Synthetic random flux model in a periodically driven optical lattice

We propose a realization of a synthetic random flux model in a two-dimensional optical lattice. Starting from Bose-Hubbard Hamiltonian for two atom species, we show how to use fast-periodic modulation of the system parameters to construct a random gauge field. We investigate the transport properties of such a system and describe the impact of time-reversal symmetry breaking and correlations in disorder on Anderson localization length.

Figure 1

Anderson localization length (in units of the lattice constant) in function of the energy (in units of tunneling amplitude). Diagonal disorder is given by Poisson distribution of frozen atoms (with mean ${\rho }_{\mathrm{f}}=2.5$) and interaction amplitude $V_0=1.5$. Black solid curve is for undriven system and red dashed is for $\delta$ modulation (9) with modulation parameter $V_1/\omega =1$ (for the correlated disorder case).

Figure 2

The maximum localization length (in units of the lattice constant) as a function of the parameter of modulation $V_1/\omega$. Top: Antisymmetric lattice modulation $t_1^{\left(\mathrm{x}\right)}=-t_1^{\left(\mathrm{y}\right)}$. Red squares and black disks shows results for harmonic modulation (7) for correlated and uncorrelated disorder respectively. Green diamonds and blue triangles are results for approximated harmonic modulation (8) also for correlated and uncorrelated cases. Bottom: Results for $\delta$ lattice modulation (9) red squares are results for diagonal disorder correlated with off-diagonal, while black circles are for uncorrelated case (lines are guides for the eye).

Figure 3

Top panel: A single lattice plaquette. By cutting the outer connections at sites A and B, we could calculate tunneling through plaquette from site 1 to site 2 as given by (10). Bottom panel: The effective tunneling across the diagonal of the plaquette as a function of $V_1/\omega$ for uncorrelated (black circles) and correlated (red squares) of $\delta$-type lattice modulations at a single energy $E$ value. Similar behavior is observed at other energies.

Figure 4

Maximum localization length as a function of the mean of the absolute flux through a single plaquette (left) and as a function of the variance of the flux through plaquette (right). Results are presented for the case of no correlation between the diagonal and the off-diagonal disorder. Black diamonds correspond to the approximate symmetric harmonic modulation (8) while red circles to the approximate antisymmetric harmonic modulation ($t_1^{\left(\mathrm{x}\right)}=-t_1^{\left(\mathrm{y}\right)}$). Blue squares stand for the $\delta$ modulation (9) and green triangles denote for the pure diagonal disorder in the staggered field (lines are drawn to guide the eye).