Measuring the Acceleration of Free Fall with an Atom Chip BEC Interferometer

Abstract

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.