Time-modulated Hamiltonian for interpreting Mach-Zehnder interferometer delayed-choice experiments

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Many delayed-choice experiments based on Mach-Zehnder interferometers (MZI) have been thought and made to address the fundamental problem of wave-particle duality. Conventional wisdoms long hold that by inserting or removing the second beam splitter (BS2) in a controllable way, microscopic particles (photons, electrons, etc.) transporting within the MZI can lie in the quantum superposition of the wave and particle state as ψ=awψwave+aₚψₚarticle. Here we present an alternative interpretation to these delayed-choice experiments. We notice that as all composite devices of MZI including BS2 are purely classical, the inserting and removing operation of BS2 imposes a time-modulated Hamiltonian Hₘod(t)=a(t)Hᵢn+b(t)Hₒut, instead of a quantum superposition of Hᵢn and Hₒut as H=awHᵢn+bₚHₒut, to act upon the incident wave function. Solution of this quantum scattering problem, rather than the long held quantum eigen-problem yields a synchronically time-modulated output wave function as ψₘod=a(t)ψwave+b(t)ψₚarticle. As a result, the probability of particle output from the MZI behaves as if they are in the superposition of the wave and particle state when many events over time accumulation are counted and averaged. We expect these elementary but insightful analyses will shed a new light on exploring basic physics beyond the long-held wisdom of wave-particle duality and principle of complementarity.