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.
REFERENCES
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
).© 2020 American Association of Physics Teachers.
2020
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.
