gyroscopes and gravitational wave detectors.

Quantum clock frames: Uncertainty relations, non-Hermitian dynamics and nonlocality in time

“…Below we elaborate on these two works as well as on a different result obtained lately within the Page-Wootters framework: dynamical nonlocality in time [16]. Following our earlier studies of dynamical nonlocality in space [21,22,23,24,25], an interesting notion which seems to deserve more exploration [26], we shall study equations of motion which depend on two remote points in time.…”

Interferometry and higher-dimensional phase measurements using directionally unbiased linear optics

“…The well-known Sagnac effect [26][27][28][29] allows rotation rates to be measured via interference, and has a number of applications to fiber-optical gyroscopes [30], measurement of gravitational effects [31], and quantum sensing [32]. Sagnac-based system have even been devised [33,34] to test quantum effects such as HOM interference and the Aharonov-Bohm effect in non-inertial frames.…”

Quantum Vacuum Sagnac Effect

“…r V (r)|n n| V (r)|0 + 0| V (r)|n n|∇ r V (r)|0 (ω n − ω 0 ) 2 + O V (r) 3(48)yielding the Berry connectioni ψ 0 (r) |∇ r ψ 0 (r) = i 2 2 n =0 0| V (r)|n n|∇ r V (r)|0 − 0|∇ r V (r)|n n| V (r)|0 (ω n − ω 0 ) 2 + O V (r) 3(49)This shows that the QVSP(45) corresponds to the Berry phase (46), i.e. φ Ω k = φ Berry k .…”

“…Such connection is well understood in the case of the standard Sagnac effect (see Ref. [45] for a recent review), as a rotating referential emulates the presence of magnetic fields thanks to the similarity between Coriolis and Lorentz forces [46]. This analogy has enabled the production of artificial effective magnetic fields in neutral cold-atom gases set into rotation [47].…”