Joseph Ben Geloun and Mahouton Norbert Hounkonnou 2009 J. Phys. A: Math. Theor. 42 295202 doi:10.1088/1751-8113/42/29/295202
Joseph Ben Geloun1,2,3 and Mahouton Norbert Hounkonnou2,4
Show affiliationsThis paper deals with an extension of our previous work (Ben Geloun and Hounkonnou 2007 J. Phys. A: Math. Theor. 40 F817) by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau–Klauder type associated with generalized spin–orbit Hamiltonians. We define an annihilation operator which takes into account the finite-dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their 'dual' counterparts are also discussed. Also, by using the Hilbert space structure, a new family of NVCSs parametrized by unit vectors of the S3 sphere has been identified without making use of the annihilation operator.
15A18 Eigenvalues, singular values, and eigenvectors
81R15 Operator algebra methods (See also 46Lxx, 81T05)
81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
Issue 29 (24 July 2009)
Received 9 February 2009, in final form 13 May 2009
Published 30 June 2009
Joseph Ben Geloun and Mahouton Norbert Hounkonnou 2009 J. Phys. A: Math. Theor. 42 295202
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