A Weak Stern-Gerlach Measurement: Measuring the Spin of a Spin-1/2 System and Getting a Result of 5

The weak value of an operator is the average result of measuring that operator on a quantum system given specified initial and final states. The overlap between these states appears in the denominator of the weak value, and thus if that overlap is small, the weak value can be arbitrarily large. In 1988, Albert, Aharonov, and Vaidman proposed a weak Stern-Gerlach experiment which would be able to measure a so-called anomalous weak value, where the measurement result lies outside of the eigenvalue spectrum of the operator being measured. We have performed the first such realization of this experiment using massive particles. By placing a BEC of 87Rb in a magnetic gradient and performing an unlikely postselection, we measure an effective magnification of the weak magnetic momentum kick (~20 um/s) of over a factor of 5. We also, for the same kick, measure the negative weak value, where the apparent momentum shift is in the opposite direction as the magnetic kick.