Detecting Hidden Nonlinear High Frequency Modes Beyond Fundamental Minimal Temporal Resolution Using Weak Measurements

Abstract

In this work we study whether nonlinear models of quantum mechanics can avoid detection by strong measurements, if the nonlinear effects only exist as high frequency modes. A potential physical process which could hide such modes would be amplitude level time averaging over fundamentally indistinguishable times. To that end, we have defined a temporal indistinguishability postulate which describes the averaging process, and handcrafted a nonlinear toy model well suited to avoid detection. We have demonstrated that even in such an ideal setup, tabletop weak postselected measurements can still detect nonlinear behavior and put constraints on nonlinear high frequency modes of evolution, even at frequencies beyond fundamental minimal temporal resolution.