Basic Properties of Coherent and Generalized Coherent Operators Revisited

Abstract

In this letter we make a brief review of some basic properties (the matrix elements, the trace, the Glauber formula) of coherent operators and study the corresponding ones for generalized coherent operators based on Lie algebra su(1,1). We also propose some problems. *

The Wigner-Heisenberg Algebra in Quantum Mechanics

“…. Let us to conclude this section presenting the following comments: one can generate the called canonical coherent states, which are defined as the eigenstates of the lowering operator B − ( c 2 − 1) of the bosonic sector, according to the Barut-Girardello approach [12,13] and generalized coherent states according to Perelomov [14,15]. Results of our investigations on these coherent states will be reported separately.…”

Mathematical structure of Rabi oscillations in the strong coupling regime

“…We have written |J, 0 instead of |0 to emphasize the spin J representation, see [4]. From (14), states |J, n are given by…”

“…We can construct the spin K and J representations by making use of Schwinger's boson method. But we don't repeat here, see for example [7]. We list matrix elements of coherent operators U(z).…”

“…But they are not so easy to handle in spite of having the disentangling one corresponding to the elementary BCH formula. In [7] and [14] the author determined all matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su (2).…”

Mathematical foundations of holonomic quantum computer

“…In this section we make a generalization of coherent operators based on C and su(2) and su(1, 1) [31] and [32], and propose a generalization of the method in sect.3.3.…”