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Bulletin of the American Physical Society

Atom interferometry, microscopy, complementarity, and the perfect lens

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

Published Jun 9, 2007• 0 citations
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Atom interferometry and quantum optics

Herman C. W. Beijerinck, K. A. H. van Leeuwen

•Jan 1, 2007•0 citations
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.
Abstract Well-collimated, high-intensity beams of neutral atoms have many applications ranging from atom microscopy to atom interferometry to ultracold atomic physics. We experimentally demonstrate a method for brightening a supersonic atomic beam and observe an increase in the phase space density by a factor of at least 20. Our scheme relies upon a permanent magnetic hexapole lens to focus a divergent beam of neutral atoms emitted from a supersonic nozzle and transverse laser cooling as the beam converges downstream from the lens so as to create a dense, narrow, Doppler-collimated atomic beam. In principle, this method can be repeated multiple times in series for further beam brightening.
Bohr's principle of complementarity predicts that in a welcher weg ("which-way") experiment, obtaining fully visible interference pattern should lead to the destruction of the path knowledge. Here I report a failure for this prediction in an optical interferometry experiment. Coherent laser light is passed through a dual pinhole and allowed to go through a converging lens, which forms well-resolved images of the respective pinholes, providing complete path knowledge. A series of thin wires are then placed at previously measured positions corresponding to the dark fringes of the interference pattern upstream of the lens. No reduction in the resolution and total radiant flux of either image is found in direct disagreement with the predictions of the principle of complementarity. In this paper, a critique of the current measurement theory is offered, and a novel nonperturbative technique for ensemble properties is introduced. Also, another version of this experiment without an imaging lens is suggested, and some of the implications of the violation of complementarity for another suggested experiment to investigate the nature of the photon and its "empty wave" is briefly discussed.