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 phaseshiftAfter 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

Proceedings annual meeting Electron Microscopy Society of AmericaAug 12, 19902 citations

Sagnac effect as viewed by a co-rotating observer

Benno H. W. Hendriks, Gerard Nienhuis

Quantum Optics Journal of the European Optical Society Part BJun 1, 19901 citation

Several experiments in optics and atomic physics

B. Sh. Perkal'skis, Виктор Лаврентьевич Ларин, A. A. Eliseev

Russian Physics JournalApr 1, 19690 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.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 AJul 1, 1993153 citations

Electron Interference Experiments

J. Arol Simpson

Reviews of Modern PhysicsJul 1, 195616 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.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 AJul 1, 199816 citations

{\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.