Long-Lived Bloch Oscillations with Bosonic Sr Atoms and Application to Gravity Measurement at the Micrometer Scale

We report on the observation of Bloch oscillations on the unprecedented time scale of several seconds. The experiment is carried out with ultracold bosonic ${}^{88}\mathrm{Sr}$ atoms loaded into a vertical optical standing wave. The negligible atom-atom elastic cross section and zero angular momentum in the ground state makes ${}^{88}\mathrm{Sr}$ an almost ideal Bose gas, insensitive to typical mechanisms of decoherence due to thermalization and external stray fields. The small size of the system enables precision measurements of forces at micrometer scale. This is a challenge in physics for studies of surfaces, Casimir effects, and searches for deviations from Newtonian gravity predicted by theories beyond the standard model.

Figure 1

Simplified scheme of the apparatus used to observe Bloch oscillations and to measure $g$: Sr atoms are laser cooled and trapped at a temperature of about 400 nK in a red magneto-optical trap (MOT). The MOT laser beams are then switched off and the atoms are transferred in a vertical one-dimensional optical lattice generated by a laser beam retroreflected by a mirror; atoms are confined in a series of layers at the antinodes of the standing wave by the dipole force. We measure the momentum distribution of the atoms, after the coherent evolution in the potential given by the periodic potential plus gravity, by a time-of-flight measurement, after a free fall of 12 ms, using a resonant probe laser beam and absorption imaging on a CCD camera.

Figure 2

Time-of-flight images of the atoms recorded for different times of evolution in the optical lattice potential after switching off the MOT. In the upper part of each frame, the atoms confined in the optical lattice perform Bloch oscillations for the combined effect of the periodic and gravitational potential. The average force arising from the photon recoils transferred to the atoms compensates gravity. In the lower part, untrapped atoms fall down freely under the effect of gravity.

Figure 3

Bloch oscillation of ${}^{88}\mathrm{Sr}$ atoms in the vertical one-dimensional optical lattice under the effect of gravity. Two quantities are extracted from the analysis of the data: (a) the vertical momentum of the oscillating atoms and (b) the width of the atomic momentum distribution. From the fit of the data in (b), a Bloch frequency ${\nu }_B=574.568(3)\mathrm{Hz}$ is obtained with a damping time $\tau \sim 12\mathrm{s}$ for the oscillations. Each point is obtained by averaging over four measurements, and the error bars correspond to the mean standard deviation.

Figure 4

Vertical momentum distribution of the atoms at the Bragg reflection recorded after an evolution time in the lattice of 4 ms, 3 s, and 7 s. Bloch oscillations can be detected with a good contrast for times as long as 7 s with more than ${10}^4$ atoms. At longer times the signal-to-noise ratio is degraded due to loss of atoms induced by collisions with the background vapor pressure. For a better visibility the vertical scale was rescaled among the three graphs.