Interferometry with Bose-Einstein Condensates in Microgravity

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.

Figure 1

Temporal AMZI for a BEC based on Bragg scattering at a light grating: experimental images on ground (a), schematic sequence (b), and analogy to the Young double-slit experiment (c). The evolution of the BEC and the AMZI is visualized by a series of absorption images (a) of the atomic densities separated by 1 ms. The incomplete transfer is a consequence of the larger mean-field energy of the BEC necessary for the ground experiment. The interferometer starts at the time $T_0$ after the release of the BEC, when a $\pi /2$ pulse (b) made out of two counter-propagating light beams of frequency $\omega$ and $\omega +\delta$ creates a coherent superposition of two wave packets that drift apart with the two-photon recoil velocity $v_{\mathrm{rec}}=11.8\mathrm{mm}/\mathrm{s}$. After $T$ they are redirected by a $\pi$ pulse and partially recombined after $T-\delta T$ by a second $\pi /2$ pulse. A nonzero value of $\delta T$ leads to a spatial interference pattern, which we record after $\tau =53\mathrm{ms}$ in free fall. Similar to the far-field pattern observed in the Young double-slit experiment (c), the fringe spacing $l$ scales linearly with the time of expansion $T_{\mathrm{ex}}=T_0+2T-\delta T+\tau$ and is inversely proportional to the separation $d=v_{\mathrm{rec}}\delta T$ of the wave packets. The scaling factor is the ratio of Planck’s constant $h$ and the mass $m_{\mathrm{Rb}}$ of the Rubidium atoms.

Figure 2

Mach-Zehnder interferometry of a BEC in microgravity as realized in the ZARM drop tower in Bremen (a) where absorption imaging (b) brings out the interference fringes (c). The preparatory experimental sequence (a) includes capturing cold atoms in a magneto-optical trap (MOT), loading an Ioffe-Pritchard trap, creating a BEC, and applying the DKC followed by the adiabatic rapid passage (ARP). The remaining time before the capture of the capsule at the bottom of the tower is used for AI and imaging of the atoms. The AMZI below the atom chip [top plane of (b)] is formed by scattering the BEC off moving Bragg gratings generated by two counter-propagating laser beams (red arrows directed along the $y$ axis), resulting in two pairs of interfering BECs. A resonant laser beam propagating along the $x$ axis projects the shadow of the BEC onto a CCD camera. Typical interference patterns and the corresponding column densities (c) are shown for $T_{\mathrm{ex}}$ of 180 and 260 ms with corresponding fringe spacing of 75 and $107\mu \mathrm{m}$.

Figure 3

Fringe spacing (a) of two interfering BECs observed at each exit port of an AMZI with (red squares, black triangles, solid red line) and without (blue dots, solid blue line) DKC as a function of the expansion time $T_{\mathrm{ex}}$, and contrast (b) in its dependence on the time $2T-\delta T$ spent in the interferometer. Our data (blue dots, red boxes, black triangles) agree well with our models of free expansion (solid blue line) and DKC (solid red line). In the case of DKC, the temporal asymmetry $\delta T$ was increased from 1 to 2.5 ms in order to preserve the number of visible fringes across the smaller BEC by rescaling the fringes, which decreased the slope in (a). With and without DKC, the observed linear dependence has the slope of the approximation of the double slit for point particles (dash-dotted lines). An offset arises from the initial size and the nonlinear expansion of the BEC due to mean-field energy or from the focusing in DKC, which shifts the apparent location of the double slit to earlier or later times, respectively. The high contrast of the interference fringes (b), obtained by absorption imaging, typically exceeds 40% but fades away for increasing $T$. Error bars depict 1-$\sigma$-confidence bounds of the fitted parameters.