Abstract
In most experiments which search for violations of Born’s rule using light the diffractive elements are formed from material slits, or waveguides, which are treated classically. In this article we propose an alternative approach where the internal energy levels of particles are used instead of slits to test the superposition principle, thus removing the effect of the finite width of the slits. By quantising both the light field and the diffraction elements we propose a new way to probe Born’s rule for light in a fully quantum mechanical way.
Highlights
Non-relativistic quantum theory uses the Schrödinger equation, i ¶Y(r, ¶t t) = H Y(r, t), (1)to describe the dynamics of quantum systems.Here, ÿ is the reduced Planck constant,r is a position vector, t is time, and Hand Ψ are the Hamiltonian and the wavefunction of the system concerned
In this article we consider what happens when the internal states of spatially separated single particles are used instead of slits in an interference experiment. By quantising both the field and the diffraction element we propose a way to probe multi-path interference and test Born’s rule in a fully quantum mechanical framework
We have derived the probability density of detecting single photons scattered by linear arrays of particles each containing two internal states
Summary
To describe the dynamics of quantum systems. r is a position vector, t is time, and Hand Ψ are the Hamiltonian and the wavefunction of the system concerned. Referred to as Born’s rule, equation (2) is firmly embedded within the modern formalism of quantum mechanics, and it can be shown to arise quite naturally from the unitary, linear structure of the dynamics of the Schrödinger equation [4,5,6] Despite this fundamental role within quantum theory, there are relatively few experiments which seek to directly verify this relation [7,8,9,10,11,12,13]. In this article we consider what happens when the internal states of spatially separated single particles are used instead of slits in an interference experiment By quantising both the field and the diffraction element we propose a way to probe multi-path interference and test Born’s rule in a fully quantum mechanical framework
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