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

Modern Physics Letters A

THE NON-CYCLIC BERRY PHASE

Harald Weinfurter, G. Badurek

Published Nov 10, 1990• 1 citation
Publisher

Abstract

By analyzing the change of the polarization of a thermal neutron beam on its passage through a magnetic field rotating at various speeds, it is demonstrated that geometric phase shifts of quantum states first introduced by Berry can be observed also for non-cyclic incomplete evolutions in parameter space.
DOI
10.1142/s0217732390002626

Related papers

Measurement of Berry’s phase for noncyclic evolution

Harald Weinfurter, G. Badurek

Tracing the neutron spin on its passage through a magnetic field which rotates at various frequencies it was possible to observe geometrically induced phase shifts of a quantum-mechanical state even for incomplete revolutions of this field. The experiments show that we can extract such purely geometric effects also from nonadiabatic evolutions.

Physical Review Letters•Mar 19, 1990•88 citations

The Pancharatnam-Berry Phase: Theoretical and Experimental Aspects

Francisco De

In 1984 Berry addressed a quantum system undergoing a unitary and cyclic evolution under the action of a time-dependent Hamiltonian (M. V. Berry, 1984). The process was supposed to be adiabatic, meaning that the time scale of the system’s evolution was much shorter than the time scale of the changing Hamiltonian. Until Berry’s study, it was assumed that for a cyclic Hamiltonian the quantum state would acquire only so-called dynamical phases, deprived of physical meaning. Such phases could be eliminated by redefining the quantum state through a “gauge” transformation of the form |ψ〉 → eiα |ψ〉. However, Berry discovered that besides the dynamical, there was an additional phase that could not be “gauged away” and whose origin was geometric or topological. It depended on the path that |ψ〉 describes in the parameter space spanned by those parameters to which the Hamiltonian owed its time dependence. Berry’s discovery was the starting point for a great amount of investigations that brought to light topological aspects of both quantum and classical systems. Berry’s phase was soon recognized as a special case of more general phases that showed up when dealing with topological aspects of different systems. For example, the Aharonov-Bohm phase could be understood as a geometric phase. The rotation angle acquired by a parallel-transported vector after completing a closed loop in a gravitationally curved space-time region, is also a geometric, Berry-like phase. Another example is the precession of the plane of oscillation of a Foucault pendulum. Berry’s original formulation was directly applicable to the case of a spin-1/2 system evolving under the action of a slowly varying magnetic field that undergoes cyclic changes. A spin-1/2 system is a special case of a two-level system. Another instances are two-level atoms and polarized light, so that also in these cases we should expect to find geometric phases. In fact, the first experimental test of Berry’s phase was done using polarized, classical light (A. Tomita, 1986). Pancharatnam (S. Pancharatnam, 1956) anticipated Berry’s phase when he proposed, back in 1956, how to decide whether two polarization states are “in phase”. Pancharatnam’s prescription is an operational one, based upon observing whether the intensity of the interferogram formed by two polarized beams has maximal intensity. In that case, the two polarized beams are said to be “in phase”. Such a definition is analogous to the definition of distant parallelism in differential geometry. Polarized states can be subjected to different transformations which could be cyclic or not, adiabatic or not, unitary or not. The Pancharatnam-Berry Phase: Theoretical and Experimental Aspects

InTech eBooks•Feb 24, 2012•16 citations

Berry's phase and orbital angular momentum

Paolo Martelli, Annalaura Fasiello, Mario Martinelli

In 1984 Berry showed that a quantum system evolving in a cyclic and adiabatic way acquires in addition to the dynamic phase also a phase which of geometric nature, depending on the path on the parameter space [1]. This geometric phase, also named Berry's phase, can be generalized to non-adiabatic situations [2] and presents some classical analogues, as in the case of the motion of a Foucault pendulum [3].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•2 citations

Geometrical phase effects in neutron optics

V. I. Bodnarchuk, Levon S. Davtyan, D.A. Korneev

The aim of this paper is to study in detail the geometric phase (Berry phase) and to discuss peculiarities of its measurements in the most typical physical case, i.e., the problem of neutron spin evolution in a precessing magnetic field.

Physics-Uspekhi•Feb 28, 1996•19 citations

Phase change during a cyclic quantum evolution

Yakir Aharonov, J. Anandan

A new geometric phase factor is defined for any cyclic evolution of a quantum system. This is independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a given projection of the evolution on the projective space of rays of the Hilbert space. Some applications, including the Aharonov-Bohm effect, are considered. For the special case of adiabatic evolution, this phase factor is a gauge-invariant generalization of the one found by Berry.

Physical Review Letters•Apr 20, 1987•2,185 citations

Demonstration of Berry's Phase Using Stored Ultracold Neutrons

David John Richardson, A.I. Kilvington, K. Green +1 more

Using stored spin-polarized ultracold neutrons subjected to a temporally varying magnetic field, we have demonstrated a manifestation of Berry's phase. We verified several properties of Berry's phase which include its solid-angle dependency and additivity for multiple excursions along the same path in parameter space.

Physical Review Letters•Oct 31, 1988•110 citations
In 1984 Berry addressed a quantum system undergoing a unitary and cyclic evolution under the action of a time-dependent Hamiltonian (M. V. Berry, 1984). The process was supposed to be adiabatic, meaning that the time scale of the system’s evolution was much shorter than the time scale of the changing Hamiltonian. Until Berry’s study, it was assumed that for a cyclic Hamiltonian the quantum state would acquire only so-called dynamical phases, deprived of physical meaning. Such phases could be eliminated by redefining the quantum state through a “gauge” transformation of the form |ψ〉 → eiα |ψ〉. However, Berry discovered that besides the dynamical, there was an additional phase that could not be “gauged away” and whose origin was geometric or topological. It depended on the path that |ψ〉 describes in the parameter space spanned by those parameters to which the Hamiltonian owed its time dependence. Berry’s discovery was the starting point for a great amount of investigations that brought to light topological aspects of both quantum and classical systems. Berry’s phase was soon recognized as a special case of more general phases that showed up when dealing with topological aspects of different systems. For example, the Aharonov-Bohm phase could be understood as a geometric phase. The rotation angle acquired by a parallel-transported vector after completing a closed loop in a gravitationally curved space-time region, is also a geometric, Berry-like phase. Another example is the precession of the plane of oscillation of a Foucault pendulum. Berry’s original formulation was directly applicable to the case of a spin-1/2 system evolving under the action of a slowly varying magnetic field that undergoes cyclic changes. A spin-1/2 system is a special case of a two-level system. Another instances are two-level atoms and polarized light, so that also in these cases we should expect to find geometric phases. In fact, the first experimental test of Berry’s phase was done using polarized, classical light (A. Tomita, 1986). Pancharatnam (S. Pancharatnam, 1956) anticipated Berry’s phase when he proposed, back in 1956, how to decide whether two polarization states are “in phase”. Pancharatnam’s prescription is an operational one, based upon observing whether the intensity of the interferogram formed by two polarized beams has maximal intensity. In that case, the two polarized beams are said to be “in phase”. Such a definition is analogous to the definition of distant parallelism in differential geometry. Polarized states can be subjected to different transformations which could be cyclic or not, adiabatic or not, unitary or not. The Pancharatnam-Berry Phase: Theoretical and Experimental Aspects