We show that a Bose-Einstein condensate (BEC) interferometer on an atom chip is capable
of making an absolute force measurement. We demonstrate this by making an absolute
measurement of the gravitational acceleration g.
We implement two interferometer arms by splitting a BEC into two symmetric wells using
radio-frequency (rf) adiabatic potentials. The independent control of the rf currents
running through the chip surface allows us to change the polarisation of the rf field and
hence the orientation of the double well potential. Tilting of the system with respect to the
horizontal introduces an energy difference Δ V and the relative phase between the BECs
starts to evolve. After moving the atoms back to their initial position and overlapping the
clouds in free fall we measure the resulting phase from the interference pattern.
In order to derive a number for g from experimental results a detailed analysis and understanding
of the interferometer scheme is essential. For this type of interferometer we have
identified two main limitations to the accuracy of the measurement: a systematic error due
to rf field gradients, and a statistical error due to phase spreading from atom-atom interactions.
Taking all errors into account we expect a value for g to within 16%. The statistical
uncertainty of the measurement is 5%.
We have a strategy for reducing all systematic errors to less than 1%. In order to reduce
the rate of phase spreading we want to squeeze the relative number of atoms between the
wells in future experiments.