The double slit experiment provides a classic example of both interference and the effect of observation in quantum physics. When particles are sent individually through a pair of slits, a wave-like interference pattern develops, but no such interference is found when one observes which “path” the particles take. We present a model of interference, dephasing, and measurement-induced decoherence in a one-dimensional version of the double-slit experiment. Using this model, we demonstrate how the loss of interference in the system is correlated with the information gain by the measuring apparatus/observer. In doing so, we give a modern account of measurement in this paradigmatic example of quantum physics that is accessible to students taking quantum mechanics at the graduate or senior undergraduate levels.
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The exact wavefunction emerging from the slits in an experimental set-up will be complicated, depending on the exact slit shape geometry, the incoming state, particle type, etc. A superposition of Gaussian wavepackets, which we consider, leads to a clean presentation of interference and measurement. A square wavepacket, for , with being the Heaviside step-function at each slit, which matches the ideal geometry of the slit, is also tractable, and can give a suitable extension of this work for class projects. The actual wavefunction, however, will be more complicated. Indeed, a reasonable approximate form is (and zero for and ) at each slit of width . This function, while only approximate, is already non-analytic, but can both match the geometry and have smooth boundaries.
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Students reading this might find it enlightening to perform the computation showing that the entropies remain unchanged by independent evolution of the system and apparatus.
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