Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings annual meeting Electron Microscopy Society of America

Phase Shift of Electron Waves in A Rotating Frame of Reference

FRANZ HASSELBACH, M. Nicklaus

Published Aug 12, 1990• 2 citations
Publisher

Abstract

After the first matter wave version of Sagnac’s classical light optical experiment of 1913, performed by Mercereau and Zimmermann with electron Cooper pairs in 1965, and the Sagnac experiment realized with neutrons by Werner et al. in 1979 , we report here on the first observation of the rotational phase shift of electron waves in vacuum. Theory. The Sagnac effect links classical physics, quantum physics and relativity. Using the special theory of relativity it can be derived that coherent waves, e.g. of light, neutrons or electrons, travelling around a finite area A experience a relative phaseshift

DOI
10.1017/s0424820100179816

Related papers

Accurate measurement of the Sagnac effect for matter waves

Romain Gautier, Mohamed Guessoum, Leonid A. Sidorenkov +3 more

A rotating interferometer with paths that enclose a physical area exhibits a phase shift proportional to this area and to the rotation rate of the frame. Understanding the origin of this so-called Sagnac effect has played a key role in the establishment of the theory of relativity and has pushed for the development of precision optical interferometers. The fundamental importance of the Sagnac effect motivated the realization of experiments to test its validity for waves beyond optical, but precision measurements remained a challenge. Here, we report the accurate test of the Sagnac effect for matter waves, by using a Cesium atom interferometer featuring a geometrical area of 11 cm 2 and two sensitive axes of measurements. We measure the phase shift induced by Earth’s rotation and find agreement with the theoretical prediction at an accuracy level of 25 parts per million. Beyond the importance for fundamental physics, our work opens practical applications in seismology and geodesy.

arXiv:2206.06696•Science Advances•Jun 10, 2022•53 citations

Sagnac experiment with electrons: Reanalysis of a rotationally induced phase shift for charged particles

Richard Neutze, FRANZ HASSELBACH

Using a path-integral formalism, we present a reanalysis of the Sagnac experiment with electrons of Hasselbach and Nicklaus [Phys. Rev. A 48, 143 (1993)]. Our analysis, from an inertial frame of reference, makes explicit the central role of the electrostatic biprism in generating interference fringes and recovers the Sagnac formula for the phase shift induced when rotating the interferometer. This phase shift, however, is shown to differ significantly in physical origin from the similar experiment with neutrons. In the electron Sagnac experiment, rotation displaces all classical electron paths closer to (or further from, depending upon direction) the electrostatic biprisms, thereby perturbing the electrostatic potential along these paths, and a phase shift of an electrostatic nature arises. Our analysis yields a corrected expression for the projected area of the interferometer and small numerical corrections to previous work are consequently given.

Physical Review A•Jul 1, 1998•16 citations

Sagnac experiment with electrons: Observation of the rotational phase shift of electron waves in vacuum

FRANZ HASSELBACH, Marc C. Nicklaus

A Sagnac experiment with electron waves in vacuum is reported. The phase shift caused by rotation of an electron biprism interferometer placed on a turntable has been measured. It was found to agree with prediction within error margins of about 30%. A compact ruggedized electron interferometer was used. It is based on a high-precision optical bench of 36-cm length. This interferometer is less sensitive by orders of magnitude to mechanical vibrations and electromagnetic stray fields than conventional electron interferometers. A beam of low-energy electrons (150--3000 eV) emitted by a field-emission electron source was used. For the most part, electrostatic electron optical components were employed. The magnified interference fringe pattern was intensified by a dual-stage multichannel-plate intensifier, recorded by a charge-coupled-device video camera, transmitted from the turntable to the laboratory system via a slip ring, and evaluated by an image-processing system. Both the rotation rate and the area enclosed between the two partial waves were varied (up to values of 0.5 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and 3.9 ${\mathrm{mm}}^{2}$, respectively). Fringe shifts on the order of 5% of a fringe period were attained. Some historical aspects of the Sagnac effect as well as some aspects of its interpretation are mentioned. A brief informal discussion is included of the interpretation of the Sagnac phase shift as a geometric phase (``Berry phase'') caused by the global anholonomy of the local phase factor that is produced by the gauge field induced by rotation.

Physical Review A•Jul 1, 1993•153 citations

Slow wave atom interferometers for rotation sensing

Meriç Özcan

A gyroscope based on Sagnac interferometer measures the rotation rate relative to an inertial frame of reference. Sagnac effect originally has been derived and experimentally demonstrated with optical waves. Later, matter wave based Sagnac interferometers were developed due to inherent sensitivity over a photon based system. However in any interferometer whether it is photon or matter wave based the resultant phase shift due to counter-rotating waves is independent of the wave velocity. Here we show that one can have a larger phase shift with slower matter waves using Aharonov-Bohm effect: the phase difference of the counter propagating waves is proportional to the inverse square of the particle velocity.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 8, 2007•0 citations

Spin-rotation coupling observed in neutron interferometry

Armin Danner, Demirel, Buelent, Wenzel Kersten +4 more

Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.

•Feb 14, 2020•21 citations

Spin-rotation coupling observed in neutron interferometry

Armin Danner, Bülent Demirel, Wenzel Kersten +4 more

Abstract Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.

arXiv:1904.07085•npj Quantum Information•Feb 14, 2020•23 citations
After the first matter wave version of Sagnac’s classical light optical experiment of 1913, performed by Mercereau and Zimmermann with electron Cooper pairs in 1965, and the Sagnac experiment realized with neutrons by Werner et al. in 1979 , we report here on the first observation of the rotational phase shift of electron waves in vacuum. Theory. The Sagnac effect links classical physics, quantum physics and relativity. Using the special theory of relativity it can be derived that coherent waves, e.g. of light, neutrons or electrons, travelling around a finite area A experience a relative phaseshift
A rotating interferometer with paths that enclose a physical area exhibits a phase shift proportional to this area and to the rotation rate of the frame. Understanding the origin of this so-called Sagnac effect has played a key role in the establishment of the theory of relativity and has pushed for the development of precision optical interferometers. The fundamental importance of the Sagnac effect motivated the realization of experiments to test its validity for waves beyond optical, but precision measurements remained a challenge. Here, we report the accurate test of the Sagnac effect for matter waves, by using a Cesium atom interferometer featuring a geometrical area of 11 cm 2 and two sensitive axes of measurements. We measure the phase shift induced by Earth’s rotation and find agreement with the theoretical prediction at an accuracy level of 25 parts per million. Beyond the importance for fundamental physics, our work opens practical applications in seismology and geodesy.
Using a path-integral formalism, we present a reanalysis of the Sagnac experiment with electrons of Hasselbach and Nicklaus [Phys. Rev. A 48, 143 (1993)]. Our analysis, from an inertial frame of reference, makes explicit the central role of the electrostatic biprism in generating interference fringes and recovers the Sagnac formula for the phase shift induced when rotating the interferometer. This phase shift, however, is shown to differ significantly in physical origin from the similar experiment with neutrons. In the electron Sagnac experiment, rotation displaces all classical electron paths closer to (or further from, depending upon direction) the electrostatic biprisms, thereby perturbing the electrostatic potential along these paths, and a phase shift of an electrostatic nature arises. Our analysis yields a corrected expression for the projected area of the interferometer and small numerical corrections to previous work are consequently given.
A Sagnac experiment with electron waves in vacuum is reported. The phase shift caused by rotation of an electron biprism interferometer placed on a turntable has been measured. It was found to agree with prediction within error margins of about 30%. A compact ruggedized electron interferometer was used. It is based on a high-precision optical bench of 36-cm length. This interferometer is less sensitive by orders of magnitude to mechanical vibrations and electromagnetic stray fields than conventional electron interferometers. A beam of low-energy electrons (150--3000 eV) emitted by a field-emission electron source was used. For the most part, electrostatic electron optical components were employed. The magnified interference fringe pattern was intensified by a dual-stage multichannel-plate intensifier, recorded by a charge-coupled-device video camera, transmitted from the turntable to the laboratory system via a slip ring, and evaluated by an image-processing system. Both the rotation rate and the area enclosed between the two partial waves were varied (up to values of 0.5 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and 3.9 mm2{\mathrm{mm}}^{2}mm2, respectively). Fringe shifts on the order of 5% of a fringe period were attained. Some historical aspects of the Sagnac effect as well as some aspects of its interpretation are mentioned. A brief informal discussion is included of the interpretation of the Sagnac phase shift as a geometric phase (``Berry phase'') caused by the global anholonomy of the local phase factor that is produced by the gauge field induced by rotation.
A gyroscope based on Sagnac interferometer measures the rotation rate relative to an inertial frame of reference. Sagnac effect originally has been derived and experimentally demonstrated with optical waves. Later, matter wave based Sagnac interferometers were developed due to inherent sensitivity over a photon based system. However in any interferometer whether it is photon or matter wave based the resultant phase shift due to counter-rotating waves is independent of the wave velocity. Here we show that one can have a larger phase shift with slower matter waves using Aharonov-Bohm effect: the phase difference of the counter propagating waves is proportional to the inverse square of the particle velocity.
Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.
Abstract Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.