Photon Quantum Mechanics

This is a project funded by the National Science Foundation to establish a set of undergraduate  laboratories to study the fundamentals of quantum mechanics. The experiments are laboratory exercises on topics of quantum mechanics that are otherwise theoretical, abstract or even unintuitive. The central issue of the experiments is quantum superposition: the ability of a quantum to be in two places at the same time or to be in to be in a correlated superposition of states with other quanta. Our original ideas were published in the American Journal of Physics [C.H. Holbrow, E.J. Galvez and M.E. Parks, "Photon Quantum Mechanics and beam splitters," Am. J. Phys. 70, 260-265 (2002)  Reprint].

Simplicity and cost are primary concerns. A first stage of the project is now complete. An article describing these experiments has been published: “Interference with correlated photons: Five quantum mechanics experiments for undergraduates,”  E. J. Galvez, C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer,  Am. J. of Phys. 73, 127-140 (2005) Reprint [Erratum: in Eq. 13, k₀ in the Dirac delta should be multiplied by 2 (thanks to J.-T. Shen); page 139, 1st column, before-last line: should read n_e = 1.561 instead of n_e = 1.542--the latter is the extraordinary index of refraction at 915.8 nm.] 

A more general article on this project appeared recently as a chapter of a book: “Undergraduate Laboratories Using Correlated Photons: Experiments on the Fundamentals of Quantum Physics,” E.J.Galvez, in Invention and Impact: Building Excellence in Undergraduate Science, Technology, Engineering and Mathematics (STEM) Education, (AAAS, 2004) pp 113-118. Reprint.

Free download of Summer Workshop materials given at the 2008 AAPT Meeting in Edmonton, Canada (funded by NSF):
-- Lab Manual: comprehensive step-by-step instructions for setting up the labs.
-- PDF of Mathcad worksheet for calculating the phase-matching angle for type-I parametric down-conversion with BBO crystal.
-- Labview files for doing experiments:
             --- Dynamical phase: records photon counts as voltage sent to piezo is stepwise increased.
             --- Geometrical Phase: records photon counts pausing after every point--for manually changing a parameter, such as the orientation of a wave-plate or polarizer.

Check also Mark Beck's website (Whitman College) for more information and downloads on similar types of experiments.

General

The source of single photons involves the use of photon pairs produced by spontaneous parametric down conversion. The pairs are detected in coincidence. Below we describe our more recent results plus experimental details. We are currently updating this page (EG 7/29/05).

• Introduction

• Quantum mechanics a la Feynman

• Photon Quantum Mechanics for first-year students (taught in our intro course Phys120):

  • Probability amplitudes and the Quantum Eraser.

  • Entanglement.

  • A lab on the quantum eraser. and results taken by students.

• Lab for a Quantum Mechanics Course (NEW!)

  • Lab1: Superposition (revised 4/05)

  • Lab1: Superposition (2007 version)

  • Lab2: Photon Wavepackets (revised 4/05). See the results that students obtained!

  • Lab3: Quantum Eraser. (4/05) In contrast to our previous experiment, in this one we use polarizers instead of a half wave plate.

  • Lab3: Eraser (2007 version)

  • Lab4: Identical Photons. (4/05) Two photons go through a Mach-Zehnder interferometer.

  • Lab4: IdenticalPhotons (2007 version)

  • Lab5: Entanglement and Bell (2007)

• The apparatus:

  • The laser

  • Spontaneous parametric down conversion

  • The detection system

  • Aligning the optics

  • Interferometer path length alignment

  • Collinear down-conversion makes alignment easier

  • Low-cost alternatives:

    • Inexpensive piezo-driver.

    • Home-made counter.

• New Experiments:

  • Hong-Ou-Mandel dip-like result when two photons enter a Mach-Zehnder interferometer and leave separate ports. The report on this experiment appeared in a joint paper with Mark Beck presented at ETOP conference. Reprint.
     

• Research Experiments (which were parts of capstone undergraduate projects):

  • We could not help ourselves but to ask a few questions about a few topics:

    • The Entangled Quantum Eraser. This is an experiment with entangled photons where the labeling of paths of photons going through an interferometer is done by entangled partners in a remote location. "Nonlocal Labeling of Paths in a Single-Photon Interferometer," M.J. Pysher,* E.J. Galvez, K. Misra,* K.R. Wilson,* B.C. Melius,* and M. Malik* Physical Review A 72, 052327 (2005). Reprint.

    • Remote interferometer. This is a really cool experiment. Correlations between entangled photons are manipulated in such a way that the phase of the interference pattern of photons going through an interferometer is changed by actions on entangled photons that do not go through the interferometer. "Phase Shifting of an Interferometer using Nonlocal Quantum-State Correlations," E.J. Galvez, M. Malik,* and B.C. Melius,* Physical Review A-Rapid Communications 75, 020302(R) (2007). Reprint

    • Up-coming: Bell inequalities on single photons entangled in space and polarization.

Work in progress...

Thanks

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