The Siegert relation relates electric field and intensity correlations of light, under given assumptions. After a brief derivation of the relation, we present an experimental setup that can be implemented in a student laboratory: it allows measuring both field and intensity correlations at the same time, thus providing a direct test of the Siegert relation. Some experimental results are presented when the scattering medium corresponds to a cold atomic cloud. As a conclusion, we discuss typical situations where the relation fails.

1.
L.
Mandel
and
E.
Wolf
, “
Coherence properties of optical fields
,”
Rev. Mod. Phys.
37
,
231
287
(
1965
).
2.
G.
Maret
and
P. E.
Wolf
, “
Multiple light scattering from disordered media. The effect of Brownian motion of scatterers
,”
Z. Phys. B
65
(
4
),
409
413
(
1987
).
3.
D. J.
Pine
,
D. A.
Weitz
,
P. M.
Chaikin
, and
E.
Herbolzheimer
, “
Diffusing wave spectroscopy
,”
Phys. Rev. Lett.
60
,
1134
1137
(
1988
).
4.
A.
Eloy
,
Z.
Yao
,
R.
Bachelard
,
W.
Guerin
,
M.
Fouché
, and
R.
Kaiser
, “
Diffusing-wave spectroscopy of cold atoms in ballistic motion
,”
Phys. Rev. A
97
,
013810
(
2018
).
5.
N.
Wiener
, “
Generalized harmonic analysis
,”
Acta Math.
55
,
117
258
(
1930
).
6.
A.
Khintchine
, “
Korrelationstheorie der stationären stochastischen prozesse
,”
Math. Ann.
109
(
1
),
604
615
(
1934
).
7.
R. J.
Glauber
, “
The quantum theory of optical coherence
,”
Phys. Rev.
130
,
2529
2539
(
1963
).
8.
N. G.
van Kampen
,
Stochastic Processes in Physics and Chemistry
, 3rd ed. (
Elsevier
,
Amsterdam
,
2007
).
9.
A. J. F.
Siegert
, “
On the fluctuations in signals returned by many independently moving scatterers
,” Report No. 465 (Radiation laboratory, Massachusetts Institute of Technology,
1943
).
10.
R. H.
Brown
and
R. Q.
Twiss
, “
Correlation between photons in two coherent beams of light
,”
Nature
177
,
27
29
(
1956
).
11.
R. H.
Brown
and
R. Q.
Twiss
, “
A test of a new type of stellar interferometer on Sirius
,”
Nature
178
,
1046
1048
(
1956
).
12.
W.
Guerin
,
A.
Dussaux
,
M.
Fouché
,
G.
Labeyrie
,
J.-P.
Rivet
,
D.
Vernet
,
F.
Vakili
, and
R.
Kaiser
, “
Temporal intensity interferometry: Photon bunching in three bright stars
,”
Mon. Not. R. Astron. Soc.
472
,
4126
4132
(
2017
).
13.
R.
Loudon
,
The Quantum Theory of Light
(
Oxford Science Publications
,
Oxford
,
1973
).
14.
L.
Basano
and
P.
Ottonello
, “
New correlator-photon counter to illustrate the fundamentals of light statistics
,”
Am. J. Phys.
50
(
11
),
996
1000
(
1982
).
15.
W. I.
Goldburg
, “
Dynamic light scattering
,”
Am. J. Phys.
67
(
12
),
1152
1160
(
1999
).
16.
T. A.
Kuusela
, “
Measurement of the second-order coherence of pseudothermal light
,”
Am. J. Phys.
85
(
4
),
289
294
(
2017
).
17.
B.
Chu
,
Laser Light Scattering: Basic Principles and Practice
(
Academic Press
,
Amsterdam
,
2012
).
18.
T.
Okoshi
,
K.
Kikuchi
, and
A.
Nakayama
, “
Novel method for high resolution measurement of laser output spectrum
,”
Electron. Lett.
16
,
630–631
(
1980
).
19.
P.-A.
Lemieux
and
D. J.
Durian
, “
Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions
,”
J. Opt. Soc. Am. A
16
(
7
),
1651
1664
(
1999
).
20.
P. E.
Wolf
,
G.
Maret
,
E.
Akkermans
, and
R.
Maynard
, “
Optical coherent backscattering by random media: An experimental study
,”
J. Phys.
49
(
1
),
63
75
(
1988
).
21.
D. J.
Pine
,
D. A.
Weitz
,
J. X.
Zhu
, and
E.
Herbolzheimer
, “
Diffusing-wave spectroscopy: Dynamic light scattering in the multiple scattering limit
,”
J. Phys.
51
(
18
),
2101
2127
(
1990
).
22.
W.
Martienssen
and
E.
Spiller
, “
Coherence and fluctuations in light beams
,”
Am. J. Phys.
32
(
12
),
919
926
(
1964
).
23.
A. B.
Haner
and
N. R.
Isenor
, “
Intensity correlations from pseudothermal light sources
,”
Am. J. Phys.
38
(
6
),
748
750
(
1970
).
24.
H.-G.
Hong
,
W.
Seo
,
M.
Lee
,
W.
Choi
,
J.-H.
Lee
, and
K.
An
, “
Spectral line-shape measurement of an extremely weak amplitude-fluctuating light source by photon-counting-based second-order correlation spectroscopy
,”
Opt. Lett.
31
(
21
),
3182
3184
(
2006
).
25.
S. V.
Kashanian
,
A.
Eloy
,
W.
Guerin
,
M.
Lintz
,
M.
Fouché
, and
R.
Kaiser
, “
Noise spectroscopy with large clouds of cold atoms
,”
Phys. Rev. A
94
,
043622
(
2016
).
26.
B. R.
Mollow
, “
Power spectrum of light scattered by two-level systems
,”
Phys. Rev.
188
,
1969
1975
(
1969
).
27.
L.
Ortiz
,
R. C.
Teixeira
,
A.
Eloy
,
D.
Ferreira
,
R.
Kaiser
,
R.
Bachelard
, and
M.
Fouché
, “
Mollow triplet in cold atoms
,”
New J. Phys.
21
,
093019
(
2019
).
28.
F.
Lamelas
and
S.
Swaminathan
, “
Optical absorption, scattering, and multiple scattering: Experimental measurements using food coloring, India ink, and milk
,”
Am. J. Phys.
88
(
2
),
137
140
(
2020
).
29.
T. R.
Watts
,
K. I.
Hopcraft
, and
T. R.
Faulkner
, “
Single measurements on probability density functions and their use in non-Gaussian light scattering
,”
J. Phys. A
29
(
23
),
7501
7517
(
1996
).
30.
D. W.
Schaefer
and
B. J.
Berne
, “
Light scattering from non-Gaussian concentration fluctuations
,”
Phys. Rev. Lett.
28
(
8
),
475
478
(
1972
).
31.
H.
Paul
, “
Photon antibunching
,”
Rev. Mod. Phys.
54
(
4
),
1061
1102
(
1982
).
32.
H. J.
Kimble
,
M.
Dagenais
, and
L.
Mandel
, “
Photon antibunching in resonance fluorescence
,”
Phys. Rev. Lett.
39
(
11
),
691
695
(
1977
).
33.
H.
Voigt
and
S.
Hess
, “
Comparison of the intensity correlation function and the intermediate scattering function of fluids: A molecular dynamics study of the Siegert relation
,”
Physica A
202
(
1-2
),
145
164
(
1994
).
34.
J. H.
Page
,
M. L.
Cowan
,
D. A.
Weitz
, and
B. A.
Tiggelen
, “
Diffusing acoustic wave spectroscopy: Field fluctuation spectroscopy with multiply scattered ultrasonic waves
,”
Wave Scattering in Complex Media: From Theory to Applications
(
Springer Netherlands
,
Dordrecht
,
2003
), pp.
151
174
.
35.
D. A.
Boas
and
A. G.
Yodh
, “
Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation
,”
J. Opt. Soc. Am. A
14
(
1
),
192
215
(
1997
).
36.
D.
Borycki
,
O.
Kholiqov
, and
V. J.
Srinivasan
, “
Interferometric near-infrared spectroscopy directly quantifies optical field dynamics in turbid media
,”
Optica
3
(
12
),
1471
1476
(
2016
).
37.
A. S.
Gittings
and
D. J.
Durian
, “
Gaussian and non-Gaussian speckle fluctuations in the diffusing-wave spectroscopy signal of a coarsening foam
,”
Appl. Opt.
45
(
10
),
2199
2204
(
2006
).
38.
M. J.
Stevens
,
B.
Baek
,
E. A.
Dauler
,
A. J.
Kerman
,
R. J.
Molnar
,
S. A.
Hamilton
,
K. K.
Berggren
,
R. P.
Mirin
, and
S. W.
Nam
, “
High-order temporal coherences of chaotic and laser light
,”
Opt. Express
18
(
2
),
1430
1437
(
2010
).
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.