Quantum transport of bosonic cold atoms in double-well optical lattices

We numerically investigate, using the time evolving block decimation algorithm, the quantum transport of ultracold bosonic atoms in a double-well optical lattice through slow and periodic modulation of the lattice parameters (intra- and inter-well tunneling, chemical potential, etc.). The transport of atoms does not depend on the rate of change of the parameters (as along as the change is slow) and can distribute atoms in optical lattices at the quantized level without involving external forces. The transport of atoms depends on the atom filling in each double well and the interaction between atoms. In the strongly interacting region, the bosonic atoms share the same transport properties as noninteracting fermions with quantized transport at the half filling and no atom transport at the integer filling. In the weakly interacting region, the number of the transported atoms is proportional to the atom filling. We show the signature of the quantum transport from the momentum distribution of atoms that can be measured in the time-of-flight image. A semiclassical transport model is developed to explain the numerically observed transport of bosonic atoms in the noninteracting and strongly interacting limits. The scheme may serve as an quantized battery for atomtronics applications.

Figure 1

Schematic plot of the quantum transport of ultracold bosonic atoms in a double-well optical lattice. (a) Illustration of the double-well optical lattice parameters. (b) Illustration of the quantum transport process of bosonic atoms from region A to region B in the lattice. (c) The periodic modulation of the lattice parameters for the quantum transport process. Two different types of loops in the parameter space are considered: square (solid line) and elliptical (dashed line).

Figure 2

Plot of the lowest two eigenenergies with respect to $U$ for two atoms in a double well. Solid line: $\Delta =0$. Dashed line: $\Delta =10J$.

Figure 3

Plot of the number of atoms in the lattice sites 15 and 16 with respect to the atom interaction strength $U$ after one cycle of the parameter modulation illustrated in the insets. Initially ten atoms uniformly occupy the lattice sites 5 to 14. (a) A square loop. (b) An elliptical loop.

Figure 4

Plot of the density distribution of atoms after 10 cycles of the parameter modulation with the square loop. Solid line: Initial density distribution. Dashed line: Final density distribution. (a) $U=5J$. (b) $U=20J$.

Figure 5

Plot of the diffusion of atoms after one cycle of the parameter modulation. $\Delta$ is fixed at 0. $\delta$ varies from $J$ to $-J$ and then back to $J$. Solid line: Initial density distribution. Dashed line: Final density distribution after one cycle. (a) $U=5J$. (b) $U=20J$.

Figure 6

Plot of the center-of-mass motion of the atoms in one cycle of the potential modulation. Initially six atoms are uniformly distributed in three double wells. Solid line: $U=5J$, square loop. Dashed line: $U=5J$, elliptical loop. Dotted line: $U=20J$, square loop. Dashed-dotted line: $U=20J$, elliptical loop.

Figure 7

(a) Plot of the center-of-mass motion of the atoms in one cycle of the potential modulation. Initially six atoms are uniformly distributed in six double wells. Solid line: $U=5J$, square loop. Dashed line: $U=5J$, elliptical loop. Dotted line: $U=20J$, square loop. Dashed-dotted line: $U=20J$, elliptical loop.

Figure 8

The transport of atoms in the presence of a harmonic trapping potential $V_i=V_0{(i-x_o)}^2$, where $x_o$ locates at the center of the lattice.

Figure 9

Plot of the momentum distribution of atoms in the time-of-flight image. (a) $U=5J$. (b) $U=20J$.