Vol.2, No 1, 1999 pp. 31 - 38
UDC 514.84
BOSON BOGOLIUBOV GROUP
AND GENERALIZED SQUEEZED STATES
I. Mendaš1, M. J. Djordjević2
1Institute of Physics, P.O. Box 57, 11001 Belgrade,Yugoslavia
2Faculty of Physics, University of Belgrade, P.O. Box 386,
11001 Belgrade, Yugoslavia
Abstract. A convenient choice of the arbitrary phase of the Bogoliubov
unitary operator, providing the homogeneous Bogoliubov transformation of
the boson annihilation and creation operators, is proposed so that the
Bogoliubov transformations form a continuos non-Abelian subgroup of the
SL(2,C) group. Two operator identities involving this Bogoliubov operator
are established and, with their help, the closed form expressions for the
correlation amplitude and the geometric Pancharatnam) phase for ordinary
and also generalized squeezed states are obtained. Applications of these
general results to certain special cases of practical importance in the
realm of quantum optics, such as two-photon interaction process, are briefly
discussed.
Key words: Boson Bogoliubov transformation, geometric
phase, squeezed states
BOZONSKA BOGOLJUBOVLJEVA GRUPA
I GENERALIZOVANA SAŽETA STANJA
Predložen je izbor proizvoljne faze Bogoljubovljevog unitarnog operatora
koji obezbeđuje da skup svih homogenih Bogoljubovljevih transformacija
bozonskih anihilacionih i kreacionih operatora čini kontinualnu neabelovu
podrgupu SL(2,C) grupe. Ustanovljena su dva identiteta koja zadovoljava
ovakav Bogoljubovljev operator i pomoću njih su nađeni izrazi za korelacionu
amplitudu i geometrijsku (Pančaratnamovu) fazu generalizovanih sažetih
stanja. Kratko je prodiskutovana primena ovih opštih rezultata na dvofotonske
interakcione procese u kvantnoj optici.
Ključne reči: Bozonska Bogoljubovljeva transformacija, geometrijska
faza, sažeta stanja
