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 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 enough the Hamiltonian in the sense that, in an exact way, it “eliminates” one of the three-subsystems, namely the quantized field.
Ju?rez-Amaro, R.; Z??iga-Segundo, A.; Soto-Eguibar, F.; and Moya-Cessa, H.M.
"Equivalence between mirror-field-atom and ion-laser interactions,"
Applied Mathematics & Information Sciences: Vol. 07:
4, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss4/6