We present in the following a quantum optics experiment appropriate for advanced undergraduate students with former experience in quantum optics. It extends classical single photon setups to the time dependent domain. We demonstrate self-heterodyning of heralded single photons using a Mach-Zehnder like interferometer where beamsplitters are replaced by two acousto-optic modulators (AOMs). The single photon beat note is recorded over time at the frequency difference between the RF generators driving the AOMs, which makes it observable directly on a human time scale, i.e., with periods above a fraction of a second. To compare with our observations, we tailor the standard quantum optics formalism for beam splitters to take into account the frequency shifts associated with the AOMs.

1.
P. G.
Merli
,
G. F.
Missiroli
, and
G.
Pozzi
, “
On the statistical aspect of electron interference phenomena
,”
Am. J. Phys.
44
(
3
),
306
307
(
1976
).
2.
R.
Bach
,
D.
Pope
,
S. H.
Liou
, and
H.
Batelaan
, “
Controlled double-slit electron diffraction
,”
New J. Phys.
15
,
033018
(
2013
).
3.
A.
Aspect
,
P.
Grangier
, and
G.
Roger
, “
Wave particle duality for a single photon
,”
J. Opt.
20
(
3
),
119
129
(
1989
).
4.
V.
Jacques
,
E.
Wu
,
F.
Grosshans
 et al, “
Experimental realization of Wheeler's delayed-choice Gedanken experiment
,”
Science
315
(
5814
),
966
968
(
2007
).
5.
D.
Dehlinger
and
M. W.
Mitchell
, “
Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory
,”
Am. J. Phys.
70
(
9
),
903
910
(
2002
).
6.
E. J.
Galvez
,
C. H.
Holbrow
,
M. J.
Pysher
 et al, “
Interference with correlated photons: Five quantum mechanics experiments for undergraduates
,”
Am. J. Phys.
73
(
2
),
127
140
(
2005
).
7.
E. J.
Galvez
, “
Resource Letter SPE-1: Single-photon experiments in the undergraduate laboratory
,”
Am. J. Phys.
82
(
11
),
1018
1028
(
2014
).
8.
Y.
Okawa
,
F.
Omura
,
Y.
Yasutake
, and
S.
Fukatsu
, “
Photon heterodyning
,”
Opt. Express
25
(
17
),
20156
20161
(
2017
).
9.
L.
Olislager
,
J.
Cussey
,
A. T.
Nguyen
 et al, “
Frequency-bin entangled photons
,”
Phys. Rev. A
82
(
1
),
013804
(
2010
).
10.
See supplementary material at https://doi.org/10.1119/10.0000299 for a more detailed analysis of quantum beam splitters and AOMs.
11.
R.
Loudon
,
The Quantum Theory of Light
, 3rd ed. (
Oxford U. P.
,
New York
,
2000
).
12.
A.
Zeilinger
, “
General properties of lossless beam splitters in interferometry
,”
Am. J. Phys.
49
(
19
),
882
883
(
1981
).
13.
Y.
Park
and
K.
Cho
, “
Heterodyne interferometer scheme using a double pass in an acousto-optic modulator
,”
Opt. Lett.
36
(
3
),
331
333
(
2011
).
14.
P. G.
Kwiat
,
K.
Mattle
,
H.
Weinfurter
 et al, “
New high-intensity source of polarization-entangled photon pairs
,”
Phys. Rev. Lett.
75
(
24
),
4337
4341
(
1995
).
15.
J. J.
Thorn
,
M. S.
Neel
,
V. W.
Donato
 et al, “
Observing the quantum behavior of light in an undergraduate laboratory
,”
Am. J. Phys.
72
(
9
),
1210
1219
(
2004
).
16.
D.
Branning
,
S.
Bhandari
, and
M.
Beck
, “
Low-cost coincidence-counting electronics for undergraduate quantum optics
,”
Am. J. Phys.
77
(
7
),
667
670
(
2009
).
17.
D.
Branning
and
M.
Beck
, “
An FPGA-based module for multiphoton coincidence counting
,”
Proc. SPIE
8375
,
83750F
(
2012
).
18.
C.
Davis
, “
Single-photon optical heterodyning
,”
IEEE J. Quantum Electron.
15
(
1
),
26
29
(
1979
).
19.
G.
Grynberg
,
A.
Aspect
, and
C.
Fabre
,
Introduction to Quantum Optics: From the Semi-Classical Approach to Quantized Light
(
Cambridge U. P
.,
Cambridge
,
2010
).
20.
R. P.
Feynman
,
R. B.
Leighton
, and
M.
Sands
,
The Feynman Lectures on Physics
(
Addison-Wesley
,
Reading Massachusetts
,
1964
), Vol.
I
.
21.
E.
Smith
,
A.-A.
Dhirani
,
D. A.
Kokorowski
 et al, “
Velocity rephased longitudinal momentum coherences with differentially detuned separated oscillatory fields
,”
Phys. Rev. Lett.
81
(
10
),
1996
1999
(
1998
).
22.
R. A.
Rubenstein
,
A.-A.
Dhirani
,
D. A.
Kokorowski
 et al, “
Search for off-diagonal density matrix elements for atoms in a supersonic beam
,”
Phys. Rev. Lett.
82
(
10
),
2018
2021
(
1999
).
23.
K.
Rubin
,
M.
Eminyan
,
F.
Perales
 et al, “
Atom interferometer using two Stern-Gerlach magnets
,”
Laser Phys. Lett.
1
(
4
),
184
193
(
2004
).

Supplementary Material

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.