quantumphysics.iop€¦ · focus on quantum information theory (two-level systems are qubits)....

Research-based interactive simulations to support quantum mechanics

learning and teaching

Antje Kohnle

University of St Andrews

GIREP-MPTL 2014 International Conference, 7-12 July, Palermo

www.st-andrews.ac.uk/physics/quvis

quantumphysics.iop.org

The QuVis team

Development of simulations and accompanying activites: Antje Kohnle

Students coding simulations: Martynas Prokopas, Aleksejs Fomins, Joe Llama, Inna Bozhinova, Gytis Kulaitis + others

Final year project students: Bruce Torrance, Anna Campbell, Scott Ruby, Cory Benfield + others

Technical support: Tom Edwards, Alastair Gillies

Faculty involved in evaluation: Christopher Hooley, Charles Baily, Natalia Korolkova, Donatella Cassettari, Bruce Sinclair, Georg Hähner, Friedrich Koenig, Noah Finkelstein, Catherine Crouch, Gina Passante + others

Eur. J. Phys. 31 (2010) 1441-1455; Am. J. Phys. 80 (2012) 148-153

Outline

Challenges of quantum mechanics instruction

Interactive simulations

Overview of the QuVis resources

Development process and evaluation outcomes

Conclusions and future plans


“I will never believe that god plays dice with the universe.”

– Albert Einstein “I think I can safely say that nobody understands quantum mechanics.”

– Richard Feynman

“Learning quantum mechanics is challenging.”

– Chandralekah Singh, University of Pittsburgh

Counterintuitive behaviour which disagrees with our classical intuition.

Phenomena that can not be observed directly.

(c) 1989 Hitachi Ltd.

Complicated mathematics required to solve even simple phenomena.

Instruction often focuses on simplified abstract models.

Observing screen

Double slit

Electron source

Observing screen


Outline






Resources shown recommended in the 2014 MPTL review Review process: E Debowska et al., Eur. J. Phys. 34 (2013) L47 www.um.es/fem/PersonalWiki/pmwiki.php/MPTL/Evaluations

Making the invisible visible

S B McKagan et al, AJP, 76, 406 (2008) http://phet.colorado.edu/

Zhu and Singh, Phys Rev ST PER 8, 010118 (2012)

http://www.compadre.org/psrc/items/detail.cfm?ID=6814 Belloni and Christian, Am J Phys, 76, 385 (2008)

position x

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Visualizing complicated time-dependent behaviour to help build physical intuition

Challenging students’ classical ideas by allowing them to assess whether they can explain experimental outcomes

The potential of interactive simulations

Engage students to explore physics topics through interactivity (student agency), prompt feedback (trial and error exploration) and multiple representations.

Through careful interaction design, implicitly guide students towards the learning goals.

Activities promote guided exploration and sense-making.

e.g. Podolefsky et al., Phys Rev ST PER, 6, 020117 (2010)

Interactivity and student agency

Simulation/activity Group 2 (N=48):

Group 1 (N=34): Screenshots/activity

not enjoyable

very enjoyable

Group 1: 20/29 comments similar to “Much easier to play around with simulations so that you can run tests and experiments.”

13/14 St Andrews level 2 Quantum Physics

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Outline






QuVis: www.st-andrews.ac.uk/physics/quvis

17 simulations 50 simulations 18 simulations NEW: sims for touchscreens

research-based; freely available for use online or download; introductory to advanced level


problem sets, password-protected solutions available to instructors


One collection embedded in a full curriculum at quantumphysics.iop.org developing introductory quantum theory using two-level systems

IOP quantum physics: quantumphysics.iop.org

Kohnle et al., Eur J Phys, 35, 015001 (2014)

Derek Raine (Leicester)

Project lead and editor

Pieter Kok (Sheffield)

Author Quantum

information

Mark Everitt (Loughborough)

Author Foundations

of qm

Dan Browne (UCL)

Author Quantum

information

Antje Kohnle (St Andrews) Simulations

Physics education

Elizabeth Swinbank (York) Editor;

Physics education


Christina Walker (IOP)

Project manager

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Quantum mechanics curricula in the UK

Survey by Derek Raine (Leicester), 2011

Birmingham

Bristol Cambridge

Exeter Galway

Glasgow Heriot-Watt

Hertfordshire Hull Imperial

Kent King's

Leicester Loughborough

Sheffield St Andrews Strathclyde

Sussex Swansea

UCL Warwick York

IOP resources: novel material for these and other topics suitable for a first university course in quantum physics

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Advantages of developing introductory quantum theory using two level systems (spin ½ particle, two-level atom, single photons in an interferometer):

Focus on experiments that have no classical explanation.

Focus on interpretive aspects of quantum mechanics.

Focus on quantum information theory (two-level systems are qubits).

Mathematically less challenging: basic algebra versus differential equations and calculus. Some linear algebra included in the IOP resources.


Michelini, Ragazzon, Santi and Stefanel (2000), Scarani (2010), Malgieri, Onorato & De Ambrosis (GIREP 2014)

In-class trials: level two Quantum Physics (Scottish level two = first year university elsewhere)

The photoelectric effect; single photon experiments.

Spin; successive Stern-Gerlach experiments; entanglement; hidden variables

Matter waves; the Schrödinger equation; energy eigenstates; infinite and finite square wells

Pre-lecture readings from the IOP Quantum Physics resource Workshop: Interferometer experiments simulation Homework: Phase shifter in a Mach-Zehnder interferometer

Workshop: The expectation value of an operator Workshop: Entangled spin ½ particle pairs versus hidden variables Homework: Quantum cryptography

PART 1

PART 2

Two-level systems at the introductory level

9/18 lectures on two-level systems

2014 (N=73):

2013 (N=68):

5/16 lectures on two-level systems

level 2 Quantum Physics

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Perceived difficulty of Quantum Physics part 1 (two-level systems) compared

with part 2 (wave mechanics)

Two-level systems at the introductory level

2013 (N=70) 2014 (N=87)

Significant differences with large effect sizes.

Two-level systems

Wave mechanics

p-value for paired t-test

Effect size

Exam 2013 (Instructor A)

71.7% 56.7% p

Outline






“How useful for learning quantum physics have you found the simulations used in the course?”

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5 simulations

13/14 level three Quantum Mechanics (N=57)

17 simulations

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Student perceptions

“I wish for the simulations to

remain in Advanced Quantum Mechanics.”

13/14 level four Advanced Quantum Mechanics (N=16)

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Evaluation and refinement using student feedback key in developing educationally effective resources.

Student perceptions

Developing educationally effective simulations

considers research on

student difficulties

interaction design

visualization

Initial design

physics student coders

iterative revisions during coding

Coding

revisions to all simulations and activities wherever appropriate

Observation sessions

revisions

ideas for new simulations

In-class trials

student difficulties: Johnston et al (1998), Bao & Redish (2002), Wittmann et al (2005), Singh (2008) , ... interaction design: Clark & Mayer (2008), Adams et al (2008), Podolefsky et al (2010), Saffer (2010), ... visual representations: Adams et al (2008), Lopez and Pinto (2014), Chen and Gladding (2014), ...

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Free exploration (implicit scaffolding)

Work on activity (difficulties, revisions)

Investigating visualizations

In-c

lass

tri

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Surveys (student perceptions)

Observations (interface design)

Analytics of control use (interface design)

Activity responses (difficulties)

Pre- and post-tests (learning gains)

Comparative studies (effectiveness)

Research methods

New Quantum curriculum collection (17 simulations) 42 hours of observation sessions (17 sims, 19 students) in-class trials in using 9 simulations

Kohnle et al., 2013 PERC Proceedings

At the heart of quantum mechanics lies the superposition principle:

physics.stackexchange.com

Visualizing non-classical states

For a single photon in an interferometer:

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2 |top path > +

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2 |bottom path >

Example: Visualizing the photon superposition state Aim: facilitate the development of a productive mental model

for introductory-level students

importance of mental models: Baily & Finkelstein, Phys Rev ST PER (2010)


2013 in-class trials at St Andrews and US institution: V1 led some students to develop incorrect ideas about quantum superposition.

Animations for four revised visualizations of photon superposition Student interviews (N=9): students describe what the visualizations

suggest to them and choose from a list of 13 statements.

Original (V1)

(V2) (V3)

(V4, adopted) (V5)


Limitations: Small region of “parameter

space” explored Small number of interviews

(N=9)

Revised (V4) adopted

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productive: Phase relationship between the two paths is maintained

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incorrect: Photon splits into two half-energy photons

Results from in-class trials

Limitations: 2013 only use of simulation, 2014 additional reading and lecture on single photon interference

“What happens when a photon encounters a beamsplitter?” Interferometer simulation, St Andrews level two, coded responses

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takes one path

detection reveals

path

takes both paths

splits into two photons

other

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V4

inter-rater reliability: Cohen's Kappa 0.62-1 𝜒2 4, 𝑁 = 104 = 15.9, exact 𝑝 = 0.003

making sense of the visualizations

“Ah yes, so, umh, again these two are connected. One is slightly brighter than the other suggesting that the probability of them arriving at detector 1 is greater than at detector 2. That does seem to be the case as they pass through – there seems to be a bit more in detector 1 than in detector 2.”


making predictions and testing them experimentally


[moves phase shift to 2π] “I guess this will go back to detector 1 as you would suspect. And again with 4π.” [moves phase shift to 4π]”

generalizing results to come up with general rules


[moves to 3π] “... an odd number of π produces a wave going directly to detector 2, an even number produces a photon heading directly to detector 1 and then in between sort of the probability slowly gradually shifts from detector 1 to detector 2.”


[points to expectation value panel] “The expectation value – I’m not really sure what that is. It’s got a kind of hat on it. Is there something I missed in the introduction?”


Is there anything in the simulation you can find to help you understand the expectation value better?

Would the following additional control / information .... help you?

Would the following rephrasing of the text / activity help you? ...

Using this, can you derive / explain the formula for the expectation value shown?

aim: find patterns in student difficulties and ways to overcome them.

Hilbert space; Matrix formalism of QM; Pure and mixed states via the density matrix.

Entanglement; reduced density matrix; entropy of entanglement

Quantum teleportation; quantum cryptography – the BB84 protocol

Quantum computing

Homework (review): Graphical representation of complex eigenvectors

Homework: Superposition states and mixed states

Homework: Entanglement: the nature of quantum correlations

Homework: Quantum key distribution

In-class trials: Advanced Quantum Mechanics (Scottish level four = third year university elsewhere)

Do students achieve the learning goals?

assess success in completing challenges

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unanswered

incorrect

partiallycorrect

correct

? is mixture

20/80 mixture

?? is super-position, correct

coefficients

N=20, level 4 Advanced QM

Superposition states and mixed states: success in completing challenges

Pre- and post-test question (abbreviated)

An equal mixture of | ↑> and | ↓> and particles each in a

superposition 1/ 2(| ↑> + ↓> are experimentally indistinguishable.

Particles in a superposition are actually in state | ↑> and | ↓> , we just don’t know which.

Particles in a superposition state actually oscillate rapidly in time between | ↑> and | ↓> .

If we measure a different component of spin than Sz, we can experimentally distinguish between the two.

Simulation/activity Pre-test Post-test

1 week

Does the simulation enhance student learning?

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N=20, level 4 Advanced QM

Pre-test Post-test

Superposition states and mixed states: pre- and post-test outcomes

Simulation activities

1) Have a play with the simulation for a few minutes, getting to understand the controls and displays. Note down five things about the controls and displayed quantities that you have found out.

Question 1 correct (N=52)

Question 1 not answered

(N=13)

p-value for t-test

(two-tailed)

Correct activity problems

(excludes Q1) 5.2 4.1 0.01

Cryptography simulation, level 2, 2014

Question 1 may be important for success on the activity.

Question 1 for all simulation activities:

Driving questions may optimize exploration: Adams et al., PERC Proceedings, 2009

Outline






Conclusions

Research-based interactive simulations can address challenges of quantum mechanics instruction (and other topics) through student agency, implicit guidance, trial and error exploration and multiple representations.

An iterative development process informed by student feedback from individual sessions and in-class trials is key to developing educationally effective resources.

Initial evidence that QuVis simulations are helping students learn quantum mechanics topics, including topics such as entanglement and hidden variables at the introductory level.

Future plans

Extend the QuVis HTML5 collection to include amongst other topics more simulations on quantum information processing and single photon experiments; for the school and university level; revise old simulations.

Include more game-like elements aligned with learning goals.

More open and exploratory activities, including intrinsically collaborative activities.

Multi-institution evaluation studies and more community input into development. Volunteers welcome! Contact: Antje Kohnle, [email protected]

quantumphysics.iop€¦ · focus on quantum information theory (two-level systems are qubits)....

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