In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical path length of the photons carrying which-way information. In the second setup, we use fiber-optic cables to elongate the path of these photons after their passage through the polarization analyzer but prior to their arrival at the detector. We compare our results to data obtained in the absence of a delay and find excellent agreement. This shows that the timing of the erasure is irrelevant, as also predicted by quantum mechanics. The experiment can serve as a valuable pedagogical tool for conveying the fundamentals of quantum mechanics.
References
1.
J. A.
Wheeler
, “The “past” and the “delayed-choice” double-slit experiment
,” in Mathematical Foundations of Quantum Theory
, edited by A. R.
Marlow
(Academic Press
, New York
, 1978
), pp. 9
–48
.2.
J. A.
Wheeler
, “Law without law
,” in Quantum Theory and Measurement
(Princeton U.P.
, Princeton, NJ
, 1983
), pp. 182
–213
.3.
M. O.
Scully
and K.
Drühl
, “Quantum eraser: A proposed photon correlation experiment concerning observation and “delayed choice” in quantum mechanics
,” Phys. Rev. A
25
, 2208
–2213
(1982
).4.
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
).5.
P.
Mittelstaedt
, A.
Prieur
, and R.
Schieder
, “Unsharp particle-wave duality in a photon slit-beam experiment
,” Found. Phys.
17
, 891
–903
(1987
).6.
D. M.
Greenberger
and A.
Yasin
, “Simultaneous wave and particle knowledge in a neutron interferometer
,” Phys. Lett. A
128
, 391
–394
(1988
).7.
G.
Jaeger
, A.
Shimony
, and L.
Vaidman
, “Two interferometric complementarities
,” Phys. Rev. A
51
, 54
–67
(1995
).8.
B.-G.
Englert
, “Fringe visibility and which-way information: An inequality
,” Phys. Rev. Lett.
77
, 2154
–2157
(1996
).9.
S.
Dürr
and G.
Rempe
, “Can waveparticle duality be based on the uncertainty relation?
,” Am. J. Phys.
68
, 1021
–1024
(2000
).10.
D. M.
Greenberger
, M. A.
Horne
, and A.
Zeilinger
, “Multiparticle interferometry and the superposition principle
,” Phys. Today
46
(8
), 22
–29
(1993
).11.
M. O.
Scully
, B. G.
Englert
, and H.
Walther
, “Quantum optical tests of complementarity
,” Nature (London)
351
, 111
–116
(1991
).12.
B.-G.
Englert
, M. O.
Scully
, and H.
Walther
, “Quantum erasure in double-slit interferometers with which-way detectors
,” Am. J. Phys.
67
, 325
–329
(1999
).13.
J. J.
Thorn
, M. S.
Neel
, V. W.
Donato
, G. S.
Bergreen
, R. E.
Davies
, and M.
Beck
, “Observing the quantum behavior of light in an undergraduate laboratory
,” Am. J. Phys.
72
, 1210
–1219
(2004
).14.
A.
Gogo
, W. D.
Snyder
, and M.
Beck
, “Comparing quantum and classical correlations in a quantum eraser
,” Phys. Rev. A
71
, 052103-1
–1052103-6
(2005
).15.
J. A.
Carlson
, M. D.
Olmstead
, and M.
Beck
, “Quantum mysteries tested: An experiment implementing Hardy's test of local realism
,” Am. J. Phys.
74
, 180
–186
(2006
).16.
M.
Beck
, “Comparing measurements of
performed with different coincidence detection techniques
,” J. Opt. Soc. Am. B
24
, 2972
–2978
(2007
).17.
18.
19.
E. J.
Galvez
, C. H.
Holbrow
, M. J.
Pysher
, J. W.
Martin
, N.
Courtemanche
, L.
Heilig
, and J.
Spencer
, “Interference with correlated photons: Five quantum mechanics experiments for undergraduates
,” Am. J. Phys.
73
, 127
–140
(2005
).20.
D.
Dehlinger
and M. W.
Mitchell
, “Entangled photon apparatus for the undergraduate laboratory
,” Am. J. Phys.
70
, 898
–902
(2002
).21.
D.
Dehlinger
and M. W.
Mitchell
, “Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory
,” Am. J. Phys.
70
, 903
–910
(2002
).22.
E.
Dederick
and M.
Beck
, “Exploring entanglement with the help of quantum state measurement
,” Am. J. Phys.
82
, 962
–971
(2014
).23.
E. T.
Burch
, C.
Henelsmith
, W.
Larson
, and M.
Beck
, “Quantum-state tomography of single-photon entangled states
,” Phys. Rev. A
92
, 032328-1
–032328-8
(2015
).24.
C. F.
von Weizsäcker
, “Ortsbestimmung eines Elektrons durch ein Mikroskop
,” Z. Phys.
70
, 114
–130
(1931
).25.
C. F.
von Weizsäcker
, “Zur deutung der quantenmechanik
,” Z. Phys.
118
, 489
–509
(1941
).26.
W.
Heisenberg
, “Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik
,” Z. Phys.
43
, 172
–198
(1927
).27.
E.
Schrödinger
, “The present situation in quantum mechanics: A translation of Schrödinger's “cat paradox” paper
,” Proc. Am. Philos. Soc.
124
, 323
–338
(1980
), translated by John D. Trimmer; available at http://www.jstor.org/stable/986572.28.
R.
Ionicioiu
and D. R.
Terno
, “Proposal for a quantum delayed-choice experiment
,” Phys. Rev. Lett.
107
, 230406-1
–230406-5
(2011
).29.
N.
Bohr
, “Discussions with Einstein on epistemological problems in atomic physics
,” in Albert Einstein: Philosopher–Scientist
, edited by P. A.
Schilpp
(Library of Living Philosophers
, Evanston, Illinois
, 1949
), vol. 7
, pp. 201
–241
.30.
V.
Jacques
, E.
Wu
, F.
Grosshans
, F.
Treussart
, P.
Grangier
, A.
Aspect
, and J.-F.
Roch
, “Experimental realization of Wheeler's delayed-choice gedanken experiment
,” Science
315
, 966
–968
(2007
).31.
J.-S.
Tang
, Y.-L.
Li
, X.-Y.
Xu
, G.-Y.
Xiang
, C.-F.
Li
, and G.-C.
Guo
, “Realization of quantum Wheeler's delayed-choice experiment
,” Nat. Photonics
6
, 600
–604
(2012
).32.
A.
Peres
, “Delayed choice for entanglement swapping
,” J. Mod. Opt.
47
, 139
–143
(2000
).33.
F.
Sciarrino
, E.
Lombardi
, G.
Milani
, and F. D.
Martini
, “Delayed-choice entanglement swapping with vacuum-one-photon quantum states
,” Phys. Rev. A
66
, 024309-1
–024309-4
(2002
).34.
X.-S.
Ma
, S.
Zotter
, J.
Kofler
, R.
Ursin
, T.
Jennewein
, Č.
Brukner
, and A.
Zeilinger
, “Experimental delayed-choice entanglement swapping
,” Nat. Phys.
8
, 479
–484
(2012
).35.
While not physically necessary for quantum erasure to obtain, this separation aids pedagogical clarity and is therefore one of the desirable features of an “ideal” quantum eraser (Ref. 39). It is also a prerequisite for delayed-choice implementations that causally disconnect the erasure measurement from the interfering particle (Ref. 48).
36.
L. A.
Rozema
, A.
Darabi
, D. H.
Mahler
, A.
Hayat
, Y.
Soudagar
, and A. M.
Steinberg
, “Violation of Heisenberg's measurement-disturbance relationship by weak measurements
,” Phys. Rev. Lett.
109
, 100404-1
–100404-5
(2012
).37.
M. O.
Scully
and H.
Walther
, “An operational analysis of quantum eraser and delayed choice
,” Found. Phys.
28
, 399
–413
(1998
).38.
M.
Bahrami
and A.
Shafiee
, “Postponing the past: An operational analysis of delayed-choice experiments
,” Found. Phys.
40
, 55
–92
(2010
).39.
P. G.
Kwiat
, A. M.
Steinberg
, and R. Y.
Chiao
, “Three proposed “quantum erasers”
,” Phys. Rev. A
49
, 61
–68
(1994
).40.
T. J.
Herzog
, P. G.
Kwiat
, H.
Weinfurter
, and A.
Zeilinger
, “Complementarity and the quantum eraser
,” Phys. Rev. Lett.
75
, 3034
–3037
(1995
).41.
Y.-H.
Kim
, R.
Yu
, S. P.
Kulik
, Y.
Shih
, and M. O.
Scully
, “Delayed “choice” quantum eraser
,” Phys. Rev. Lett.
84
, 1
–5
(2000
).42.
S. P.
Walborn
, M. O. T.
Cunha
, S.
Pádua
, and C. H.
Monken
, “Double-slit quantum eraser
,” Phys. Rev. A
65
, 033818-1
–1033818-6
(2002
).43.
W. H.
Zurek
, “Decoherence, einselection, and the quantum origins of the classical
,” Rev. Mod. Phys.
75
, 715
–775
(2003
).44.
M.
Schlosshauer
, Decoherence and the Quantum-to-Classical Transition
(Springer
, Berlin/Heidelberg
, 2007
).45.
A.
Einstein
, B.
Podolsky
, and N.
Rosen
, “Can quantum-mechanical description of physical reality be considered complete?
,” Phys. Rev.
47
, 777
–780
(1935
).46.
J. W.
Lord
and M.
Beck
, “Coincidence counting unit using the Altera DE2
,” URL <http://people.whitman.edu/beckmk/QM/circuit/circuit.html>.47.
J.
Åke Larsson
, “Loopholes in Bell inequality tests of local realism
,” J. Phys. A: Math. Theor.
47
, 424003-1
–424003-33
(2014
).48.
X.-S.
Ma
, J.
Kofler
, A.
Qarry
, N.
Tetik
, T.
Scheidl
, R.
Ursin
, S.
Ramelow
, T.
Herbst
, L.
Ratschbacher
, A.
Fedrizzi
, T.
Jennewein
, and A.
Zeilinger
, “Quantum erasure with causally disconnected choice
,” Proc. Natl. Acad. Sci. U.S.A.
110
, 1221
–1226
(2013
).© 2016 American Association of Physics Teachers.
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