A general formula of frequency and amplitude for shaking induced Mott insulator in atomtronic transistors

Abstract

Mott insulator of atomic transport can be realized in driven optical lattices by choosing particular ratio of driving frequency and amplitude, which has been studied as Floquet engineering with time-independent effective Hamiltonian approach. Here, we give a general formula of frequency-amplitude radio for realization of the driving 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 more wide 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.

Figures (6)

• Figure 1: (a) In the laboratory frame, the double-well potential is shaking, coupling to two atomic baths. (b) In the oscillating frame, tunneling coefficients become time dependent. (c) Atom wave packet occupies both the two optical wells, which leads to stationary current. (d) Atom population is trapped in the first well by the choice of driven frequency $\omega_{n}$ and driven amplitude $K_{n}$ ($n=1$, $2$, $3$,...). As a result, atomic current is stopped.
• Figure 2: (Color on line) (a) Atomic current as a function of time with different driving frequencies at $K=5J$. (b)-(d) Time evolution of diagonal density matrix elements (probabilities of atom occupation) corresponding to the lines in (a) for different shaking frequencies.
• Figure 3: (Color on line) (a) Atomic current as a function of time with different driving amplitudes in the case of $\omega=0.2J$. In (b)-(d), the destructed current at the driving amplitude $K=3.614J$ in (a) has is plotted under different system-reservoir coupling rates.
• Figure 4: (Color on line) (a)-(c) Spectrum of the averaged current $\langle I_{R}\rangle$, the off-diagonal density matrix element $\langle \rho_{0110}\rangle$ and the phase term $\langle e^{i\phi}\rangle$ versus the shaking frequency $\omega$. (d)-(f) Spectrum of the averaged current $\langle I_{R}\rangle$, the off-diagonal density matrix element $\langle \rho_{0110}\rangle$ and the phase term $\langle e^{i\phi}\rangle$ as a function of the shaking amplitude $K$. Here, $\omega\geq 0.1J$.
• Figure 5: (Color on line) Current spectrum in the space of shaking frequency $\omega$ and shaking strength $K$. Blue lines are the area in which system would behaves as insulation.