An Uncertainty Relation in Interferometry

Jos Uffink

Karl-Peter Marzlin, Barry C. Sanders, P. L. Knight

We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenberg's uncertainty relation for position and modular momentum. We apply our theory to atom interferometry, wherein spontaneously emitted photons provide which-way information and unambiguously resolve the challenge posed by the metamaterial ``perfect lens'' to complementarity and to the Heisenberg-Bohr interpretation of the Heisenberg microscope thought experiment.

Peter Hawkes, Erwin K. Kasper

A. F. Boden

Johannes C. G. Biniok, Paul Busch, Jukka Kiukas

A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting ``modular'' position and momentum operators and their complementary counterparts, originally introduced by Aharonov and co-workers. We provide a precise argument as to why these relations are superior to the standard Heisenberg uncertainty relation at expressing the complementarity between spatial localization and the appearance of fringes. We further support the argument with explicit computations involving wave functions specifically tailored to the interference setup. Conceptually developing the idea of Aharonov and co-workers, we show how the modular momentum should reflect the given experimental setup, yielding a refined observable that accurately captures the fine structure of the interference pattern.

Ángel S. Sanz, Salvador Miret-Artés