近日，美国查普曼大学的Andrew N. Jordan与美国罗切斯特大学的 A. Nick Vamivakas等人合作并取得一项新进展。经过不懈努力，他们揭示了任意量子可观测值的超现象。相关研究成果已于2024年7月8日在国际知名学术期刊《物理评论A》上发表。

据悉，当一个全局有限带宽函数局部振荡快于它的最高傅立叶分量时，就会发生超振荡。

该研究团队将这一独特效应拓展至任意量子力学算子，将其弱值作为研究对象，其中预选态设定为一系列本征态的叠加，这些本征态对应着一定的本征值范围，而后选态则聚焦于粒子的局部位置。当该算子的弱值超出其固有的特征值边界时，即展现出一种超越常规的行为模式。对于总角动量和总能量，研究人员给出了这种效应的示例性说明。在后一种情况下，研究人员通过仅使用有限能量态的有界叠加，可以构造出一个在实线上处处收敛的势序列，其渐近能量趋于零，实现了“从无到有”的能量现象。

这个极限要求在其大小偏离所考虑极限区域中对粒子进行后选。在这个例子中，他们进一步表明，超能量与时间上的超振荡有关，其速率由局部超能量除以约化普朗克常数给出。这个例子展示了在尽可能宽的空间区域内，用接近零能态的相干叠加来模拟高能量态的可能性。研究人员提供了这些特征的数值证据，以进一步支持和阐明他们的主张。

附：英文原文

Title: Superphenomena for arbitrary quantum observables

Author: Andrew N. Jordan, Yakir Aharonov, Daniele C. Struppa, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Jeff Tollaksen, John C. Howell, A. Nick Vamivakas

Issue&Volume: 2024/07/08

Abstract: Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier component. We generalize this effect to arbitrary quantum-mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehavior of this operator occurs whenever the operator's weak value exceeds its eigenvalue bound. We give illustrative examples of this effect for total angular momentum and energy. In the latter case, we demonstrate a sequence of harmonic oscillator potentials where a finite-energy state converges everywhere on the real line, using only bounded superpositions of states whose asymptotic energy vanishes—“energy out of nothing.” This limit requires postselecting the particle in a region whose size diverges in the considered limit. We further show in this example that the superenergy is associated with superoscillations in time with a rate given by the local superenergy divided by the reduced Planck's constant. This example demonstrates the possibility of mimicking a high-energy state with coherent superpositions of nearly zero-energy states for as wide a spatial region as desired. We provide numerical evidence of these features to further bolster and elucidate our claims.

DOI: 10.1103/PhysRevA.110.012206

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.012206