Quantum motor: Directed wave-packet motion in an optical lattice

We propose a method for arbitrary manipulations of a quantum wave packet in an optical lattice by a suitable modulation of the lattice amplitude. A theoretical model allows us to determine the modulation needed to generate an arbitrary atomic trajectory; wave-packet rotations can also be implemented. The method is immediately usable in state-of-the-art experiments.

Figure 1

Directed wave-packet motion in two dimensions, obtained by direct integration of the Schrödinger equation. The plots display the probability of presence $|{\Psi }_{xy}{\left(t\right)|}^2$ integrated in time, and the arrows indicate the sense of the motion. (a) Square path formed by four straight lines; the motion starts from the left lower corner. (b) $\infty$ path, obtained by choosing ${\alpha }_x=\cos \left(\Omega t\right)$, ${\alpha }_y=\cos \left(2\Omega t\right)$; the motion starts from the intersection point. (c) The Greek letter β is formed by a combination of straight lines and arcs (motion starts from the tail of the $\beta$). Parameters of the potential are $V_{x,y}=2.5$, $F_{x,y}=0.2$, and ${\beta }_x={\beta }_y=0$ (note the different scales in each plot). The initial wave packet is a Gaussian defined by Eq. (12).

Figure 2

(a) The left plot in the top row displays eight independent atomic wave packets arbitrarily distributed in space. The potential defined by Eq. (13) sets the different wave packets in motion with a velocity directed toward the origin (situated close to the top right corner), whose amplitude increases with the distance from the origin. The atoms are thus progressively concentrated around the origin. (b) The evolution of the total spatial dispersion with respect to the origin. Parameters of the potential are $V_{x,y}=2.5$, $F_{x,y}=0.25$, $k/k_L=0.02$, and ${\beta }_x={\beta }_y=0$.

Figure 3

Rotation of the wave packet, obtained by using both a spatial and a temporal modulation of the driving.