Two-site Bose-Hubbard model with nonlinear tunneling: Classical and quantum analysis

Abstract

The extended Bose-Hubbard model for a double-well potential with atom-pair tunneling is studied. Starting with a classical analysis we determine the existence of three different quantum phases: selftrapping, phase-locking and Josephson states. From this analysis we built the parameter space of quantum phase transitions between degenerate and non-degenerate ground states driven by the atom-pair tunneling. Considering only the repulsive case, we confirm the phase transition by the measure of the energy gap between the ground state and the first excited state. We study the structure of the solutions of the Bethe ansatz equations for a small number of particles. An inspection of the roots for the ground state suggests a relationship to the physical properties of the system. By studying the energy gap we find that the profile of the roots of the Bethe ansatz equations is related to a quantum phase transition.

Energy-level crossings and number-parity effects in a bosonic tunneling model

“…Fig. 6in[20])• Self-Trapping/Josephson: γ + λ = −1 for λ ≤ −1/2;• Phase-Locking/Self-Trapping: γ = λ for λ ≤ −1/2;• Josephson/Phase-Locking: γ = −1/2 for λ ≥ −1/2.The three boundaries meet at the triple point (λ, γ) = (−1/2, −1/2).…”

Arnold web and dynamical tunneling in a four-site Bose-Hubbard model

“…The Bose-Hubbard model has been particularly useful [4][5][6] in understanding several aspects of the trapped BECs. Interestingly, insights into the fragmentation of the two [7][8][9][10][11][12] and the three [13][14][15][16] well trapped BECs have been gained from analyzing the classical dynamics associated with the Bose-Hubbard Hamiltonian (BHH). As the classical limit Hamiltonian is nonlinear, phenomenon such as bifurcations, chaos leave their imprint on the quantum dynamics of the condensate.…”

Phononic Josephson oscillation and self-trapping with two-phonon exchange interaction

“…In contrast to all hitherto realized BJJs, where two nonlinear bosonic systems are coupled by hopping of single bosons, we here propose a BJJ in two nonlinear mechanical modes coupled through two-phonon exchange interaction. The Bose-Hubbard model with atom-pair tunneling [22][23][24][25][26] or twophoton exchange [27][28][29][30][31][32][33] has been studied for years. However, the realization of two-phonon exchange interaction in the mechanical systems is still lack of effective method.…”