Multislit interferometry and commuting functions of position and momentum

J. C. G. Biniok, P. Busch

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In a recent, modified double-pinhole diffraction experiment the existence of an interference pattern was established indirectly along with a near-perfect imaging of the double pinhole. Our theoretical analysis shows that the experiment constitutes a preparation of a quantum state that is, to a good approximation, a joint eigenstate of commuting functions of position and momentum. Gaining information about the momentum distribution by means of the particular experimental setup is thus possible with negligible impact on the position distribution. Furthermore, we construct explicitly a class of states simultaneously localised on periodic sets in position and momentum space, which are therefore eigenstates of the properties being measured jointly (to a good approximation) in multi-slit interferometry. Finally, we show that with an appropriate change of settings the experiment demonstrates the mutual disturbance of position and momentum measurements.
Original languageEnglish
Article number062116
Number of pages7
JournalPhysical Review A
Issue number6
Early online date21 Jun 2013
Publication statusPublished - 21 Jun 2013

Bibliographical note

©2013 American Physical Society. This is an author produced version of a paper published in Physical Review A. Uploaded in accordance with the publisher's self-archiving policy.


  • 81P15, 81P50,
  • quant-ph

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