General Multimode Squeezed States
Abstract
By the complex multimode Bogoliubov transformation, we obtain the general forms of squeeze operators and squeezed states including squeezed vacuum states, squeezed coherent states, squeezed Fock states and squeezed coherent Fock states, for a general multimode boson system. We decompose the squeezed operator into disentangling form in normal ordering to simplify the expressions of the squeezed states. We also calculate the statistical properties of the SS. Furthermore we prove that if it is nondegenerate, a Bogoliubov transformation matrix can be decomposed into three basic matrix, by which we can not only check the criterion of the minimum uncertainty state (MUS) found by Milburn, but also prove that except the special cases, any multimode squeezed state is MUS after the original creation and annihilation operators rotate properly. We also discuss some special cases of the three basic matrices. Finally we give an analytical results of a twomode system as an example.
 Publication:

arXiv eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:quantph/0109020
 Bibcode:
 2001quant.ph..9020Q
 Keywords:

 Quantum Physics
 EPrint:
 15 pages, 0 figures, 12 references, RevTeX file