Bloch oscillations and accelerated Bose-Einstein condensates in an optical lattice

TL;DR

This paper demonstrates that Bloch oscillations of a Bose-Einstein condensate in an optical lattice can be reliably used to measure gravity and atomic scattering lengths, with minimal dependence on initial wavepacket shape.

Contribution

The study shows that the Bloch oscillation period is independent of the initial wavepacket shape and linearly related to the scattering length, enabling precise measurements.

Findings

Oscillation period is shape-independent in real experiments.

The relation between period and scattering length is linear.

Uncertainty due to wavepacket shape is smaller than experimental errors.

Abstract

We discuss the method for the measurement of the gravity acceleration g by means of Bloch oscillations of an accelerated BEC in an optical lattice. This method has a theoretical critical point due to the fact that the period of the Bloch oscillations depends, in principle, on the initial shape of the BEC wavepacket. Here, by making use of the nearest-neighbor model for the numerical analysis of the BEC wavefunction, we show that in real experiments the period of the Bloch oscillations does not really depend on the shape of the initial wavepacket and that the relative uncertainty, due to the fact that the initial shape of the wavepacket may be asymmetrical, is smaller than the one due to experimental errors. Furthermore, we also show that the relation between the oscillation period and the scattering length of the BEC's atoms is linear; this fact suggest us a new experimental procedure for the measurement of the scattering length of atoms.