Different effective Hamiltonians in a periodic-driven Bose-Josephson junction

Area of Science:

• Quantum physics
• Many-body systems
• Condensed matter physics

Background:

• The bosonic Josephson junction is a fundamental model for studying driven many-body systems.
• It has been extensively researched for two decades, with various theoretical approaches developed.

Purpose of the Study:

• To compare five distinct theoretical methods for analyzing the bosonic Josephson junction.
• To identify the most accurate method for describing its dynamics and effective Hamiltonians.

Main Methods:

• Analysis of the bosonic Josephson junction using five different theoretical approaches.
• Verification of model validity through population imbalance dynamics and self-trapping phase transitions.
• Comparison of effective Hamiltonians derived from each method, considering terms up to order ω^{-2}.

Main Results:

• All five methods yield slightly different effective Hamiltonians, with parameter variations and potential new interactions.
• The method employing a unitary transformation to a rotating frame demonstrates the highest accuracy.
• Discrepancies between methods become pronounced when driving amplitude or interaction strengths approach the driving frequency.

Conclusions:

• The choice of theoretical method significantly impacts the description of the bosonic Josephson junction, particularly concerning effective Hamiltonian parameters and interactions.
• The rotating frame approach provides the most accurate representation among the methods studied.
• Experimental verification using quantum simulators like ultracold atoms is encouraged to validate these findings.