Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations

We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.Comment: LaTex file, 13 pages, 3 figure

An algebraic approach to the Tavis-Cummings problem

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.Comment: 13 pages, 7 figure

Polarization dependent behavior of CdS around the first and second LO-phonon modes

The concept of squeezing is discussed for multimode quantum light beams with the consideration of polarization using the polarization gauge SU (2) invariance of free electromagnetic fields. We separate the polarization degrees of freedom from other ones, and consider uncertainty relations characterizing polarization observables. As a consequence, we obtain a new classification of polarization states of light within quantum optics. " 1994.",,,,,,"10.1016/0375-9601(94)90720-X",,,"http://hdl.handle.net/20.500.12104/43685","http://www.scopus.com/inward/record.url?eid=2-s2.0-29344441313&partnerID=40&md5=b2733fefcb2c3e4031426649479670f1",,,,,,"05-jun",,"Physics Letters A",,"38

Polarization squeezing and new states of light in quantum optics

The concept of squeezing is discussed for multimode quantum light beams with the consideration of polarization using the polarization gauge SU (2) invariance of free electromagnetic fields. We separate the polarization degrees of freedom from other ones, and consider uncertainty relations characterizing polarization observables. As a consequence, we obtain a new classification of polarization states of light within quantum optics. © 1994