Diffraction of a Bose-Einstein Condensate from a Magnetic Lattice on a Microchip

We experimentally study the diffraction of a Bose-Einstein condensate from a magnetic lattice, realized by a set of 372 parallel gold conductors which are microfabricated on a silicon substrate. The conductors generate a periodic potential for the atoms with a lattice constant of $4\mu \mathrm{m}$. After exposing the condensate to the lattice for several milliseconds we observe diffraction up to fifth order by standard time of flight imaging techniques. The experimental data can be quantitatively interpreted with a simple phase imprinting model. The demonstrated diffraction grating offers promising perspectives for the construction of an integrated atom interferometer.

Figure 1

Sketch of the experimental situation. (a) Current scheme of the magnetic lattice. The currents in neighboring conductors are equal and oppositely poled. (b) The condensate approaches the lattice during a vertical oscillation ($y$ direction) in an elongated harmonic trap. After phase imprinting the condensate is released from the trapping potential.

Figure 2

Shape of the lattice potential (to scale). Close to the surface (small values of $y$) the harmonic trapping potential is distorted by the periodic magnetic field of the lattice. The lower figure shows vertical cuts of the potential. Initially the condensate is generated in a harmonic trap at a distance of $30\mu \mathrm{m}$ from the surface (a). Then the minimum is suddenly shifted closer to the surface by a controlled displacement $d$. In curve (b) $d$ amounts to a value of $15\mu \mathrm{m}$. The dashed line indicates the potential energy of the condensate after the displacement.

Figure 3

Absorption images and vertically integrated density profiles after $\tau =20\mathrm{ms}$ time of ballistic expansion for three different displacements $d$ of 13, 14, and $14.6\mu \mathrm{m}$. The distance $z_0=v_l\times \tau$ corresponds to one reciprocal lattice velocity $v_l$. The density profiles can be described by the sum of up to 5 overlapping diffraction orders (solid line). While the relative strength of each diffraction order is given by the phase imprint parameter $S$ an additional Gaussian density distribution (dashed line) is used to take account of the fraction of thermal atoms.

Figure 4

For each displacement $d$ the fit of the density profiles (Fig. 3) yield the corresponding imprint parameter $S$. Significant phase imprinting starts at a displacement of about $12\mu \mathrm{m}$ and raises steadily with increasing displacement.