Modern Undergraduate Quantum Mechanics Experiments

Beck Lab

Dept. of Physics, Reed College

Textbook

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.

Here are the errata for the book.

Description

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.

Overview

· 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.

Experiments

Proof of the Existence of Photons (the Grangier Experiment)

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).

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.

Bell Inequalities

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).

Quantum Eraser with Polarization Entangled Photons

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.

Hardy’s Test of Local Realism

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).

EPR Steering

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.

Entanglement Witness

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.

Other Stuff

Important information about detectors! Good news!

Coincidence Counting Units

The coincidence counting unit that we designed is now 20years old, and as such it is essentially obsolete. I cannot support it any more. If I was starting over, I would use a time-to-digital converter (time tagger) to do coincidence counting.

Parts List

Here’s the parts list a lot of people have been asking for. It’s reasonably comprehensive and up to date as of December 2021. It describes the equipment needed do all the experiments described on these pages.

LabView vi's

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

Pictures of the Experiments

Links

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)

Notes

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: beckmATreed.edu (replace "at" with @)

People Involved

Faculty:

· Mark Beck, Principle Investigator

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

Former Students (Whitman College):

· 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)

· Aidan McCormick (SPAM tomography)

· Meghan Feldman (SPAM tomography)

· Gabe Juul (SPAM tomography)

Others:

· 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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