A general formula for the amplitude-frequency ratio in shaking induced Mott insulator of atomtronic transistors

Mott insulator of atomic transport can be realized in shaken optical lattices by choosing particular ratio of driving amplitude and frequency, which has been studied as Floquet engineering with time-independent effective Hamiltonian approach. Here, we give a general formula of amplitude-frequency ratio for realization of the shaking induced insulator-conductor transition in a double-well open system, using numerical computation with instantaneous eigenstates approach. The result is owing to the fact that the instantaneous eigenstates approach is applicable in wider parameter range compared with the time-independent effective Hamiltonian approach. Analysis from the results of quantum master equation shows that the insulator effect is originated from coherent localization of atom wave packets in optical wells.