My book is titled *Quantum Mechanics: Theory and Experiment*, and is written for a
junior/senior level quantum mechanics class. It is unique in that it describes
not only quantum theory, but also presents laboratories that explore truly
modern aspects of quantum mechanics. The book begins the presentation of
quantum mechanics using photon polarization as a prototypical two-dimensional
quantum system. It also has chapters describing **quantum measurement, entanglement, quantum
field theory and quantum information.** You can order the book
from the publisher,
or from Amazon.

Technology has advanced to the point where truly modern experiments which explore the fundamentals of quantum mechanics are accessible to undergraduates. Whitman College has developed a series of such experiments. We have also developed course materials and computer simulations which complement the experiments. This work was funded by the National Science Foundation* and by Whitman College.

· Slides of a talk given at Amherst College in Oct. 2004. This talk gives an overview of some of our earlier work: Proving light is made of photons, single photon interference, and the quantum eraser.

· Slides of a talk given at AAPT Meeting, July 2006. This talk overviews other experiments, with an emphasis on Hardy’s test of local realism.

· Slides of a talk given at AAPT Meeting, July 2006. This talk describes some of the equipment we use, and some of our “tricks of the trade”.

This experiment duplicates the experiment of Grangier, Roger and Aspect [1], in which they demonstrate that if a single photon is incident on a beamsplitter, it can only be detected at one of the outputs (not both.) To quote these authors, "a single photon can only be detected once!"

[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).

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.

We have replicated the experiment of Dehlinger and Mitchell [2,3], testing a Bell inequality using polarization
entangled photons. We have measured
S=2.467 __+__ 0.015, which violates the Bell inequality S__<__2 by
over 30 standard deviations.

[2] D. Dehlinger and M. W. Mitchell, "Entangled
photons, nonlocality, and Bell inequalities in the undergraduate
laboratory," Am. J. Phys. 70, 903-910 (2002).

[3] D. Dehlinger and M. W. Mitchell, "Entangled
photon apparatus for the undergraduate laboratory," Am. J. Phys. 70, 898-902 (2002).

We have constructed an experiment where the visibility of an observed fringe pattern is affected by the types of measurements performed on two spatially separated beams.

We have performed
a test of local realism using entangled photons produced by spontaneous
parametric downconversion. This
experiment is based on an idea originally proposed by Hardy for a test of local
realism without inequalities [4,5].
We find an over 70 standard deviation violation of the predictions of
local realism.

[4] L. Hardy,
‘‘Nonlocality for two particles without inequalities for almost all
entangled states,’’ Phys. Rev. Lett. 71, 1665–1668 (1993).

[5] P. G. Kwiat and L. Hardy, “The mystery of the quantum cakes,” Am. J. Phys. 68, 33-36 (2000).

We have performed an experiment that demonstrates that measurements performed on one beam can influence the quantum state of another beam. This is a form of EPR steering. Details are here.

**Abstract: **

We have performed a series of experiments using a spontaneous parametric down-conversion source to produce pairs of photons in either entangled or non-entangled polarization states. We determine the full quantum mechanical polarization state of one photon, conditioned on the results of measurements performed on the other photon. For non-entangled states, we find that the measured state of one photon is independent of measurements performed on the other. However, for entangled states, the measured state does depend on the results of measurements performed on the other photon. This is possible because of the nonlocal nature of entangled states. These experiments are suitable for an undergraduate teaching laboratory.

We have performed an experiment that measures entanglement witnesses. Entanglement witnesses tell you whether or not the state you have measured is entangled. Details are here.

**Abstract: **

An entangled state of a two-particle system is a
quantum state that cannot be separated—it cannot be written as the
product of states of the individual particles. One way to tell if a system is
entangled is to use it to violate a Bell inequality (such as the
Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is
necessary to violate these inequalities. However, there are other, easier to
perform measurements that determine whether or not a system is entangled; an
operator that corresponds to such a measurement is referred to as an
entanglement witness. We present the theory of witness operators, and an
undergraduate experiment that measures entanglement witnesses for the joint
polarization state of two photons. We are able to produce states for which the
expectation value of a witness operator is entangled by more than 300 standard
deviations. In order to further examine the performance of these witness operators,
we present a simple way to generate states that closely approximate Werner
states, which have a controllable degree of entanglement.

We have built computer simulations of some of our experiments. The programs are built from similar programs used to control actual experiments, so they have the same look and feel as the experimental programs. In particular, experimental noise is incorporated into the simulations in a realistic way.

We have designed two different coincidence counting units (CCUs) that measure all the coincidences you need to do all these experiments. 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 $10K of NIM electronics used in time-to-amplitude converter based coincidence measurements. Our CCUs even have higher count rates than the expensive stuff!! Click the above link to learn more about the units, and to get the info you’ll need to build one yourself. Done in collaboration with Dave Branning and his students at Trinity College.

Here’s the parts list a lot of people have been asking for. It’s reasonably comprehensive and up to date as of May 2013. It describes the equipment needed do all the experiments described on these pages.

Copies of the LabView
vi’s we use to do most of our experiments.

Some other groups we’ve collaborated with:

·
Colgate
University (Prof. Enrique Galvez)

·
Trinity College (Prof. David Branning)

·
Harvey Mudd College (Prof. Richard Haskell)

·
Reed College (Prof. John Essick)

Updates The latest info we have on tips,
equipment, etc.

We intend to add more material as it gets developed; please check back for updates.

Many of the files in this archive are stored in portable document format (.pdf). This format is viewable and printable by using Adobe Acrobat Reader. Acrobat Reader is free, and runs on Macintosh, Windows and UNIX.

If you have any problems downloading or printing the documents, please
let me know at: beckmk at
whitman.edu (replace "at" with @)

Faculty:

· Mark Beck, Principle Investigator

· Rob Davies, presently at Utah State University (Grangier expt., single photon interference)

Present and Former Students:

· Jeremy Thorn (Grangier expt.)

· Matt Neal (Grangier expt.)

· Vinsunt Donato (Grangier expt., single photon interference)

· Geoffrey Bergreen (Grangier expt., single photon interference)

· Ashifi Gogo (Bell, quantum eraser)

·
Will
Snyder (Bell, quantum eraser)

· J. Alex Carlson (Hardy test)

· Matt Olmstead (Hardy test)

· Jesse Lord (Coincidence Counting Electronics)

· Ethan Dederick (EPR Steering)

· Walker Larson (Single-Photon Entangled States)

· Elliot Burch (Single-Photon Entangled States)

· Celina Henelsmith (Single-Photon Entangled States)

· Marisol Beck, Harvey Mudd College (Entanglement Witness)

*Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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webpage updated 2/11/2016

*beckmk
at whitman.edu* (replace "at" with @)