We have developed a which-way experiment using visible light that is completely analogous to a recent experiment involving which-way measurement in atom interference. This simple experiment, easily accessible to undergraduate students and the resources of undergraduate departments, facilitates the examination of the key elements of which-way measurement, quantum erasure, and related mysteries of quantum measurement. The experiment utilizes a Mach–Zehnder interferometer, and visually demonstrates the loss of interference fringes when a which-way measurement is imposed, and the restoration of that pattern when the which-way information is destroyed. This device is also sensitive enough to observe interference fringes arising from single photons. We present a simple analysis of the interference appropriate for the coherent classical field limit and the single photon limit at a level accessible to undergraduates. We also briefly mention related issues on the nature of the photon.
REFERENCES
1.
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
).2.
Peter D. D.
Schwindt
, Paul G.
Kwiat
, and Berthold-Georg
Englert
, “Quantitative wave-particle duality and non-erasing quantum erasure
,” Phys. Rev. A
60
, 4285
–4290
(1999
).3.
Two such articles are by
Wendell
Holladay
, “A simple quantum eraser
,” Phys. Lett. A
183
, 280
–282
(1993
),and by
Thomas F.
Jordan
, “Disappearance and reappearance of macroscopic quantum interference
,” Phys. Rev. A
48
, 2449
–2450
(1993
).4.
Two examples are
D. F.
Walls
, “A simple field theoretic description of photon interference
,” Am. J. Phys.
45
, 952
–956
(1977
),and
Thomas F.
Jordan
, “Choosing and rechoosing to have or have not interference
,” Am. J. Phys.
69
, 155
–157
(2001
). Jordan’s article also analyzes a two-slit gedanken experiment with polarizers behind slits providing which-way information.5.
Y.
Ben-Aryeh
, D.
Ludwin
, and A.
Mann
, “A quantum mechanical description of electromagnetic and atom Mach–Zehnder interferometers
,” J. Opt. B: Quantum Semiclassical Opt.
3
, 138
–145
(2001
).6.
Ilki
Kim
and Günter
Mahler
, “Uncertainty rescued, Bohr’s complementarity for composite systems
,” Phys. Lett. A
269
, 287
–292
(2000
).7.
V.
Kidambi
, A.
Widom
, C.
Lerner
, and Y. N.
Srivastava
, “Photon polarization measurements without the quantum Zeno effect
,” Am. J. Phys.
68
, 475
–481
(2000
).8.
Berthold-Georg
Englert
, “Remarks on some basic issues in quantum mechanics
,” Z. Naturforsch., A: Phys. Sci.
54
, 11
–32
(1999
).9.
D. F. Walls, in Ref. 4.
10.
An analogy to the nonrelativistic Schrödinger equation can be developed, but its application is limited; for example, see
Richard A.
Young
, “Thinking of the photon as a quantum-mechanical particle
,” Am. J. Phys.
44
, 1043
–1046
(1976
).11.
Gordon Baym, Lectures on Quantum Mechanics (W. A. Benjamin, New York, 1969), pp. 20–25.
12.
A similar analysis is done for neutron interferometry by
G.
Badurek
and H.
Rauch
, “Neutron interferometery
,” Physica B
276
, 964
–967
(2000
).13.
A.
Einstein
, B.
Podolsky
, and N.
Rosen
, “Can quantum-mechanical description of reality be considered complete?
,” Phys. Rev.
47
, 777
–780
(1935
).14.
P.
Bertet
, S.
Osnaghi
, A.
Rauschenbeutel
, G.
Nogues
, A.
Auffeves
, M.
Brune
, J. M.
Raimond
, and S.
Haroche
, “A complementarity experiment with an interferometer at the quantum-classical boundary
,” Nature (London)
411
, 166
–170
(2001
).15.
Rodney Loudon, The Quantum Theory of Light (Oxford U.P., Oxford, 1983), 2nd ed., pp. 226–229.
16.
P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon, Oxford, 1930), p. 15.
17.
F.
Louradour
, F.
Reynaud
, B.
Colombeau
, and C.
Froehly
, “Interference fringes between two separate lasers
,” Am. J. Phys.
61
, 242
–245
(1993
).18.
A review of such experiments is provided by
H.
Paul
, “Interference between independent photons
,” Rev. Mod. Phys.
58
, 209
–231
(1986
).19.
Lloyd M.
Davis
and C.
Parigger
, “Comment on ’Interference fringes between two separate lasers,’ by F. Louradour
et al. [Am. J. Phys. 61, 242–245 (1993)],” Am. J. Phys.
62
, 951
–952
(1994
);Philip R.
Wallace
, “Comment on ’Interference fringes between two separate lasers,’
by F. Louradour et al. [Am. J. Phys. 61, 242–245 (1993)],” Am. J. Phys.
62
, 950
(1994
);Roy J.
Glauber
, “Dirac’s famous dictum on interference: one photon or two?
,” Am. J. Phys.
63
, 12
(1995
).20.
The relevant details are the subject of the quantization of the electromagnetic field, but the essential features are summarized nicely for the nonpractitioner by Walls, see Ref. 4.
21.
Two examples of such work are
G.
Badurek
, H.
Rauch
, and D.
Tuppinger
, “Neutron interferometric double-resonance experiment
,” Phys. Rev. A
34
, 2600
–2608
(1986
)and
H.
Rauch
et al., “Verification of coherent spinor rotation of fermions
,” Phys. Lett. A
54
, 425
–427
(1975
).22.
T. J.
Axon
, “Introducing Schrodinger’s cat in the laboratory
,” Am. J. Phys.
57
, 317
–321
(1989
).
This content is only available via PDF.
© 2002 American Association of Physics Teachers.
2002
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.
