We formulate radial coherent states for the isotropic harmonic oscillator from the unitary irreducible representations associated with the radial spectrum-generating group Sp(2) which is locally isomorphic to SU(1,1) and SO(2,1). We further consider the time evolution of a coherent-state wave packet and show that, in contrast to the ordinary oscillator coherent states, this wave packet does change its shape (periodically) as it evolves. This change of shape may be interpreted in terms of a generalized squeezing.We formulate radial coherent states for the isotropic harmonic oscillator from the unitary irreducible representations associated with the radial spectrum-generating group Sp(2) which is locally isomorphic to SU(1,1) and SO(2,1). We further consider the time evolution of a coherent-state wave packet and show that, in contrast to the ordinary oscillator coherent states, this wave packet does change its shape (periodically) as it evolves. This change of shape may be interpreted in terms of a generalized squeezing.

Physical Review AJul 1, 198815 citations

Harmonic Oscillator and Coherent and Squeezed States

Kazutaka G. Nakamura

Springer tracts in modern physicsJan 1, 20190 citations

On the construction of generalized su(1, 1) coherent states

K. Berrada, M. El Baz, Y. Hassouni

Reports on Mathematical PhysicsJan 1, 201125 citations

Generalized intelligent states and SU(1,1) and SU(2) squeezing

D. A. Trifonov

A sufficient condition for a state |ψ> to minimize the Robertson-Schrödinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized intelligent states (GIS), exhibit arbitrarily strong squeezing (after Eberly) of A and B. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the Bloch CS are subset of SU(2) GIS.A sufficient condition for a state |ψ> to minimize the Robertson-Schrödinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized intelligent states (GIS), exhibit arbitrarily strong squeezing (after Eberly) of A and B. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the Bloch CS are subset of SU(2) GIS.

arXiv:quant-ph/0001028Jan 10, 20003 citations

Squeezed and coherent states of fractional photons

Jacob Katriel, Mario Rasetti, A. I. Solomon

We define k'-photon uncertainties \ensuremath{\Delta} ${X}_{(k\mathcal{'})}$ ,\ensuremath{\Delta} ${P}_{(k\mathcal{'})}$ in k-photon states, and show that all such calculations can be correlated using a fractional photon index r\ensuremath{\equiv}k'/k. We exemplify by choosing as k-photon states the coherent states of the k-photon generalized harmonic oscillator, and also the group-theoretic coherent states corresponding to Holstein-Primakoff realizations of SU(2) and SU(1,1). We compute the squeezing obtained in these cases, and show that they have a common limit.We define k'-photon uncertainties \ensuremath{\Delta}${X}_{(k\mathcal{'})}$,\ensuremath{\Delta}${P}_{(k\mathcal{'})}$ in k-photon states, and show that all such calculations can be correlated using a fractional photon index r\ensuremath{\equiv}k'/k. We exemplify by choosing as k-photon states the coherent states of the k-photon generalized harmonic oscillator, and also the group-theoretic coherent states corresponding to Holstein-Primakoff realizations of SU(2) and SU(1,1). We compute the squeezing obtained in these cases, and show that they have a common limit.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 198746 citations

Coherent states and squeezed states of massless and massive relativistic harmonic oscillators

Jau Tang

Physics Letters AAug 1, 19961 citation

We define k'-photon uncertainties \ensuremath{\Delta}

{X}_{(k\mathcal{'})}

,\ensuremath{\Delta}

{P}_{(k\mathcal{'})}

in k-photon states, and show that all such calculations can be correlated using a fractional photon index r\ensuremath{\equiv}k'/k. We exemplify by choosing as k-photon states the coherent states of the k-photon generalized harmonic oscillator, and also the group-theoretic coherent states corresponding to Holstein-Primakoff realizations of SU(2) and SU(1,1). We compute the squeezing obtained in these cases, and show that they have a common limit.