Wave and particle properties of a quantum object cannot be observed simultaneously. In particular, the fringe visibility in an interferometer is limited by the amount of which-way information which can be obtained. This limit is set by the recently discovered duality relation. So far, all derivations of the duality relation are independent of Heisenberg’s uncertainty relation. Here we demonstrate that it is alternatively possible to derive the duality relation in the form of an uncertainty relation for some suitably chosen observables.
REFERENCES
1.
N. Bohr, “Discussion with Einstein on epistemological problems in atomic physics,” in Albert Einstein: Philosopher-Scientist, edited by P. A. Schilpp (Library of Living Philosophers, Evanston, 1949), pp. 200–241, reprinted in J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton U.P., Princeton, 1983), pp. 9–49.
2.
R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison–Wesley, Reading, MA, 1965), Vol. III, Chap. 1.
3.
H. M.
Wiseman
, F. E.
Harrison
, M. J.
Collett
, S. M.
Tan
, D. F.
Walls
, and R. B.
Killip
, “Nonlocal momentum transfer in welcher weg measurements
,” Phys. Rev. A
56
, 55
–75
(1997
).4.
M. O.
Scully
, B.-G.
Englert
, and H.
Walther
, “Quantum optical tests of complementarity
,” Nature (London)
351
, 111
–116
(1991
).5.
S. Haroche, “Quantum beats and time-resolved fluorescence spectroscopy”, in High-resolution Laser Spectroscopy, edited by K. Shimoda, Topics in Applied Physics Vol. 13 (Springer, New York, 1976), pp. 253–313.
6.
X. Y.
Zou
, L. J.
Wang
, and L.
Mandel
, “Induced coherence and indistinguishability in optical interference
,” Phys. Rev. Lett.
67
, 318
–321
(1991
).7.
T. J.
Herzog
, P. G.
Kwiat
, H.
Weinfurter
, and A.
Zeilinger
, “Complementarity and the quantum eraser
,” Phys. Rev. Lett.
75
, 3034
–3037
(1995
).8.
U.
Eichmann
, J. C.
Bergquist
, J. J.
Bollinger
, J. M.
Gilliban
, W. M.
Itano
, D. J.
Wineland
, and M. G.
Raizen
, “Young’s interference experiment with light scattered from two atoms
,” Phys. Rev. Lett.
70
, 2359
–2362
(1993
).9.
H.
Rauch
, A.
Zeilinger
, G.
Badurek
, A.
Wilfing
, W.
Bauspiess
, and U.
Bonse
, “Verification of coherent spinor rotation of fermions
,” Phys. Lett. A
54
, 425
–427
(1975
).10.
G.
Badurek
, H.
Rauch
, and D.
Tuppinger
, “Neutron interferometric double-resonance experiment
,” Phys. Rev. A
34
, 2600
–2608
(1986
).11.
S.
Dürr
, T.
Nonn
, and G.
Rempe
, “Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer
,” Nature (London)
395
, 33
–37
(1998
).12.
G.
Jaeger
, A.
Shimony
, and L.
Vaidman
, “Two interferometric complementarities
,” Phys. Rev. A
51
, 54
–67
(1995
).13.
B.-G.
Englert
, “Fringe visibility and which-way information: An inequality
,” Phys. Rev. Lett.
77
, 2154
–2157
(1996
).14.
S.
Dürr
, T.
Nonn
, and G.
Rempe
, “Fringe visibility and which-way information in an atom interferometer
,” Phys. Rev. Lett.
81
, 5705
–5709
(1998
).15.
P. D. D.
Schwindt
, P. G.
Kwiat
, and B.-G.
Englert
, “Quantitative wave–particle duality and nonerasing quantum erasure
,” Phys. Rev. A
60
, 4285
–4290
(1999
).16.
W. K.
Wootters
and W. H.
Zurek
, “Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr’s principle
,” Phys. Rev. D
19
, 473
–484
(1979
).17.
L. S.
Bartell
, “Complementarity in the double-slit experiment: On simple realizable systems for observing intermediate particle–wave behavior
,” Phys. Rev. D
21
, 1698
–1699
(1980
).18.
R. J.
Glauber
, “Amplifiers, attenuators, and Schrödinger’s cat
,” Ann. (N.Y.) Acad. Sci.
480
, 336
–372
(1986
).19.
D. M.
Greenberger
and A.
Yasin
, “Simultaneous wave and particle knowledge in a neutron interferometer
,” Phys. Lett. A
128
, 391
–394
(1988
).20.
L.
Mandel
, “Coherence and indistinguishability
,” Opt. Lett.
16
, 1882
–1883
(1991
).21.
J.
Summhammer
, H.
Rauch
, and D.
Tuppinger
, “Stochastic and deterministic absorption in neutron-interference experiments
,” Phys. Rev. A
36
, 4447
–4455
(1987
).22.
P.
Mittelstaedt
, A.
Prieur
, and R.
Schieder
, “Unsharp particle–wave duality in a photon split-beam experiment
,” Found. Phys.
17
, 891
–903
(1987
).23.
W.
Heisenberg
, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
,” Z. Phys.
43
, 172
–198
(1927
);for an English translation see J. A. Wheeler and W. H. Zurek in Ref. 1, pp. 62–84.
24.
H. P.
Robertson
, “The uncertainty principle
,” Phys. Rev.
34
, 163
–164
(1929
).25.
W. H.
Zurek
, “Decoherence and the transition from quantum to classical
,” Phys. Today
44
, 36
–44
(October 1991
).26.
B.-G.
Englert
, “Remarks on some basic issues in quantum mechanics
,” Z. Naturforsch., A: Phys. Sci.
54
, 11
–32
(1999
).
This content is only available via PDF.
© 2000 American Association of Physics Teachers.
2000
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
