A double-slit ‘which-way’ experiment on the complementarity–uncertainty debate

A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle-behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions at a distance s apart transfers a random momentum q ~ /s to the particle. This claim has been subject to debate: Scully et al (1991 Nature?351 111) asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al (1994 Nature?367 626) asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond [?/s, /s], but nevertheless has a variance consistent with zero. This weak-valued momentum-transfer distribution Pwv(q) thus reflects both sides of the debate.

[1]  H. Wiseman.  Grounding Bohmian mechanics in weak values and bayesianism , 2007, 0706.2522.

[2]  J. Wheeler,et al.  Quantum theory and measurement , 1983 .

[3]  H M Wiseman,et al.  Measurement of quantum weak values of photon polarization. , 2005, Physical review letters.

[4]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[5]  Fast light, slow light, and phase singularities: a connection to generalized weak values. , 2003, Physical review letters.

[6]  H. Wiseman,et al.  Uncertainty over complementarity? , 1995, Nature.

[7]  H. Jehle,et al.  Albert Einstein: Philosopher-Scientist. , 1951 .

[8]  D. Rohrlich,et al.  Cherenkov radiation of superluminal particles , 2001, quant-ph/0107025.

[9]  M. Scully,et al.  Quantum eraser: A proposed photon correlation experiment concerning observation and , 1982 .

[10]  D. Walls,et al.  NONLOCAL MOMENTUM TRANSFER IN WELCHER WEG MEASUREMENTS , 1997 .

[11]  Ritchie,et al.  Realization of a measurement of a "weak value" , 1991, Physical review letters.

[12]  Steinberg.  How much time does a tunneling particle spend in the barrier region? , 1995, Physical review letters.

[13]  G. Rempe,et al.  Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer , 1998, Nature.

[14]  Experimental realization of the quantum box problem , 2003, quant-ph/0310091.

[15]  D. Allen-Booth,et al.  Classical Mechanics 2nd edn , 1974 .

[16]  W. Heisenberg.  Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[17]  K. Mølmer.  Counterfactual statements and weak measurements: an experimental proposal , 2001, quant-ph/0109042.

[18]  R. Leighton,et al.  Feynman Lectures on Physics , 1971 .

[19]  Michael Seadle.  Measurement , 2007, The Measurement of Information Integrity.

[20]  Y. Aharonov,et al.  Modular variables in quantum theory , 1969 .

[21]  H. Weyl.  The Theory Of Groups And Quantum Mechanics , 1931 .

[22]  Howard Mark Wiseman,et al.  Weak values, quantum trajectories, and the cavity-QED experiment on wave-particle correlation , 2002 .

[23]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[24]  H. Wiseman,et al.  The Uncertainty Relation in "which-way" experiments: How to Observe Directly the Momentum Transfer. , 2003, quant-ph/0310081.

[25]  D. Walls,et al.  Path detection and the uncertainty principle , 1994, Nature.

[26]  H. Weyl.  Gruppentheorie und Quantenmechanik , 1928 .

[27]  C. Ross.  Found , 1869, The Dental register.

[28]  Benni Reznik,et al.  Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values , 2001 .

[29]  D. Walls,et al.  Complementarity and uncertainty , 1995, Nature.

[30]  B. Englert,et al.  Quantum optical tests of complementarity , 1991, Nature.

[31]  H. M. Wiseman,et al.  Extending Heisenberg's Measurement-Disturbance Relation to the Twin-Slit Case , 1998 .

[32]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[33]  B. Englert,et al.  Complementarity and uncertainty , 1995, Nature.

[34]  William K. Wootters,et al.  Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle , 1979 .

[35]  Vaidman,et al.  How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. , 1988, Physical review letters.

[36]  Directly observing momentum transfer in twin-slit “which-way” experiments , 2003, quant-ph/0303139.

[37]  V. Scarani,et al.  Optical telecom networks as weak quantum measurements with postselection. , 2003, Physical review letters.