The uncertainty relation in which-way experiments: how to observe directly the momentum transfer using weak values

作者：J L Garretson, Howard M. Wiseman, D. T. Pope, David Thomas Pegg · 发表于：Journal of Optics B Quantum and Semiclassical Optics · 年份：2004 · DOI：10.1088/1464-4266/6/6/008 · 被引用次数：22 · 研究领域：Quantum Mechanics and Applications、Quantum Information and Cryptography、Spectroscopy and Quantum Chemical Studies

A which-way measurement destroys the twin-slit interference pattern. Bohr argued that this can be attributed to the Heisenberg uncertainty relation: distinguishing between two slits a distance s apart gives the particle a random momentum transfer of order h / s . This was accepted for more than 60 years, until Scully, Englert and Walther (SEW) proposed a which-way scheme that, they claimed, entailed no momentum transfer. Storey, Tan, Collett and Walls (STCW), on the other hand, proved a theorem that, they claimed, showed that Bohr was right. This work reviews and extends a recent proposal (Wiseman 2003 Phys. Lett. A 311 285) to resolve the issue using a weak-valued probability distribution for momentum transfer, . We show that must be nonzero for some . However, its moments can be identically zero, such as in the experiment proposed by SEW. This is possible because is not necessarily positive definite. Nevertheless, it is measurable experimentally in a way understandable to a classical physicist. The new results in this paper include the following. We introduce a new measure of spread for : half the length of the unit-confidence interval. We conjecture that it is never less than h /4 s , and find numerically that it is approximately h /1.59 s for an idealized version of the SEW scheme with infinitely narrow slits. For this example, the moments of , and of the momentum distributions, are undefined unless a process of apodization is used. However, we show that by considering su...