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

Optics Express

Non-linear wave packet dynamics of coherent states of various symmetry groups

J. Banerji, G. S. Agarwal

Published Nov 8, 1999• 21 citations
Publisher

Abstract

We present a comparative study of the non-linear wave packet dynamics of two-mode coherent states of the Heisenberg-Weyl group, the SU(1,1) group and the SU(2) group under the action of a model anharmonic Hamiltonian. In each case, we find certain generic signatures of non-linear evolution such as quick onset of decoherence followed by Schrödinger cat formation and revival. We also report important differences in the evolution of coherent states belonging to different symmetry groups.

DOI
10.1364/oe.5.000220

Related papers

A Comparative Analysis of a Nonlinear Phase Space Evolution of SU(2) and SU(1,1) Coherent States

Rodrigo D. Aceves, Miguel Baltazar, Ivan F. Valtierra +1 more

We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical effects: the squeezing of the appropriate observables and the Schrödinger’s cat state generation characteristic of both the considered symmetry groups.

Quantum Reports•Jul 5, 2025•1 citation

Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states

J. Banerji, G. S. Agarwal

We have used a generic two-mode Hamiltonian with two associated time scales to study the evolution of generalized SU(1,1) coherent states, in particular the pair and Perelomov coherent states, which have been realized in many systems such as radiation fields, trapped ions, and phonons. We have found that their dynamics does not depend on the ratio of these time scales but is instead determined crucially by the difference in photon numbers of the two modes. This is in stark contrast to the previously studied harmonic-oscillator coherent states and can be attributed to the different nature of the underlying algebra. We provide analytical results for their revival and fractional revival along with numerical plots of the autocorrelation function and the quadrature distribution and demonstrate the formation of Schr\"odinger cats. The results are extremely sensitive to the Casimir invariant and the complex parameters characterizing SU(1,1) coherent states.

Physical Review A•Jun 1, 1999•25 citations

Wave packet dynamics of photon-added coherent states

C. Sudheesh, S. Lakshmibala, V. Balakrishnan

We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of an initial state of the radiation field propagating in a nonlinear medium. We establish this by considering a generic Hamiltonian which models wave packet propagation in a Kerr-like medium, and comparing the non-classical effects displayed by an initial photon-added coherent state with that of an inital ideal coherent state.

arXiv:quant-ph/0408071•Europhysics Letters (EPL)•Aug 2, 2005•14 citations

Fractional revivals in systems with two time scales

G. S. Agarwal, J. Banerji

We examine the dynamical evolution of wave packets in a large class of quantum systems where two quantum numbers determine the energy spectrum and consequently the dynamical behavior. Using a generic Hamiltonian, we study the formation of coherent structures. The ratio of two time scales as well as the symmetry of the initial wave packet decisively determines the revival and fractional revivals of the system for which we give analytical results. The theory is applicable to a wide class of systems from diatomic molecules to ions in two-dimensional traps and two interacting Bose condensates.

Physical Review A•May 1, 1998•37 citations

Non-classical effects in wave packet dynamics

C. Sudheesh

Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such as revivals, fractional revivals, squeezing and higher-order squeezing during its temporal evolution. Further, these studies were extended to examine the role of quantum entanglement in bipartite systems. The dynamics of quantum expectation values were tracked carefully in various cases and the conditions under which a wave packet spreads chaotically, were investigated.

arXiv:0707.0996•Jul 6, 2007•1 citation

Wave-packet dynamics in nonlinear Schrödinger equations

Simon Moulieras, Alejandro Monastra, Marcos Saraceno +1 more

Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schr\"odinger equations, which describe weakly interacting Bose-Einstein condensates or light propagation in a nonlinear medium. It is shown that the dynamics of phase-space translations of the ground state of a harmonic potential is quite simple: The center follows a classical trajectory whereas its shape does not vary in time. The parabolic potential is the only one that satisfies this property. We study the time evolution of these nonlinear coherent states under perturbations of their shape or of the confining potential. A rich variety of effects emerges. In particular, in the presence of anharmonicities, we observe that the packet splits into two distinct components. A fraction of the wavepacket is transferred toward incoherent high-energy modes, while the amplitude of oscillation of the remaining coherent component is damped toward the bottom of the well.

arXiv:1107.0259•Physical Review A•Jan 26, 2012•8 citations
We present a comparative study of the non-linear wave packet dynamics of two-mode coherent states of the Heisenberg-Weyl group, the SU(1,1) group and the SU(2) group under the action of a model anharmonic Hamiltonian. In each case, we find certain generic signatures of non-linear evolution such as quick onset of decoherence followed by Schrödinger cat formation and revival. We also report important differences in the evolution of coherent states belonging to different symmetry groups.
We have used a generic two-mode Hamiltonian with two associated time scales to study the evolution of generalized SU(1,1) coherent states, in particular the pair and Perelomov coherent states, which have been realized in many systems such as radiation fields, trapped ions, and phonons. We have found that their dynamics does not depend on the ratio of these time scales but is instead determined crucially by the difference in photon numbers of the two modes. This is in stark contrast to the previously studied harmonic-oscillator coherent states and can be attributed to the different nature of the underlying algebra. We provide analytical results for their revival and fractional revival along with numerical plots of the autocorrelation function and the quadrature distribution and demonstrate the formation of Schr\"odinger cats. The results are extremely sensitive to the Casimir invariant and the complex parameters characterizing SU(1,1) coherent states.
We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of an initial state of the radiation field propagating in a nonlinear medium. We establish this by considering a generic Hamiltonian which models wave packet propagation in a Kerr-like medium, and comparing the non-classical effects displayed by an initial photon-added coherent state with that of an inital ideal coherent state.
We examine the dynamical evolution of wave packets in a large class of quantum systems where two quantum numbers determine the energy spectrum and consequently the dynamical behavior. Using a generic Hamiltonian, we study the formation of coherent structures. The ratio of two time scales as well as the symmetry of the initial wave packet decisively determines the revival and fractional revivals of the system for which we give analytical results. The theory is applicable to a wide class of systems from diatomic molecules to ions in two-dimensional traps and two interacting Bose condensates.
Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such as revivals, fractional revivals, squeezing and higher-order squeezing during its temporal evolution. Further, these studies were extended to examine the role of quantum entanglement in bipartite systems. The dynamics of quantum expectation values were tracked carefully in various cases and the conditions under which a wave packet spreads chaotically, were investigated.
Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schr\"odinger equations, which describe weakly interacting Bose-Einstein condensates or light propagation in a nonlinear medium. It is shown that the dynamics of phase-space translations of the ground state of a harmonic potential is quite simple: The center follows a classical trajectory whereas its shape does not vary in time. The parabolic potential is the only one that satisfies this property. We study the time evolution of these nonlinear coherent states under perturbations of their shape or of the confining potential. A rich variety of effects emerges. In particular, in the presence of anharmonicities, we observe that the packet splits into two distinct components. A fraction of the wavepacket is transferred toward incoherent high-energy modes, while the amplitude of oscillation of the remaining coherent component is damped toward the bottom of the well.