Measuring the spin of a spin-1/2 and getting a result of 7
Abstract
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, a measurement result which lies out- side of the eigenvalue spectrum of the operator being measured. Though anomalous weak values have been measured in numerous optical systems, here we present the first such realization of this experiment as originally proposed. By placing a Bose-Einstein condensate of 87Rb in a magnetic gradient and performing an unlikely postselection, we measure an effective magnification of a weak magnetic momentum kick (~ 8 μm/s) by a factor of 14. We also demonstrate that increasing the momentum kick decreases the "weakness" of the measurement and reduces the amplification.
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BibTeX
@misc{mcgowan2026measuring,
title = {{Measuring the spin of a spin-1/2 and getting a result of 7}},
author = {Joseph McGowan IV and Nicholas Mantella and Noah Baker and Aephraim M. Steinberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37822},
eprint = {2609.37822},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37822},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Measuring the spin of a spin-1/2 and getting a result of 7
AU - Joseph McGowan IV
AU - Nicholas Mantella
AU - Noah Baker
AU - Aephraim M. Steinberg
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37822
UR - https://arxiv.org/abs/2609.37822
AB - 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, a measurement result which lies out- side of the eigenvalue spectrum of the operator being measured. Though anomalous weak values have been measured in numerous optical systems, here we present the first such realization of this experiment as originally proposed. By placing a Bose-Einstein condensate of 87Rb in a magnetic gradient and performing an unlikely postselection, we measure an effective magnification of a weak magnetic momentum kick (~ 8 μm/s) by a factor of 14. We also demonstrate that increasing the momentum kick decreases the "weakness" of the measurement and reduces the amplification.
ER -