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Interference of Separate Photons by Two Independent Lasers
Jiefei Wang
DRAFT 2
Optical Sciences at the University of Arizona, Tucson Arizona
In an experiment conducted by Lorenzo Basano and Pasquale Ottonello, two independent laser
sources were able to produce fringes for a time of the order of 1ms. This experiment disproves
the second part of Dirac’s famous statement that “interference between two different photons
never occurs.1” In addition the experiment displays the advancements in both the stabilization of
lasers and the detection technology. At times, the two lasers had linewidths less than 1 kHz,
which represents the difference in operating frequencies of the lasers. This is a significant feat
because the operating frequencies of the inferred lasers are on the order of 300THz ( 3 * 1014 Hz),
represents a 3.3 *10 10 % difference in frequency. The advances in detection technology has
allowed for detection of fringes that exist for less than a millisecond. Without these fast CCD
detectors, the fringes would be impossible to observe with the naked eye.
I. Introduction
In 1805 Thomas Young conducted the double slit experiment, which consisted of a pinhole source
and two slits and a screen2. He observed an interference pattern which demonstrated the wave nature of
light. Specifically, Young’s experiment demonstrated how waves interfered with each other to create
bright and dark bands. After the double slit experiment, the existence of light in the form of a wave
became widely accepted. Around 1974 electrons were shot through the double slits one at a time, which
also created the interference pattern, which led to the conclusion that photons can interfere with itself.
However it was difficult to prove if photons could interfere with other photons, because their high
frequencies make it very difficult to produce stable (time independent) fringes.
Mathematically we can describe how two
photons interfere with each other by
describing them as two plane waves.
Equations for the superposition off two waves:
k= spatial frequency of photon
w=temporal frequency of photon
 = phase of photon
r=position
t=time
Equation 1.2 is the complex representation of
the electric field a plane wave. Since the
1.1 Intensity  I  ( E1  E2 ) 2
1.2
intensity is related to the square of the
amplitude of the electric field, we can use
Electric Field  E j  E0 j e
i ( k j r  w j t  j )
; j  1,2
1.3 I  E01  E02  2 E01E02 *
2
2
cos(k 2  k1 ) r  ( w2  w1 )t  (2  1 )
equation 1.3 to represent the intensity of two
electric fields. Since equation 1.3 is time dependent if w2  w1 is not zero, the fringes will be unstable
and change with respect time as shown in Figure 1. For example if two HeNe laser sources in the
visible spectrum with 632nm wavelengths with a difference of .001% in frequency, the fringes would
oscillate at 47GHz. If this fringe was to be viewed by the unaided eye then it would only see the time
average of the intensity at every point in space, which would appear
as a blur of light instead of fringes. In addition the phase
x
relationship, 2  1 , must also remain relatively constant, so highly
t
coherent sources are needed (i.e. lasers).
To produce stable fringes that are visible by the unaided eye the
two wave packets traveling to the slits must be coherent (same
frequency, constant phase relation) for the integration time of the
Figure 1: Unstable fringes oscillate
with time. Snapshots of fringes as
time passes
eye3, which is around .02 seconds. This would mean that the difference in frequency of the two photon
sources would have to be less than fifty hertz. Fifty hertz is such a small difference when considering
that photons oscillate at hundreds of terahertz*, it is nearly impossible to physically control lasers to that
degree of precision. For this reason, current technologies cannot produce interference patterns with two
independent lasers that are visible to the unaided eye.
Lorenzo Basano and Pasquale Ottonello’s experiment demonstrates the interference between two
different streams of photons produced by two independent lasers, by highly regulating the frequencies of
the lasers to greatly reduce the speed at which the fringes oscillate. They combined this with a fast
integrating detector that could take snapshots of fringes that exist for milliseconds.
II. Experimental Setup
Beam
Splitter
Beam
Splitter
Lorenzo Basano and Pasquale Ottonello’s
experiment uses two near-IR lasers, one of which
Slits
Actuator
has a piezoelectric actuator to adjust the cavity
Lasers
Wave
Analyzer
CCD
detector
length which changes the output frequency of the
laser. By carefully controlling the voltage of the
Figure 2. The experimental setup
actuator the frequencies of the lasers can be closely matched. The experiment uses a beam splitter to
integrate the two beams which is split into two pairs of beams by a second beam splitter. One pair goes
to the double slit, while the other pair of beams goes into a photodiode to be analyzed by a wave
analyzer. Each laser beam only goes through one slit, so it is not possible for a photon to travel though
both slits simultaneously, and therefore photons cannot interfere with itself.
The wave analyzer is able to pick up the beat frequency of the two waves which is created when
two simple harmonic waves (Equation 2.1) are combined. The
2.1
w  ( w1  w2 ) / 2
2.2
E1  E2  2 E0 cos( w * t ) * sin( w * t )
2.3 Beat Freq  w / 2
*
A terahertz is 1012 Hz
j  1,2
w  ( w1  w2 ) / 2
beat frequency is caused by the cos( w * t / 2) term from
equation 2.2. The wave analyzer only analizes the temporal
E j  E0 cos( w j t )
frequency (w) and not the spatial frequency (k) so the spatial terms are ignored. Since the beat
frequency is much smaller than the individual frequencies of the lasers and it is proportional to the
difference of the two laser frequencies4, it is used to find monitor the difference in frequencies. The beat
frequency approaches zero when the frequencies of the lasers are matched.
Figure 3. When two waves of equal amplitude but different frequencies are added, the combined wave has a
wave envelope (dotted line top graph) that composes the beat. Since the beat frequency is much smaller than
the average frequencies of the two component waves it is possible for the wave analyzier to detect.
III. Experimental procedure.
First the two lasers are calibrated so their wavelength is within .05nm of each other by the use of
a monochromator. For these coarse adjustments are made with mechanical adjustments. This is done as
a coarse adjustment to make sure that the beat frequency of the two combined beams is low enough to
be measured by the wave analyzer. Then the two lasers are aligned so that their optical axes intersect on
the CCD detector. When the lasers are activated the wave monitor will display the beat frequency, the
voltage of the actuator is adjusted until this beat frequency disappears. When this happens it means that
the frequencies are matched within a 100 kHz band5, which is the resolution limit of the the wave
analyzer†. At this point the CCD detector begins detect the light and transmits the data. The slow
random drift of the two wavelengths of laser light will eventually cause the frequencies to be matched
†
Model Tektronix 2712
for a short instance, and when this happens fringes are produced for a few milliseconds and are captured
by the CCD camera.
IV. Results
The fringes produced by this experiment followed closely with interference
6
theory . The fringe spacing matched equation 3.1, where the spacing between two
3.1 sin( )  m / d
m  0,  1,  2,  3...
when
peaks were directly related to wavelength and the distance to the screen, while
inversely related to spacing of the two slits. The fringes were clearly visible on
D  d
sin( )  x / D
3.2
x  mD / d
3.3 x  D / d
the 1ms integration time CCD and fringes were distinguishable in the 10ms
detector with 10ms integration time. This
shows that the difference in the frequencies
of the two lasers were well below 1 kHz for
that instant. This demonstrates the advances
in the control system of lasers.
x
Figure 4. The spacing of the fringes are uniform when D>>d.
x is the distance between the centers of two bright fringes.
V. Conclusion
Lorenzo Basano and Pasquale Ottonello were able to demonstrate the interference of two
independent photons by having a different photon source for each slit in their double slit
interferomenter. Though careful calibrations of their laser cavity length they were able to get the output
frequency of the lasers to within 1 kHz, and produced fringes that were detectable for about a
millisecond.
1
Dirac, P.A.M. The principles of Quantum Mechanics. London :Oxford University, 1930
Double-slit Experiment. Absolute Astronomy. 1 November 2005
<http://www.absoluteastronomy.com/encyclopedia/d/do/double-slit_experiment.htm>
3
F. Louradour, F. Reynaud, B. Colombeau, and C. Froehly. “Interference fringes between two separate
lasers.” Am. J. Phys. 61 (1993), 242-245.
4
H. Paul. “Interference between independent photons.” Rev. Mod. Phys 58, 209-231.
5
Lorenzo Basano and Pasquale Ottonello. “Interference fringes from stabilized diode lasers.” Am. J.
Phys. 68 (2000), 245-247.
6
Thornton, Stephen T. and Rex, Andrew. Modern Physics for Scientists and Engineers. Jefferson City:
Thompson Learning, 2002
2