Diffraction, Beamsplitting, and decoherence

For my ongoing rudimentary musings on this topic: decoherence.pdf

In a famous series of discussions Einstein and Bohr have shed light on several topics in quantum mechanics. One of these is the double slit interference experiment [1]. Quantum mechanics predicts an interference pattern, but only if we have no knowledge of which slit the particle went through. Einstein devised a thought-experiment that would measure through which slit the particle went and show the interference pattern. If such an experiment could be performed he hoped that it would show that quantum mechanics is incomplete. Einstein considered a particle beam illuminating a single slit screen placed in front of a double slit screen. Ingeniously he suggested that the recoil of the single slit screen could be measured to determine through which slit the particle would move. Because the recoil would be present regardless if it is measured or not, it appears that such a measurement would not affect the experiment in any way, and the interference pattern would remain. Bohr replied that when we measure the recoil, i.e. the momentum of the screen, accurately enough to determine through which slit the particle went, the uncertainty in our knowledge of the position of the slit is so large that the interference pattern is obscured. In other words, quantum mechanics, through Heisenberg’s uncertainty relation, protects itself. In a later treatise Wootters and Zurek analyze this thought experiment quantitatively [2]. This allows relating the probability of going through one slit with the contrast of the interference pattern.

It is interesting to note that in both these discussions the single slit screen is described quantum mechanically. But a single slit screen is a macroscopic object, which appears to be in conflict with its quantum mechanical description. This issue has to our knowledge not been quantitatively analyzed earlier. This issue becomes conceptually more interesting when we realize that the single slit diffraction effectively creates an entangled state.

Would not decoherence of the slit state remove the same coherence we need to see interference in the particle state? The main purpose of this paper is to address this question.

  1. Wheeler and Zurek, Quantum Theory and Measurement p.9-49, 1983
  2. Wootters K. W., and Zurek W. H., Phys. Rev. D19, 473-84 (1979)