Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing

C. L. Mehta, Anil Roy, G. M. Saxena

P. L. Knight, Vladimír Bužek

Zu‐Jian Ying, Shun-Jin Wang

We use squeezing and displacement operators and apply algebraic dynamics to develop a unified solution of general time-dependent two-photon algebra systems. A set of orthogonal-and-normalized solutions are derived with the ground state being the conventional squeezed state. Landau system is given as an example.

R. Loudon

Ying, ZJWang

We use squeezing and displacement operators and apply algebraic We use squeezing and displacement operators and apply algebraic

Brif, C

We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset of algebra eigenstates. We develop the general formalism and apply it to the SU(2) and SU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in the both cases, by a method that employs analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states and intelligent states are examined and relations between them are studied by using their analytic representations.