Difference between revisions of "Spontaneous Parametric Downconversion"

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= Quantum Optics and Spontaneous Parametric Downconversion =
 
= Quantum Optics and Spontaneous Parametric Downconversion =
  
The goal of this project is to use a series table-top laser-based optics experiments to investigate various quantum mechanical phenomena. These include, but are not limited to: quantization of the electric field (proof of the existence of photons), single-photon interference, violation of Bell inequalities, and quantum information measurement effects.
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The goal of this project is to use a series of table-top laser-based optics experiments to investigate various quantum mechanical phenomena. These include, but are not limited to: quantization of the electric field (proof of the existence of photons), single-photon interference, violation of Bell inequalities, and quantum information measurements.
  
 
= Physics Background =
 
= Physics Background =

Revision as of 17:27, 22 March 2015

Quantum Optics and Spontaneous Parametric Downconversion

The goal of this project is to use a series of table-top laser-based optics experiments to investigate various quantum mechanical phenomena. These include, but are not limited to: quantization of the electric field (proof of the existence of photons), single-photon interference, violation of Bell inequalities, and quantum information measurements.

Physics Background

Spontaneous parametric downconversion (SPDC) is a non-linear optical process that takes place with the assistance of specially-engineered optical crystals. These optical crystals are designed with specific index of refraction properties along given crystalline axis. When light of a specific frequency is incident upon the lattice, it will experience preferential absorption and re-emission as a result of this design. This will result in an overall "splitting" of one incident light beam into two; signal and idler beams, at some well-defined angle. The quanta of light will experience a downconversion but within this the momentum and energy of the beam is conserved in the signal and idler beams. The net effect of this can be seen by looking at the bulk beam properties.

In a project-specific example, consider a 405nm wavelength laser is incident upon a downconversion crystal. The net effect of the crystal refraction and re-emission results in two output beams of 810nm. The incident beam has been "downconverted" to two output beams of half-the energy and twice the wavelength. See figure 1 for an illustration, and the WikiPedia article for more detail [1].



SPDC semi-classical overview


solving energy equations for wave vectors


Downconversion

If we reduce the incident beam to a series of single photons, whose existence is a central postulate of quantum theory, the above description need only be slightly altered. A single photon incident on the crystalline lattice has a certain probability of being downconverted via the interaction with the lattice (roughly 1 in 10^12)[2]. When this conversion takes place, the single photon, with its inherent polarization properties, is converted into a pair of polarization entangled photons at half the energy and wavelength. This pair has the same polarization, but the pair is polarized orthogonal to the input beam. Type II follows the same characteristic downconversion (DC) as the Type I but with one very crucial difference. In Type II downconversion the polarizations of the output beams are now orthogonal to one another (with some overlap in their respective electric fields so that there is a possibility for photon interaction, and unlike that of Type I where there is no possibility for interaction after the downconversion crystal). The way one sets their experiment for Type I or Type II downconversion is by choosing the correct the crystal lattice cut (literally purchasing the correct crystal). The lattice will be cut in such a way that the axis with varying indices of refraction will favor one DC type over the other.

Type I SPDC: output beams are polarized orthogonal to the input beam
Type II SPDC: overlapping output fields with orthogonal polarizations

Experimental Setup

In our experiment we started with a 405nm blue diode pump laser. We then put the laser through an iris and then a linear polarizer to ensure horizontal polarization. Once through the polarizer the laser was then pushed through a half wave plate in order to change the polarization of the beam from horizontal to vertical polarization. After being reflected off of two mirrors the light is incident on the downconversion crystal, producing two 810nm output beams. A beam blocker was placed down the beam path to block any stray 405nm light. The two output beams (signal and idler beam) traveled at an angle of roughly 3 degrees off axis with respect to the input beam. These two beams would then travel down their respective legs and reach a photodetector to record their individual and coincidence counts. See the block diagram as well as the setup photograph.

block diagram of SPDC experiment. NOTE: Some optics not included in all experiments
Optics table overview. Purple beam = 405nm input, Red beams = 810 DC outputs.

In setting up the experiment we needed to vary the angle of the legs so that we could verify that the maximum count occurred at approximately 3 degrees (see results below for details). We then installed a 50/50 polarizing beam splitting cube along the signal beam in front of the B detector. We also placed another detector (designated B') the same distance for the crystal but at a 90 degree angle from detector B to match the orientation of the polarizing beam splitter. This concludes the setup for any experiment that can be done involving 3-detector coincidence.

Results

Maximizing Photon Counts

In order to have the best possible experimental results, we sought to maximize the photon counts at each leg of the experiment. To do this, we varied the angle of each optical leg from 2.5 degrees to 4 degrees by increments of one-tenth of a degree from the central axis. Recorded values of photon counts are shown below. We found that the maximum counts occurred at approximately 3.2 degrees. This matches the theoretical maximum angle for photon counts of 3 degrees.

Maximum photon counts as a function of topical leg angle. NOTE: counts were later centralized between legs to remove the offset present on this plot. This will be plotted again in the future.
Maximized coincidence counts as a function of optical leg angle

Proving the existence of individual photons

For the next part of our experiment we added the third detector and the beam splitter as described above in Experimental Setup. In this part we did a coincidence count between sensor A from the signal beam and sensor B from the idler beam from here we then were able record the g^2(0) number for the two detector case. In this case we got a number greater than one which then solidifies the fact of light having a classical characteristic about it. We then proceeded to take a 3-detector coincidence count in order to look at the g^2(o) number. From here we then took recordings from the B' sensor on the idler beam. This then allowed us to get an ABB' coincidence count. Here we got a value much less than one, which in our case as described above gives us that light has quantum characteristics to it. This then tells us that light is composed of particles and these particles are called photons. This experiment gives us a certainty to the existence of photons but not only that, it expressly shows that of which Thomas Young found in his famous nineteenth century experiment commonly called Young's experiment, which is that light has characteristics of both waves and particles.

External Resources

References

SPDC Web Page