Interference of Separate Photons by Two Independent Lasers
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Interference of Separate Photons by Two Independent Lasers
Jiefei Wang
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 this experiment displays the
advancements in both the stabilization of lasers and the detection technology since
Dirac’s times. At times, the two lasers had linewidths less than 1 kHz, which is 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), and
the difference in frequencies represents a 3.3*1010 % difference in frequency. The
detection technology has allowed for detection of fringes that exist for less than a
millisecond. Without the fast CCD detector, and highly stabilized lasers interference
between two separate photons could not be observed, which is most likely why Dirac
speculated this phenomenon to be impossible.
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 it 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 was 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. To show this effect two independent sources of photons must be used to produce interference patters. It is nearly impossible to produce stable (time-independent) interference patterns because of the difference in the temporal frequencies of the sources.
The equations for intensity of superimposed waves with electric fields E1 and E2 are as follows:
2 1.1 I (E1 E2 )
i(k j rw jt j ) 1.2 E j E0 j e ; j 1,2 2 2 1.3 I E01 E02 2E01E02 cos(k2 k1 )r (w2 w1 )t (2 1 )
Equation 1.3 describes the intensity of two superimposed waves which is dependent on both time
and position. If w2 w1 is not zero or very close to zero then the fringes will oscillate quickly between dark and bright fringes (Figure 1), which would be too fast for the naked eyes to detect.
For example if two HeNe laser sources in the visible spectrum with x
632nm wavelengths with a difference of .001% in frequency, the fringes would oscillate at 47GHz. If this fringe was to be t viewed by the naked eye then it would only see the time average of the intensity at every point in space. So it would appear as a smear of light instead of fringes. In addition to the time component the phase relation, , must also Figure 1: Unstable fringes oscillate with 2 1 time. Snapshots of fringes as time passes remain relatively constant, so very coherent sources are needed (i.e. stabilized lasers). To produce stable fringes that are visible by the naked eye the two wave packets traveling to the slits must be coherent (same frequency, constant phase relation) for the integration time of the 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 50Hz. This is currently beyond the capabilities for current laser control technology.
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 Beam Splitter Splitter This experiment uses two near-IR lasers, one of which has a piezoelectric Slit s actuator. When a voltage is applied the Lasers Wave Screen Analyzer actuator changes the length of the laser resonator which in turn changes the Figure 2. The experimental setup frequency output of the laser. By carefully controlling the voltage of the actuator the frequencies
2.1 E j E0 cos(w j t) j 1,2 of the lasers can be closely matched. The experiment w (w1 w2 ) / 2 uses a beam splitter to integrate the two beams which w (w1 w2 ) / 2 2.2 E E 2E cos(w*t) *sin(w*t) is split into two pairs of beams by a second beam 1 2 0 2.3 Beat Freq w/ 2 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. The wave analyzer is able to pick up the beat frequency of the two waves. The beat frequency is the
“envelope frequency” of the two combined waves given by equation 2.3. This wave analyzer is only concerned with the temporal frequency (w) and not the spatial frequency (k) so the spatial terms are thrown out. Since the beat frequency is much smaller than the individual frequencies of the lasers and it is proportional to the mismatch 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 combied wave has a wave envelope that composes the beat of the wave. Since the beat frequency is much smaller than the average frequencies of the two componenet waves it is easier 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 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 screen. When the lasers are fired the wave monitor will display the beat frequency, the voltage of on 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 wave analyzer. At this point the detector begins to take snapshots of the screen. The slow random drift of the two wavelengths of laser light will eventually cause them to be matched for a short instance, and when this happens fringes are produced for a few milliseconds.
IV. Results
The fringes produced by this experiment followed closely with 3.1 sin() m / d interference theory6. The fringe spacing matched equation 3.1, where m 0,1, 2, 3... when D d the spacing between two peaks were directly related to wavelength and sin() x / D the distance to the screen, while inversely related to spacing of the two 3.2 x mD / d 3.3 x D / d slits. The fringes were clearly visible on 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.
Figure 4. The spacingsx of the fringes are uniform when D>>d. is the distance between the centers of two bright finges.
1 Dirac, P.A.M. The principles of Quantum Mechanics. London :Oxford University, 1930 2 Double-slit Experiment. Absolute Astronomy. 1 November 2005