The dynamics of three-boson interaction and algebraic Bethe ansatz

V. A. Andreev, Olga Aleksandrovna Ivanova

Anatoli G. Izergin, V. E. Korepin

Anatoli G. Izergin, V. E. Korepin

V. A. Andreev

Branislav Jurčo

A unified approach based on Bethe ansatz in a large variety of integrable models in quantum optics is given. Second harmonics generation, three-boson interaction, the Dicke model, and some cases of four-boson interaction as special cases of su(2)⊕su(1,1)-Gaudin models are included.

Arlei Prestes Tonel, Leandro Hayato Ymai

We present three families of integrable models for Bose–Einstein condensates in a double-well potential which are based on the combination, two by two, of three algebraic realizations of the Lax operator: the bosonic realization and the su (2) and su (1, 1) Holstein–Primakoff realizations. The families of Hamiltonians describe Josephson tunneling between two condensates in a double-well potential with boson distribution dependence in the tunneling term. Two families describe models with interacting bosons and the other does not. The integrability is shown by using the quantum inverse scattering method and algebraic Bethe ansatz. The energy eigenvalues and the Bethe ansatz equations are obtained for each model proposed. In the end, we use the energy gap as a testing function to compare the proposed integrable models with the well-known integrable two-site Bose–Hubbard model to show the effect of the boson distribution in the tunneling.