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Analytical solution of few-body fermionic model in synthetic gauge field

Through the laser cooling technique, the temperature of cold atom or ion reaches nK level. With the advantage of highly controllable property, cold atom systems have been widely applied to quantum precision measurement, atomic spectroscopy, quantum computer, quantum simulation. It is vital to analyze the cold atom system exactly. By introducing a Bethe-type wavefunction, we investigate the two-body fermion system interacted by synthetic gauge field and contact interaction in a ring trap. The exact energy spectrum has been given, which show lower eigenenergy compared to the system without spin-orbit coupling. The density distributions and momentum distributions have been analyzed for various spin-orbit coupling parameters.