Study Of Exchange Reaction In Ultracold ²³Na⁴⁰K Molecule And Quantum Adiabatic Doping In Optical Lattice

In the present work,we study the exchange reaction of atom-dimer pair and the quantum adiabatic doping of fermionic atoms in optical lattices.We solve the Feshbach resonance in the atomic mixture of 23Na and 40K with the coupled-channel equations,and get the s-wave scattering length near the resonance.The details are presented here.We experimentally observed the atom-exchange reaction of Na atoms and NaK Feshbach molecules near the overlapping resonances.The reaction can be tuned from the exothermic side to the endothermic side by varying the magnetic field.The state-to-state reaction rate was measured for different value of magnetic field and the threshold behavior was observed.Theoretically,we calculate the reactive cross section and the finite-temperature reaction rate coefficient by solving the STM equations and discuss the threshold behavior and Efimov physics in this universal reaction.By fitting the numerical results and experimental data,we test the the van der Waals universality.We propose to dope the fermionic atoms in the one-or two-dimensional optical lattice through adiabatic evolution.It has been pointed out that there is low tempera-ture d-wave superconductor phase in he two-dimensional Fermi-Hubbard model with repulsive interactions.The adiabatic doping proposal can keep the low entropy during the conversion of lattice and prepare the final state into the superconductor phase.Ac-cording to our numerical results,the overlap between the final state and the target state are large if the depth of lattice is small and the adiabatic doping is efficient.However,for deeper lattice,the atomic localization during the evolution destroy this procedure.We propose to induce the interatomic interaction to suppress the localization and ver-ify this According to our numerical results,the overlap between the final state and the target state are large if the depth of lattice is small and the adiabatic doping is efficient.However,for deeper lattice,the atomic localization during the evolution destroys this procedure.We propose to induce the interatomic interaction to suppress the localization and prove the efficiency of this proposal with the density matrix renormalization group calculation.The research in this work may help the study of the ultracold chemistry in the cold molecules and the quantum simulation with fermionic atoms in optical lattice.