Unusual Properties of q-Deformed Quantum Optics under Extreme Conditions and Related Topics

Alexandre M. Gavrilik, A. P. Rebesh

We study main features of the exotic case of q-deformed oscillators (so-called Tamm–Dancoff cutoff oscillator) and find some special properties: (i) degeneracy of the energy levels En1 = En1 + 1, n1 ≥ 1, at the real value[Formula: see text] of deformation parameter, as well as the occurrence of other degeneracies En1 = En1 + k, for k ≥ 2, at the corresponding values of q which depend on both n1 and k; (ii) the position and momentum operators X and Pcommute on the state|n1> if q is fixed as [Formula: see text], that implies unusual uncertainty relation; (iii) two commuting copies of the creation, annihilation, and number operators of this q-oscillator generate the corresponding q-deformation of the non-simple Lie algebra su(2) ⊕ u(1)whose nontrivial q-deformed commutation relation is: [J+, J-] = 2J0q2J3-1 where [Formula: see text] and [Formula: see text].

G Vinod

Antoni Wójcik, R. Parzyński

In recent years reports on very interesting media showing unusual optical properties have appeared in literature on atomic physics. The source of these properties is quantum interference revealed in the process of interaction of atoms with coherent light. The basis of this process is the fact that if there are at least two possibilities of realization of the process of absorption or emission of light in a given medium leading to the same final state, they interfere with each other. The result of the interference depends on relative phases of the interfering processes. However, for the interference to be observable the above phases must be well determined. The phase coherence of the medium is thus a condition necessary for obtaining the optical properties characteristic of quantum interference. This fact has been underlined by the name phaseonium given to these media by Marlan O. Scully. Recently observed unusual optical properties of a phase-coherent atomic medium (phaseonium) is explained using very simple models.

Weiping Zhang, Zeng-Bing Chen

F. T. Arecchi

M. M. S. Gualini

We demonstrated through a rigorous quantum optic method the possibility to obtain extremely short wavelengths in solid-state deformed crystals hinting that the Zeeman’s effect in a crystal lattice has an essential role in contributing to the conditions of gain enhancement. We found the same conditions of gain enhancement assuming the crystal in Electro Magnetic Transparency (EIT) conditions thus suggesting that Zeeman’s effect in crystals and EIT are somehow linked together. The paper presents the first attempt to relate the crystal deformation parameters to the Rabi’s frequencies, thus confirming rigorously the link between Zeeman’s effect and EIT.