Project

About the Project

Prepare an assay report  (max 4-page, double space) about a QM subject of your preference. Particular subjects are suggested in the Cluster Topics section below.
In 2026, we suggest all student to work on any of the following topics:
      Cluster-1     Proof of the existence of Photons   
      Cluster-2     Beam Splitter  and Mach–Zehnder interferometer  
      Cluster-3      Single Photon Interference
      Cluster-5     Entangled Photons

Electronic submission of  the assay report is required. Oral presentation is optional.

Deadlines

   Abstract submission:       October 29, 2026                                                          
                                                          Submit ABSTRACT (paragraph outlining what, why and  how are you going to do it), and brief
                                                          tentative "TABLE of  CONTENTS."
                                                          Send it to  andres@pdx.edu

  Presentation (optional):  Starts on Nov 19, 2026 (Just indicate your instructor your preferred day and time)

   Assay report:                          November 26th, 2025. Electronic submission should be sent to  andres@pdx.edu  

Cluster Topics

1    Proof of the existence of Photons  
                    [1]    P. Grangier, G. Roger, and A. Aspect,
                            "Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences,"
                              Europhys. Lett. 1, 173-179 (1986).
                    [2]    C. H. Holbrow, E. Galvez, and M. E. Parks,  Photon Quantum Mechanics and Beam splitters  Am. J. Phys. 70, 260 (2002).
                                        " ... The absence of D1–D2 coincidences is what we mean when we say the photon exists.  

2. Beam Splitter  and Mach–Zehnder interferometer 
                  [1]     A. Zeilinger, "General properties of lossless beam splitters in interferometry,"  American Journal of Physics 49, 882 (1981);
                              https://doi.org/10.1119/1.12387     
                                        The author uses spinor algebra to investigate general properties of lossless beam splitters in interferometry.
                    [2]    Z. Y. Ou, and L. Mandel , "Derivation of reciprocity relations for a beam splitter from energy balance,"  American Journal of Physics 57, 66 (1998);
                              10.1119/1.15873
                                        It is shown that the usual amplitude and phase relations connecting the reflectance and transmittance ofa stratified or continuous,
                                        nonabsorbing beam splitter can be derived by a simple energy balance argument relating to a Michelson interferometer.
                    [3]   H. Fearn and R. Loudon, "Quantum theory of the lossless beam splitter", Optics Communication 64, 485 (1987)
                                        Employs  continuum input+output spatial mode operators, which conveniently describe the flow of light through the beam splitter from
                                        sources to detectors.. The method complements an alternative approach by Prasad et al[ 3 ] in which emphasis is placed on the unitary
                                        transformation operator that couples input modes to output modes. 
                    [4]    S. Prasad, M.O. Scully and W. Martienssen, "A quantum description of the beam splitter," Optics Comm. 62, 139 (1987)
                                        Authors derive the unitary transformation that embodies the action of a lossless plane-parallel beam splitter on an incident light beam.
                    [5]    Vitorio Degiorgio, "Phase shift between the transmitted and the reflected optical fields of a semireflecting lossless mirror is π/2,"  American
                              Journal of Physics 48, 81 (1980); 10.1119/1.12238
                    [6]   E. Galvez, "Qubit quantum mechanics with correlated-photon experiments , Am. J. Phys. 78 , 510 (2010).
                    [7]   C. H. Holbrow, E. Galvez, and M. E. Parks, "Photon Quantum Mechanics and Beam splitters ,"  Am. J. Phys. 70, 260 (2002).
                                        " ... The absence of D1–D2 coincidences is what we mean when we say the photon exists. Clearly the beam splitter is the heart of the apparatus here."

3.   Single Photon Interference
                  The experiment demonstrates that individual photons interfere with themselves when they traverse an interferometer
                    [1]     C. H. Holbrow, E. Galvez, and M. E. Parks,  Photon Quantum Mechanics and Beam splitters  Am. J. Phys. 70, 260 (2002).
                    [2]     Experimental results of  single photon interference                 
                               Simultaneous  measurement of both the interference and the second-order coherence g(2)(0).  Since we find g(2)(0)<1, this simultaneously
                              demonstrates both particle and wavelike behavior of light.
                    [3]    D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger. Experimental quantum teleportation. Phil. Trans. R. Soc. Lond. A
                              356, 1733 (1998). 

4  Low-cost coincidence-counting electronics for undergraduate quantum optics
                    [1]    D. Branning,  S. Bhandari, and M. Beck;  Low-cost coincidence-counting electronics for undergraduate quantum optics   Am. J. Phys. 77 , 667 (2009)
                              "We present a design of a coincidence-counting module that replaces the traditional method based on time-to-amplitude conversion and pulse-height analysis.
                              Our module accepts inputs from up to four detectors, has a coincidence-time window of less than 10 ns, and has a throughput of more than triple that of the
                               traditional  method."
                    [2]    Coincidence Counting Units built at Dr. Beck's Lab 
                            "The original CCU is based on discrete logic components, while the latest CCU is based on a programmable logic IC (an FPGA). 
                              Both CCUs are significantly cheaper than the NIM electronics used in time-to-amplitude converter based coincidence measurements. 
                              Our CCUs even have higher count rates."  
                    [3]   Coincidence Counting Unit built at PSU
                              Georges M. E. Oates Larsen, "Self-Contained Photon Coincidence Counting with National Instruments myRIO Ecosystem" ,  University Honors
                              Theses.  Portland State   University.   https://doi.org/10.15760/honors.1140 
                              "We describe the implementation of a Coincidence Counting Unit  based on the (lower cost) multipurpose fpga unit) NI myRIO, 
                              which achieves 6.9 ns minimum  guaranteed-distinguishable delay and 32:2 MHz peak coincidence counting rate, with four input
                              channels and simultaneous monitoring of all possible coincidence types."

5  Entangled Photons
                    [1]   D. Dehlinger and M. W. Mitchell, "Entangled photon apparatus for the undergraduate laboratory," Am. J. Phys. 70, 898-902 (2002).
                    [2]   D. Dehlinger and M. W. Mitchell, "Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory," Am. J. Phys. 70,
                            903-910 (2002).

6. Multiple Particle Interferometry
                    [1]  D. Greenberger, M. Horne, A. Zeilinger. Multiparticle Interferometry and the Principle of Superposition. Physics Today 46, 22-29 (August 1993).  
                            Complementary information: Andres' notes on Multiparticle Interference .
                    [2]  P. Hariharan and B.C. Sanders. II Quantum Phenomena in Optical Interferometry , in Progress in Optics, Editor  E. Wolf, Vol 36,  Pages 49-128,
                            Elsevier (1996). Includes: Second-order interference, fourth order interference, two-photon interferometry, quantum limits to interferometry .

7. Implementation of  Modern Quantum Mechanics Experiments  
        7.1    Proof of the Existence of Photons (the Grangier Experiment)         Professor Mark Beck webpage    
                    This experiment duplicates the experiment of Grangier, Roger and Aspect [1], in which they demonstrate that if a single photon is incident on a
                    beam splitter, it can only be detected at one of the outputs (not both.)  To quote these authors, "a single photon can only be detected once!"
                    Additional information
                    [1]    P. Grangier, G. Roger, and A. Aspect, "Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on
                              single-photon interferences," Europhys. Lett. 1, 173-179 (1986).
                    [2]    Photon Quantum Mechanics and Beam splitters  
                              C. H. Holbrow, E. Galvez, and M. E. Parks  260 Am. J. Phys. 70, 260 (2002).
                            " ... The absence of D1–D2 coincidences is what we mean when we say the photon exists. Clearly the beam splitter is the heart of the apparatus here."

        7.2    Quantum Optics Laboratories for Teaching Quantum Physics
                    Enrique J. Galvez, Proc. SPIE 11143, Fifteenth Conference on Education and Training in Optics and Photonics: ETOP 2019, 111431A (2 July 2019);
                    doi: 10.1117/12.2523843

        7.3     Single Photon Interference
                    This experiment demonstrates that individual photons interfere with themselves when they traverse an interferometer.  We simultaneously
                    measure both the interference and the second-order coherence g(2)(0).  Since we find g(2)(0)<1, this simultaneously demonstrates both particle
                    and wavelike behavior of light.
                    Complementary information
                    [1]    Professor Enrique Galvez,Photon Quantum Mechanics and Beam splitters 
                    [2]    D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger. Experimental quantum teleportation. Phil. Trans. R. Soc. Lond. A
                              356, 1733 (1998). 

8. Optical Parametric Downconversion (OPD) sources of Entangled Photons
        There are two ways, referred to as type I and type II, of downcoversion process.
        In type I   the downconverted photons propagate with the same polarization (that is, both photons are extraordinary rays , or both
                              photons are ordinary rays ), and the pump polarization is orthogonal to the downconverted photons.
        In type II, the downconverted photons propagate with opposite polarizations; that is, one photon is an e-ray and the other photon is an o-ray.

                    [1]   On Type-I  A. Migdall. Polarization directions of noncolinear phase matched optical parametric downconversion output.  J. Opt. Soc. Am. B 14,
                              1093 (1997).
                    [2]    On Type-I: Ultrabright source of polarization-entangled photons
                              Paul G. Kwiat, Edo Waks, Andrew G. White, Ian Appelbaum, and Philippe H. Eberhard.  Physical Review A 60 R773-R776 (1999).
                              "Using the process of spontaneous parametric down-conversion in a two-crystal geometry, we have generated a source of polarization-entangled
                              photon pairs that is more than ten times brighter, per unit of pump power, than previous sources."
                    [3]   Nonclassical Effects from Spontaneous Parametric Down-Conversion: Adventures in Quantum Wonderland.
                              Paul G. Kwiat. Ph.D. Thesis, University of California at Berkeley (1993). See Figs 2.1 and 2.2.

                    [4]   Type II:  Proposal for a loophole-free Bell inequality experiment
                              Paul G. Kwiat,  P. H. Eberhard, A. M. Steinberg,  and R. Y. Chiao,  Physical Review A  49,  3209 (1994).
                              "We propose a two-crystal down-conversion source, relying on type-II collinear phase matching, which should permit a violation of Bell's
                              inequalities without the need for supplementary assumptions. As the source can produce a true singlet like state." 
                    [5]   On Type-I and Type-II:   M. L. Fanto, R. K. Erdmann, P. M. Alsing, C. J. Peters and E. J. Galvez. Multipli-entangled photons from a parametric
                              downconversion source. Proc. of SPIE 8057, 805705-1 (In "Quantum Information and Computation IX", edited by E. Donkor, A. R.  Pirich,
                              H. E. Brandt) 2011.

9. Second Quantization 
                    [1]   "Second quantization" (the occupation-number representation)
                              http://physics.gu.se/~tfkhj/OsloSecondQuant.pdf
                              http://physics.gu.se/~tfkhj/

10.   Momentum Entangled Photons 
    - Michael A. Horne, Abner Shimony, Anton Zeilinger. Two-Particle Interferometry. Phys. Rev. Lett. 62, 2209 (1989).
    -  R. Ghosh, C. K. Hong, Z. Y. Ou, and L. Mandel    Interference of two photons in parametric down conversion   Physical Review A 34, 3962 (1986).
    - R. Ghosh, L. Mandel. Observation of Nonclassical Effects in the Interference of Two photons. Physical Review Letters 59, 1903 (1987).
    - P. Hariharan and B.C. Sanders. Quantum Phenomena in Optical Interferometry (1996).

11. Quantum Teleportation  
    - Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993).
    - Charles H. Bennett. Quantum Information and Computation. Physics Today 48,  24-30 (October 1995).
    - L. Davidovich, N. Zagury, M. Brune, J.M. Raimond, and S. Haroche. Teleportation of an atomic state between two cavities using nonlocal microwave
      fields. Phys. Rev. A 50,  R895(R) (1994).
    - Tycho Sleator' and Harald Weinfurter. Realizable Universal Quantum Logic Gates. Phys. Rev. Lett. 74, 4087 (1995).

12. Professor Anton Zeilinger, "Quantum Information and Foundation of Physics" Group. Publications

13.  Coupled-Pendulum Model of the  Stimulated Raman Effect P. R. Hemmer and M. G. Prentiss

14.  Locality, Hidden Variables
          - A. Einstein, B. Podolsky, and N. Rosen. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 777 (1935).
          - Y. H. Shih and C. O. Alley. New Type of Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Optical Parametric
              Down Conversion. Phys. Rev. Lett. 61,2921-2924  (1988).

15.   -  EPR Paradox Timeline
          -  Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. Teleporting an unknown quantum
      state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993).
        -    D. Bouwmeester, J. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger. Experimental quantum teleportation. Phil. Trans. R. Soc. Lond. A  356, 1733
             (1998).
      -    Anton Zeilinger, From Quantum Curiosity to Quantum Technology