We describe photon statistics experiments using pseudothermal light that can be performed in an undergraduate physics laboratory. We examine the light properties in terms of a second-order coherence function, as determined either by measuring the light intensity as a function of time or via coincidence analysis of a pair of photon detectors. We determine the coherence time and intensity distribution of the pseudothermal light source that exhibits either Gaussian or non-Gaussian statistics as a function of their optical parameters, and then compare the results with theoretical predictions. The simple photodiode method can be used for the qualitative analysis of the coherence time, but more accurate measurements are achieved using the coincidence method.

1.
P.
Grangier
,
G.
Roger
, and
A.
Aspect
, “
Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interference
,”
Europhys. Lett.
1
,
173
179
(
1986
).
2.
C. W.
Chou
,
S. V.
Polyakov
,
A.
Kuzmich
, and
H. J.
Kimble
, “
Single-photon generation from stored excitation in an atomic ensemble
,”
Phys. Rev. Lett.
92
,
213601
(
2004
).
3.
A. B.
U’Ren
,
C.
Silberhorn
,
J. L.
Ball
,
K.
Banaszek
, and
I. A.
Walmsley
, “
Characterization of the nonclassical nature of conditionally prepared single photons
,”
Phys. Rev. A
72
,
021802
(
2005
).
4.
C.
Santori
,
S.
Gotzinger
,
Y.
Yamamoto
,
S.
Kako
,
K.
Hoshino
, and
Y.
Arakawa
, “
Photon correlation studies of single GaN quantum dots
,”
Appl. Phys. Lett.
87
,
051916
(
2005
).
5.
R.
Hanbury Brown
and
R. Q.
Twiss
, “
Correlation between photons in two coherent beams of light
,”
Nature (London)
177
,
27
29
(
1956
).
6.
R. Q.
Twiss
,
A. G.
Little
, and
R.
Hanbury Brown
, “
Correlation between photons in two coherent beams of light, detected by a coincidence counting technique
,”
Nature (London)
180
,
324
326
(
1957
).
7.
W.
Martienssen
and
E.
Spiller
, “
Coherence and fluctuations in light beams
,”
Am. J. Phys.
32
,
919
926
(
1964
).
8.
F. T.
Arecchi
, “
Measurement of the statistical distribution of Gaussian and laser sources
,”
Phys. Rev. Lett.
15
,
912
916
(
1965
).
9.
F. T.
Arecchi
,
E.
Gatti
, and
A.
Sona
, “
Time distribution of photons from coherent and Gaussian sources
,”
Phys. Lett.
20
,
27
29
(
1966
).
10.
L.
Basano
and
P.
Ottonello
, “
New correlator-photon counter to illustrate the fundamentals of light statistics
,”
Am. J. Phys.
50
,
996
1000
(
1982
).
11.
E.
Jakeman
, “
The effect of wavefront on the coherence properties of laser light scattered by target centres in uniform motion
,”
J. Phys. A
8
,
L23
L28
(
1975
).
12.
P. N.
Pusey
, “
Photon correlation study of laser speckle produced by a moving rough surface
,”
J. Phys. D
9
,
1399
1409
(
1976
).
13.
P.
Koczyk
,
P.
Wiewior
, and
C.
Radzewicz
, “
Photon counting statistics—Undergraduate experiments
,”
Am. J. Phys.
64
,
240
245
(
1996
).
14.
M. L.
Martinez Ricci
,
J.
Mazzaferri
,
A. V.
Bargas
, and
O. E.
Martinez
, “
Photon counting statistics using a digital oscilloscope
,”
Am. J. Phys.
75
,
707
712
(
2007
).
15.
R.
Loudon
,
The Quantum Theory of Light
(
Oxford U.P.
,
New York
,
2000
).
16.

It is important not to confuse the Gaussian distribution of the electric field amplitude (or intensity) with the frequency distribution. Thermal light with a Lorentzian frequency spectrum is called Gaussian-Lorentzian and light with a Gaussian frequency spectrum is called Gaussian-Gaussian light. However, it is also possible to have chaotic or random light, which has a non-Gaussian amplitude distribution.

17.

For single photon light g(2)(0) = 0 and for coherent light g(2)(0) = 1, see Ref. 15.

18.
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 the undergraduate laboratory
,”
Am. J. Phys.
72
,
1210
1219
(
2004
).
19.
M.
Beck
, “
Comparing measurements of g(2) performed with different coincidence detection techniques
,”
J. Opt. Soc. Am. B
24
,
2972
2978
(
2007
).
20.
L.
Mandel
and
E.
Wolf
,
Optical Coherence and Quantum Optics
(
Cambridge U.P.
,
Cambridge
,
1995
).
21.
The “Central Limit Theorem” states that the sum of a large number of independent random variables (having more or less equal distribution) will be approximately normally distributed, regardless of the underlying distribution. See, for example,
P.
Billingsley
,
Probability and Measure
(
John Wiley & sons
,
New York
,
1995
).
22.
I. R.
Kenyon
,
The Light Fantastic: A Modern Introduction to Classical and Quantum Optics
(
Oxford U.P.
,
New York
,
2011
).
23.
See supplementary material at http://dx.doi.org/10.1119/1.4975212 for Software, in the form of a Windows executable program.
24.

Error estimates here and in all further analyses are based on one standard deviation calculated over 20 sets of measurements, not the standard error of the mean.

25.

The grit size comes from the number of standardized holes that fit within the standard dimensional sized screen used to characterize the particle dimensions of the polishing material. Unfortunately, this number varies from one manufacturer to another. Here, the size of the scatterers was estimated visually using a microscope.

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.