Observe the predicted amplification from reducing cloud size

Investigate whether reducing the initial atomic-cloud size while maintaining sufficient atom number causes a fixed momentum kick to become weaker, so that the measured weak-value amplification deviates from the weak-value prediction at smaller postselection angles and reaches a larger, higher, and narrower amplification peak.

Background

The experiment examines weak-value amplification in a Bose–Einstein condensate of rubidium-87 atoms subjected to a weak Stern–Gerlach interaction. For a fixed momentum kick, reducing the condensate’s initial spatial size increases its momentum uncertainty and is therefore expected to make the measurement weaker. The predicted consequence is that the experimental data should remain closer to the weak-value approximation over a narrower region near the orthogonal postselection, while producing a larger amplification factor with higher and narrower peaks.

The authors report that they could not observe this behavior because the available method for significantly reducing the cloud size also reduced the atom number, causing a loss of signal. Establishing this prediction would require an experimental protocol—possibly involving a Feshbach resonance—that reduces interaction energy and cloud size without compromising the signal.

References

If instead the initial size is made smaller, this increases the momentum uncertainty, and therefore a given momentum kick would be made ``more weak''. The expectation in this case is that the data should first deviate from the weak value prediction at a smaller value of \delta and reach a larger amplification factor; the peaks should be higher and narrower. However, we were not able to observe this; the only available method to significantly reduce the cloud size required also reducing the atom number, resulting in a loss of signal.

— Measuring the spin of a spin-1/2 and getting a result of 7  (2609.37822 - McGowan et al., 29 Sep 2026) in Section 4, Results