Double slit experiment with an astronomical CCD camera
In 2002, Robert P. Cease, science historian, surveyed readers of Physics World magazine about what he considered to be the most beautiful experiments in physics. The first of the list according to popularity turned out to be the double slit experiment conducted by Jonsson in 1961 with electrons.
One of the most attractive aspects of this experiment is that, although at the beginning of the last century quantum mechanics provided the theoretical basis for this experiment, to this day - almost a century later - Rychard's comment may still be valid. Feynman "I can say with all tranquility that nobody understands quantum mechanics" [1].
In the same way that electrons produce an interference pattern after crossing a double slit, the experiment can be done with other particles as molecules according to recent experiments or photons, which is the case presented in this article.
In the case of photons it may seem that it is not surprising to obtain an interference pattern, after all the light has a wave behavior. However, everything changes when we consider that the source of the experiment are individual photons and we guarantee with reasonable probability that only one photon goes through the double slit each time. In this case we are in a situation identical to that of the experiment with electrons or other particles. How can individual photons interact to generate the interference pattern? Is the photon capable of going through both slits at the same time?
The experiment described here is inspired by the description of the book Exploring Quantum Physics through Hands-on Projects, but with the particularity of using a commercial CCD camera, common use in amateur astronomy and much more economically that the used in the book.
Experimental setup
The experimental setup is described schematically in the following diagram:
The box has been designed using standard aluminum profiles and plywood painted black on the inside faces to result in a dark chamber with an incoming opening where the laser will strike through dimming filters, an output with a coupling designed to be exchanged the placement of a photo-multiplier (PMT) in order to count photons, and a CCD camera whose characteristics and operation are described later.
Although the photo-multiplier is not essential for the development of the experiment, it has been included in the description of the experiment since it enriches the explanation thereof.
To ensure the proper functioning of the test, and despite the fact that the box is opaque to light, the experiment takes place in a habituation with minimum ambient lighting.
The opacity of the box was checked by measuring the photon count of the photo-multiplier obtaining a very low count level (around 50 photons / s at room temperature of about 20 ° C) that we can consider as noise.
Individual photons
In this experiment, a 10mW laser of HeNe from Meredith Instruments was used.
Starting from the formula:
we obtain that the energy of each individual photon for the frequency of the laser used (632x10-9m) is:
Bearing in mind that the laser used is 10mW, the number of photons emitted per second is:
Since the box in which the experiment is developed is approximately 0.8m in length and starting from the data of the speed of light, the number of maximum photons that must be emitted so that there is not more than one photon passing through the box each it is 2.4x10^8 photons/sec.
It is therefore necessary to attenuate the laser by an order of magnitude of at least 10^8. For them we are going to consider the optical assembly:
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At the laser exit, a beam expander (# 55-582 Edmund Optics) was placed to obtain a beam of approximately 25 mm in diameter.
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The expanded beam of the laser is applied to absorption filters placed one after the other: 3 density filters 3 (# 48-093 Edmund Optics) and 1 density filter 2 (# 48-092 Edmund Optics), which add up an attenuation of 10^3x10^3x10^3x10^2 = 10^11.
The attenuation of the optical set is approximately 10^11, which implies that the number of photons that enter the box of the order of 3x10^5 photons / s, lower by 3 orders of magnitude than 10^8, are required so that there is not more than one photon to the time in the box.
To verify this data experimentally, a photo multiplier (P30USB from Sens Tech) has been used with a quantum efficiency at the laser frequency of approximately 1% and incorporating a high-voltage source and a high-speed discriminator amplifier with direct connection to the USB input of a PC.
For the tests measurements were made of 300s series with attenuation of density filters of 10^9 (3 density 3), without the slit and limiting the opening to 8.5mm in diameter. The test can not be done with the attenuation that is finally used in the experiment (10^11) since it exceeds the sensitivity of the photomultiplier. An average of 3.1x10^4 photons / s was obtained with laser on (compared to 50 / s with laser off) and considering that the beam expander evenly distributes the photons spatially in a beam of about 25mm in diameter and that we sealed with 8.5mm, The theoretical calculation for attenuation with 3 density filter 3 is approximately:
and since the quantum efficiency of the photomultiplier at the laser frequency is 1%, the verification of the theoretical calculation is correct. According to the theoretical calculations and the checks with the PMT, they enter the box in the order of 3x10^5 / s. The spectral width of the laser is of the order of 400 - 500MHz, which implies a coherence time of about 2ns (inverse of the spectral width) and consequently a coherence length of about 0.6m, compatible with the length of the box (0.8m) which allows to consider, in spite of the fluctuations of the source, a Poisson distribution, so that the probability of having k photons in the box is:
where f is the average of photons in the box calculated as the number of photons emitted per second for the time that 1 photon takes to cross the box. Considering 10^5 photons emitted per second and a distance of 0.8m, we have:
The probability of finding 2 photons in a box (k = 2) is therefore P2 = 3.6x10^-6%. It is such a small value that allows us to ensure that the photons are going through the slit one by one.
Double slit
The double slit was made using the pin of an electronic connector of 0.5mm width and approached on both sides with two small blades approximately 0.2mm apart.
The assembly was mounted on a metal washer using for fixing the quick glue elements. The washer was fixed in a lens holder (# 85-587 by Edmund Optics).
Photon capture
The capture of the photons was done by means of a CCD camera of astronomical observation model QHY IMG2PRO. Precisely because of the application for which it is intended has excellent characteristics for the experiment such as high quantum efficiency (68% at 550nm), sensor cooling (45ºC below the ambient temperature obtained during the experiment -26ºC) and the availability of software for capturing long exposures (up to 1 hour).
Taking into account the width of the slits (b = 0.2mm) the distance between them (a = 0.7mm), the distance to the CCD (L = 0.8m) and the width of the CCD (x = 1cm) the effect of the diffraction added to that of the interference obeys for λ = 632nm to a distribution of irradiance proportional to:
Where alpha and beta are respectively:
what according to the theoretical calculation should give a distribution with 5 maxima like the one shown in the figure:
Resultado
Once it has been verified with the photo-multiplier that the photon count per second is correct, the photo-multiplier is replaced by the CCD camera (thanks to a coupler compatible with both devices) and the final density filters are placed (attenuation 10^11)).
For the control of the camera, the free software EZCAP V3.13 was used, setting the exposure to the maximum allowed (3600s) and controlling the temperature of the CCD at maximum power to get 45ºC below the ambient temperature.
Consecutive shots of identical duration and in the same similar conditions of ambient temperature were made with the laser off (darks) and with the laser on to make comparisons and perform mathematical operations between both images in order to minimize the noise and maximize the image.
The images obtained leave no room for doubt: the interference pattern of individual photons based on discrete accumulation of photon impacts on the CCD during the long exposure time is clearly distinguished and coincides with the calculated theoretical irradiance distribution.
The image shown is the result of subtracting pixel to pixel the image obtained with the laser on the image obtained with the laser off:
The images were saved after capture with the FITS (Flexible Image Transport System) format camera and the operations between images as well as their conversion to PNG format (Portable Netkork Graphics) for printing were made with Maxim DL V5.23 software
Observing the accumulation of impacts of the individual photons that have passed through the double slit on the CCD according to the interference pattern described by Quantum Mechanics is a fascinating experience. The experiment is easy to assemble, without complications of adjustments or alignments.