Anomalous Stern-Gerlach Measurement of a Two-Component Bose-Einstein Condensate

The result of a strong, i.e. accurate, measurement of a quantum system is constrained to lie within the eigenvalue range of the operator being measured. On the other hand, uncertain measurements of a quantum system can, on average, yield results which lie outside this range when the measurement is conditioned on the system being found in a sufficiently unlikely final state. This effect, now known as weak value amplification, has been observed in many systems using photons, including analogues of the original experiment proposed by Aharonov, Albert, and Vaidman where a spin-1/2 system can have a measured spin component of 100. Here, we present progress toward the first realization of such an experiment using massive particles. A condensate of 87Rb in a superposition of two states with different magnetic moments experiences a weak magnetic field gradient. When the spin of the atoms is found to be almost orthogonal to the initial state, the position shift in the resulting cloud is measured. Interference between the weakly shifted and unshifted states results in the overall shift of the post-selected cloud being much larger than possible in a similar strong measurement.