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

Physical Review A

Berry’s phase for coherent states and canonical transformation

S. N. Biswas, S. K. Soni

Published May 1, 1991• 9 citations
Publisher

Abstract

Motivated by some recent remarks on the ``removability'' of Berry's phase [Ph. De Sousa Gerbert, Ann. Phys. (N.Y.) 189, 155 (1989)] or its classical counterpart, the Hannay angle, we present here a fresh analysis of Berry's-phase calculations for some coherent states of general theoretical interest. Our reasoning, though semiclassical, lends itself easily for comparison with the exact results. Unlike spin-coherent states, both the (ordinary) harmonic-oscillator and squeezed coherent states are contained in Hamiltonians for which Berry's phase can be removed globally by a canonical transformation.

DOI
10.1103/physreva.43.5717

Related papers

REALIZATION OF BERRY’S PHASE AND HANNAY’S ANGLE THROUGH CANONICAL TRANSFORMATIONS

Sagarika Biswas, K. DATTA, S. Rai Choudhury

A new relationship between Berry’s phase and Hannay’s angle (which is its classical counterpart) is established. This relationship is exact and does not depend on semiclassical arguments, though in this note the aforementioned relationship is proved only for a restricted class of Hamiltonians. It is shown that if a Hamiltonian, for which Berry’s phase and Hannay’s angle are nonvanishing, can, in classical theory, be canonically transformed into one for which both are zero, the generating function of this canonical transformation yields, through appropriate averages, both the quantal geometrical phase and its classical analog.

International Journal of Modern Physics A•Jun 20, 1994•1 citation

Berry's phase and Hannay's angle from quantum canonical transformations

Mustapha Maamache, Jean-Pierre Provost, Gérard Vallée

Using an 'action-angle' coherent states formalism, introduced by the authors in a preceding paper, it is shown that Berry's phase and Hannay's angle can both be derived from the same quantum unitary transformation; their relationship is easily established in this framework.

Journal of Physics A Mathematical and General•Feb 7, 1991•6 citations

Berry's phase for coherent states

S. Chaturvedi, M. S. Sriram, Venkatraman Srinivasan

The authors calculate Berry's phase and the Hannay angle for some physically interesting coherent states with the parameters characterising the coherent states taken to be slowly varying. Interestingly, they find that the harmonic oscillator coherent states provide an example for which, although the Hannay angle is zero, Berry's phase is non-zero.

Journal of Physics A Mathematical and General•Nov 11, 1987•88 citations

Berry's phase as the asymptotic limit of an exact evolution: an example

Meheryar Engineer, Gautam Kumar Ghosh

The authors exhibit, for arbitrary time variations of the parameters of the generalised harmonic oscillator Hamiltonian, a canonical transformation which facilitates an exact analysis of quantal phase and classical angle. Formulae for Berry's phase and Hannay's angle are readily obtained by taking the adiabatic limit of the exact theory.

Journal of Physics A Mathematical and General•Jan 21, 1988•16 citations

Berry's phase for supercoherent states

H. A. Schmitt, A. Mufti

Berry's phase is calculated for coherent states of the supersymmetric harmonic oscillator with the parameters of the coherent states taken to be slowly changing. Interestingly, these supercoherent states are eigenstates of the displaced Jaynes-Cummings Hamiltonian.

Journal of Physics A Mathematical and General•Jul 7, 1990•2 citations

Geometric phases for generalized squeezed coherent states

S. Seshadri, S. Lakshmibala, V. Balakrishnan

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.

arXiv:quant-ph/9905101•Physical Review A•Feb 1, 1997•21 citations
Motivated by some recent remarks on the ``removability'' of Berry's phase [Ph. De Sousa Gerbert, Ann. Phys. (N.Y.) 189, 155 (1989)] or its classical counterpart, the Hannay angle, we present here a fresh analysis of Berry's-phase calculations for some coherent states of general theoretical interest. Our reasoning, though semiclassical, lends itself easily for comparison with the exact results. Unlike spin-coherent states, both the (ordinary) harmonic-oscillator and squeezed coherent states are contained in Hamiltonians for which Berry's phase can be removed globally by a canonical transformation.
A new relationship between Berry’s phase and Hannay’s angle (which is its classical counterpart) is established. This relationship is exact and does not depend on semiclassical arguments, though in this note the aforementioned relationship is proved only for a restricted class of Hamiltonians. It is shown that if a Hamiltonian, for which Berry’s phase and Hannay’s angle are nonvanishing, can, in classical theory, be canonically transformed into one for which both are zero, the generating function of this canonical transformation yields, through appropriate averages, both the quantal geometrical phase and its classical analog.
A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.