Top page for development of new lab on quantum optics and single photon studies.

[[phylabs:lab_courses:phys-211-wiki-home:single-photon-studies:teaching-goals|Teaching Goals]]

[[phylabs:lab_courses:phys-211-wiki-home:single-photon-studies:sample_data|MCC Data Collected 071723]]

====== Task 1 - Underlying Assumptions ======
Underlying assumption in most of what follows is that events recorded by the detector arrive at random with a well defined average rate and can be described by Poisson statistics.   

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Experimentally verify this assumption both for ambient back ground and when the laser is on.  Include data which shows quantitatively whether or not this assumption is valid.  
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**Tech Note**
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PHA is a useful tool for this.  But the UCS 30 input requires pulse widths of ~1μs whereas SPCM's output pulses are ~5ns, which is useful for fast timing measurements but is incompatible for UCS 30.  

The {{ :phylabs:lab_courses:phys-211-wiki-home:single-photon-studies:tc862-manual.pdf |Tennelec TC 862 TAC}} has outputs on the back of the module which send out a pulse when each time a valid start is received.  The width of the valid start pulse varies as the Range setting on the TAC.  This feature of the TAC can be used to send pulses of adequate width to the UCS 30 for each pulse output from the SPCM.  Note that these pulses are positive and thus require the Direct Input be selected for the PHA mode.
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====== Task 2 - Coincidence Measurements ======
Coincidence measurements are experimental techniques which involve looking for simultaneous detections from two or more separate detectors.  They are commonly encountered in experiments ranging from particle physics to atomic molecular optics and quantum information.

These experiments typically employ detectors which are sensitive to individual particles such as NaI+PMT detectors for high energy radiation, and avalanche photo diodes (APDs) for low energy (visible and IR) radiation.  These detectors produce electrical pulses which are then sent to some form of coincidence circuitry that produces its own output in response to "simultaneous" signals from multiple detectors.

While there are many different ways to perform coincidence measurements, they all involve the following concepts.

  * Coincidence Window.  How is "simultaneous" defined?  In principle it is not possible to measure how close together in time two or more signals occur to infinite precision.  Therefor there is always finite time interval within which the experiment considers multiple signals to be "simultaneous".  
  * Accidental Coincidences.  Whenever you have two or more detectors recording events that arrive at some well defined average rate, there exists some statistical probability for uncorrelated events to be recorded at multiple detectors within a finite time interval.  

In any coincidence measurement it is necessary to understand how your experiment determines coincidence, specifically what sets the coincidence window, and how likely is it that coincidences which are detected were due to random chance.

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Experimentally determine your coincidence window.  Determine all of the factors which go into defining the coincidence window for your experiment.  Include direct measurements such as scope traces to determine τ as quantitatively and precisely as possible.
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Determine the rate of accidental coincidences which you expect under operating conditions for your experiment.  
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Perform at least one measurement under conditions where you expect to see only accidental coincidences to establish whether or not your experiment is operating as you expect. 
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====== Task 3 - Polarization Optics ======

Quantum optics are a class of experiments which involve manipulating the state characteristics of individual photons of light, and are the cornerstone of AMO and quantum information experiments.  Polarization optics are optical components which operate on the polarization state of light.  Examples of polarization optics which you will encounter in this course include:

  * [[https://en.wikipedia.org/wiki/Polarizer | Linear Polarizers]].
  * [[https://en.wikipedia.org/wiki/Waveplate | Waveplates]] with 1/2 wave and 1/4 wave being the most common.
  * Polarizing beamsplitters.

The better you understand how these components work, the better you will be able to understand and interpret experimental results and their limitations when working with quantum optics.

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**Tech Note**
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An excellent source for learning about various quantum optics components, and how they are commonly used, are the web sites of manufacturers like [[https://thorlabs.com | ThorLabs]] and [[https://https://www.edmundoptics.com/ | Edmund Optics]].  Just go to one of these sites and type in the name of the component you are interested in and you will find a plethora of useful information including the theory of how they work and useful technical specifications.

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It is not enough to know the theory of how these optical components work.  Theory is always based on assumptions and idealizations.  When working with real materials you have to be able to contend with the fact the inherent nonidealities of nature cannot be swept under the rug.  For example filters never pass just one wavelength of light, they always pass some range of wavelengths.  Furthermore wavelengths which are passed by a filter are still subject to some amount of attenuation, scattering, reflection, etc., in spite of the use of sophisticated materials and coatings.

For each of the following exercises use the low power red alignment laser on the optical table along with the appropriate optical components which are stored in the room.

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**Linear Polarizers**
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In theory what should happen when light is passed through two linear polarizers whose pass axes are set to be ;
  * Parallel
  * 45º
  * Orthogonal

How close do your measurements come to the theoretical expectation?  To what degree can you quantitatively account for any observed deviations.
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**1/2 - Waveplates**
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If a beam of polarized light passes through a 1/2 - waveplate what:
  * 2 orientations of the waveplate, with respect to the polarization axis of the incident light, leave the polarization state of the light unchanged after it has passed through the waveplate?
  * angle results in the polarization axis of the incident light to be rotated through 45º?
  * angle results in the polarization axis of the incident light being rotated through 90º?

Use the alignment laser, linear polarizers, 1/2 - waveplate and photodetector to test each of these cases.  Use your data to quantitatively assess the theoretical expectations and account as best as possible for any discrepancies.
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**Polarization Beamsplitters**
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Use the alignment laser, linear polarizers, 1/2 - waveplate, photodetector and a polarizing beamsplitter cube to convert half of the incident beam into vertically polarized light and half into horizontally polarized light.
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If you have worked through Tasks 1 through 3, and understand what you were doing (as opposed to just making the numbers work out), you should be able to conduct experiments 1 and 2 without too much difficulty.

====== Experiment 1 - Existence Of The Photon ======

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Insert section on the proof of the existence of the photon from the book by Beck.
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Insert section about SPDC using BBO crystals.
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Using the Blue, Green and White detectors, conduct an experiment to test the existence of the photon.

====== Experiment 2 - Single Photon Interference ======

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Insert section describing Mach-Zhender interferometer.
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Using the Blue, Orange and Yellow detectors conduct an experiment to show whether or not a single photon is able to interfere with itself.  This will entail:

  * Demonstrating that statistically only one photon at a time is likely to be passing through the interferometer.
  * Show that when you change the path length of one arm of the Mach-Zhender interferometer you see variations in the output from the interferometer which are consistent with interference.  Note that it is not sufficient to simply show variations in the count rates at the output detectors.  You must consider how to show that any observed variations are due to interference of 810nm light, and not some other non-interference effect.

====== Experiment 3 - Quantum Eraser ======

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Insert section describing Mach-Zhender interferometer.
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Using the Blue, Orange and Yellow detectors conduct an experiment to demonstrate the principle of the quantum eraser.  This will entail:

  * Demonstrating that statistically only one photon at a time is likely to be passing through the interferometer.
  * Showing that when you manipulate the state of the photon so that it carries "which way" information, the interference at the output goes away.
  * Manipulating the state of the photon outside the interferometer to remove (erase) the "which way" information restores the interference pattern.