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.

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
g(2)(0)
performed with different coincidence detection techniques
,”
J. Opt. Soc. Am. B
24
,
2972
2978
(
2007
).
17.
M.
Beck
,
Quantum Mechanics: Theory and Experiment
(
Oxford U.P.
,
Oxford
,
2012
).
18.
M.
Beck
, “
Modern quantum mechanics experiments
,” URL <http://www.whitman.edu/beckmk/QM>.
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
).
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