Dynamical su q(2) symmetry in nonlinear Quantum Optics

Xuesong Gao

Ángel Ballesteros, S. M. Chumakov

We consider a new exactly solvable nonlinear quantum model as a Hamiltonian defined in terms of the generators of the su q (2) algebra. The corresponding matrix elements of finite rotations (the q -deformed Wigner d functions) are introduced. It is shown that the quantum optical model of the three-wave interaction has an approximate su q (2) dynamical symmetry given by this Hamiltonian. Such q symmetry allows us to investigate the spectral and dynamical properties of the three wave model through new perturbation techniques.

Eiichi Hanamura, Yutaka Kawabe, Akio Yamanaka

A. B. Klimov, L. L. Sánchez-Soto, A. Navarro +1 more

A general and systematic method for obtaining eiective Hamiltonians that describe diierent nonlinear optical processes is discussed. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter, dictated by the process under consideration, becomes small, a diagonal eiective Hamiltonian is obtained immediately, that correctly represents the dynamics for arbitrary states and long times. The technique is extended to su(3) and su(N), finding the corresponding eiective Hamiltonians when some resonance conditions are fulfilled.

Klimov, A B, Sánchez-Soto, L L, Navarro, A +1 more

We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the dynamical symmetry of the original model. When some physical parameter, dictated by the process under consideration, becomes small, we immediately get a diagonal effective Hamiltonian that correctly represents the dynamics for arbitrary states and long times. We extend the technique to su(3) and su(N), finding the corresponding effective Hamiltonians when some resonance conditions are fulfilled.

Sigurd Dyrting, Wenyu Chen, Gerard J Milburn