Quantum Group Analogues of Squeezed States

Xiang‐Guo Meng, Ji‐Suo Wang

Song Tong-Qiang, Hong-Yi Fan

E. Celeghini, Salvatore DeMartino, S. Desiena +2 more

A. I. Solomon, Jacob Katriel

The authors present the results of an analysis of the squeezing of components of the (conventional) electromagnetic field in quantum group analogues of the Heisenberg-Weyl (HW) coherent state and SU(1,1) squeezed state. They find that squeezing occurs for all finite-q values not equal to unity in the HW q-coherent state, in contrast to the usual case; and also in the SU q (1,1) case, although here less than in the usual (q=1) SU(1,1) squeezed state.

A. I. Solomon

We start from the viewpoint of quantum canonical transformations, analogues of the usual classical canonical transformations. We show that in the quantum case, such transformations lead naturally to the definition of some important quantum optics states, including the vacuum, coherent states, squeezed vacuum and squeezed states. We then go on to consider quons, operators satisfying deformed versions of the canonical commutation relations. Extending the idea of a canonical transformation to deformed quantum commutators gives quon analogues of these states, quon states. We finally show that this approach provides us with defining relations for some quantum groups.

Sibel Başkal, Young S Kim, Marilyn E. Noz