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Applied Mathematics & Information Sciences

Equivalence between mirror-field-atom and ion-laser interactions

Raúl Juárez-Amaro, Arturo Zúñiga-Segundo, Francisco Soto, H. M. Moya-Cessa

Published Apr 4, 2013• 2 citations
Publisher

Abstract

We show that the interaction between a movable mirror with a quantized field tha t interacts with a two-level atom may be simplified via a transformation that involves Susskind-Glogower operator s (SGO). By using this transformation it is easy to show that we can cast the Hamiltonian, after a unitary transformation, into a Hamiltonian that is equivalent to the ion-laser Hamiltonian. We would like to stress that the transformation in terms of SGO already simplifies e nough the Hamiltonian in the sense that, in an exact way, it eliminates one of the three-subsystems, namely the quantized fie ld.

DOI
10.12785/amis/070406

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We show that the interaction between a movable mirror with a quantized field tha t interacts with a two-level atom may be simplified via a transformation that involves Susskind-Glogower operator s (SGO). By using this transformation it is easy to show that we can cast the Hamiltonian, after a unitary transformation, into a Hamiltonian that is equivalent to the ion-laser Hamiltonian. We would like to stress that the transformation in terms of SGO already simplifies e nough the Hamiltonian in the sense that, in an exact way, it eliminates one of the three-subsystems, namely the quantized fie ld.
We show that the interaction between a movable mirror with a quantized field that interacts with a two-level atom may be simplified via a transformation that involves Susskind-Glogower operators (SGO). By using this transformation it is easy to show that we can cast the Hamiltonian, after a series of small rotations, into an effective Hamiltonian that may be solved. We would like to stress that the transformation in terms of SGO already simplifies enough the Hamiltonian in the sense that, in an exact way, it "eliminates" one of the three-subsystems, namely the quantized field.