Nondispersive phase of the Aharonov-Bohm effect

Badurek, G.; Weinfurter, Harald; Gähler, R.; Kollmar, A.; Wehinger, Stefan; Zeilinger, Anton

doi:10.1103/physrevlett.71.307

Cited by 117 publications

(80 citation statements)

References 18 publications

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“…In this experiment, a spinindependent phase shifter was used to establish separate control over the phase shifts for the spin-up and the spindown neutron states. However, the use of unpolarized neutrons gave rise to the interpretational objection that each neutron experiences a classical torque [6], t m 3 B͑t͒, and, therefore, the observed phase shift is not strictly SAB, but an effect also observable by classical polarimetry [7]. We have now carried out a similar SAB experiment, but using neutrons polarized along the B(t) field.…”

Section: (Received 7 November 1997)mentioning

confidence: 99%

Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons

et al. 1998

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We have carried out a neutron interferometry experiment using longitudinally polarized neutrons to observe the scalar Aharonov-Bohm effect. The neutrons inside the interferometer are polarized parallel to an applied pulsed magnetic field B(t). The pulsed B field is spatially uniform so it exerts no force on the neutrons. Its direction also precludes the presence of any classical torque to change the neutron polarization. [S0031-9007(98)05764-0] PACS numbers: 03.65. Bz, One distinction that sets quantum mechanics apart from classical mechanics is the treatment of a potential. In classical mechanics, the presence of a potential can be inferred only from the motion of the particles under the influence of the force it generates. The motion of particles through a region of uniform potential is, therefore, no different from that in empty space. In quantum mechanics, however, particles passing through a potential, uniform or not, acquire a quantum mechanical phase shift through their interaction with the potential. For instance, the phase shift acquired by electrons passing through a region of space containing a magnetic vector potential A and a scalar electric potential V is given by the action integralThis phase shift can be detected by interferometric techniques, as first pointed out clearly by Aharonov and Bohm (AB) [1]. The vector AB effect arises from the vector potential A(r) in the spatial part of the action integral, while the scalar AB effect comes from the potential V(t) in the temporal part. However, the experimental realization of the scalar Aharonov-Bohm (SAB) effect has proven to be challenging due to the technical difficulties in electron interferometry. [5]. In this experiment, the magnetic moments m of unpolarized thermal neutrons were subjected to a spatially uniform, but time-dependent magnetic induction B͑t͒ B͑t͒x. The scalar interaction E 2m ? B͑t͒ produces a quantum mechanical phase shift that is measurable by neutron interferometry. In this experiment, a spinindependent phase shifter was used to establish separate control over the phase shifts for the spin-up and the spindown neutron states. However, the use of unpolarized neutrons gave rise to the interpretational objection that each neutron experiences a classical torque [6], t m 3 B͑t͒, and, therefore, the observed phase shift is not strictly SAB, but an effect also observable by classical polarimetry [7]. We have now carried out a similar SAB experiment, but using neutrons polarized along the B(t) field. In this arrangement, there is neither a classical torque nor (as before) a classical force exerted on the neutrons. The experimental setup is shown schematically in Fig. 1. The setup consists of two main parts: the neutron polarizer and the neutron interferometer. The neutron polarizer includes a double-bounce neutron reflector made from a perfect silicon crystal and a magnetic prism assembly. The principle behind the polarizer is birefringence; i.e., the polarization dependence of the neutron 0031-9007͞98͞80(15)͞3165(4)$15.00

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Section: (Received 7 November 1997)mentioning

confidence: 99%

Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons

et al. 1998

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“…In ref. [31], it was pointed out that these results cannot be generalised to the original electron-solenoid case. Moreover, the same question can be asked as stated above.…”

Section: -P1mentioning

confidence: 99%

“…If the time delay dt clas in fig. 1 Although the original Aharonov-Bohm effect has not been tested for its dispersionless nature, in a tour de force experiment, the scalar analogue of the AB-effect has been shown to be dispersionless [31]. Does this rule out the existence of dispersionless forces?…”

Section: -P1mentioning

confidence: 99%

Dispersionless forces and the Aharonov-Bohm effect

Batelaan

Becker

2015

EPL

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-The independence of the Aharonov-Bohm phase shift on particle velocity is one of its defining properties. The classical counterpart to this dispersionless behavior is the absence of forces along the direction of motion of the particle. A reevaluation of the experimental demonstration that forces are absent in the AB physical system is given, including previously unpublished data. It is shown that the debate on the presence or absence of forces is not settled. Experiments that measure the influence of magnetic permeability on forces and search for dispersionless quantum forces are proposed.

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“…In particular, the dynamics of spin- 1 2 particles in time-dependent magnetic fields is a common physical situation in neutron interferometry [7,8]. This type of physical application belongs to n-level systems with time-dependent potentials in quantum mechanics.…”

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confidence: 99%

Exact solutions ofn-level systems and gauge theories

Montesinos

Pérez‐Lorenzana

1999

Phys. Rev. A

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We find a relationship between unitary transformations of the dynamics of quantum systems with time-dependent Hamiltonians and gauge theories. In particular, we show that the nonrelativistic dynamics of spin-1 2 particles in a magnetic field B i (t) can be formulated in a natural way as an SU (2) gauge theory, with the magnetic field B i (t) playing the role of the gauge potential A i . The present approach can also be applied to systems of n levels with time-dependent potentials, U (n) being the gauge group. This geometric interpretation provides a powerful method to find exact solutions of the Schrödinger equation. The root of the present approach rests in the Hermiticity property of the Hamiltonian operators involved. In addition, the relationship with true gauge symmetries of n-level quantum systems is discussed. 03.65.Ca, The discovery of the quantum nature of matter fields is one of the most important events in physics in this century. It has been realized that the quantum nature of matter rests on a more fundamental level than the corresponding classical limit. The last one emerges as a suitable limit case of quantum behavior [1]. Also, gauge as well as geometric aspects of quantum systems are one of the most striking results in quantum theory [2][3][4][5]. Gauge theories appear in many branches of physics [6]. They are the natural language to incorporate internal symmetries of systems.On the other hand, the physics of systems of two levels has been one of the most interesting research lines followed up to now. In particular, the dynamics of spin-1 2 particles in time-dependent magnetic fields is a common physical situation in neutron interferometry [7,8]. This type of physical application belongs to n-level systems with time-dependent potentials in quantum mechanics. Nevertheless, to find exact solutions of the Schrödinger equation with time-dependent potentials for n-level systems is a hard problem. The standard theoretical techniques employed to solve this type of physical situation are limited.Here, we combine the topics of exact solutions and gauge theories. The final result is twofold. First, we exhibit the geometric structure underlying unitary transformations associated with n-level quantum systems characterized by time-dependent Hamiltonians. Second, this formalism provides a powerful method to find exact solutions to a very general class of time-dependent Hamiltonians. Moreover, because the present formalism is exact, it is a serious alternative for the standard techniques allowed in the literature to study this type of physical situation, namely, unitary evolution and time-dependent perturbation theory. Now, let us go to the nonrelativistic dynamics of spin-1 2 particles (we mean the spinorial part of the Hamiltonian of spin-1 2 particles). The nonrelativistic dynamics of spin-1 2 particles in a magnetic field B(t) = (B 1 (t), B 2 (t), B 3 (t)) is given by the Schrödinger-Pauli equationwhere µ B = eh 2mec is the Bohr magneton, S i =h 2 σ i with σ i the Pauli matrices, and g s depends on the spe...

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Nondispersive phase of the Aharonov-Bohm effect

Cited by 117 publications

References 18 publications

Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons

Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons

Dispersionless forces and the Aharonov-Bohm effect

Exact solutions ofn-level systems and gauge theories

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