Quasi-exactly solvable models in nonlinear optics

Abstract

We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic generation and photon cascades. For each model, we construct a complete set of commuting integrals of motion of the Hamiltonian, fully characterize the common eigenspaces of the integrals of motion, and show that the action of the Hamiltonian in these common eigenspaces can be represented by a quasi-exactly solvable reduced Hamiltonian, whose expression in terms of the usual generators of sl(2) is computed explicitly.

11 pages, LaTeX

References in corpus (1)

• Quasi-exactly solvable quartic Bose Hamiltonians

Cited by in corpus (8)

• Polynomial algebras and exact solutions of general quantum non-linear optical models I: Two-mode boson systems
• Intercepts of the momentum correlation functions in μ-Bose gas model and their asymptotics
• Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems
• Algebraic treatments of the problems of the spin-1/2 particles in the one and two-dimensional geometry: a systematic study
• Polynomially deformed oscillators as k-bonacci oscillators
• Hiking a generalized Dyck path: A tractable way of calculating multimode boson evolution operators
• Exact solution for a class of quantum models of interacting bosons
• Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations