quantumphysics.iop€¦ · Focus on quantum information theory (two-level systems are qubits)....
Transcript of quantumphysics.iop€¦ · Focus on quantum information theory (two-level systems are qubits)....
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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
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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
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Outline
Challenges of quantum mechanics instruction
Interactive simulations
Overview of the QuVis resources
Development process and evaluation outcomes
Conclusions and future plans
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Challenges of quantum mechanics instruction
“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
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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
Challenges of quantum mechanics instruction
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Outline
Challenges of quantum mechanics instruction
Interactive simulations
Overview of the QuVis resources
Development process and evaluation outcomes
Conclusions and future plans
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
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Making the invisible visible
S B McKagan et al, AJP, 76, 406 (2008) http://phet.colorado.edu/
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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)
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Visualizing complicated time-dependent behaviour to help build physical intuition
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Challenging students’ classical ideas by allowing them to assess whether they can explain experimental outcomes
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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)
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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
Challenges of quantum mechanics instruction
Interactive simulations
Overview of the QuVis resources
Development process and evaluation outcomes
Conclusions and future plans
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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
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QuVis: www.st-andrews.ac.uk/physics/quvis
problem sets, password-protected solutions available to instructors
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QuVis: www.st-andrews.ac.uk/physics/quvis
One collection embedded in a full curriculum at quantumphysics.iop.org developing introductory quantum theory using two-level systems
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IOP quantum physics: quantumphysics.iop.org
Kohnle et al., Eur J Phys, 35, 015001 (2014)
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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
IOP quantum physics: quantumphysics.iop.org
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.
IOP quantum physics: quantumphysics.iop.org
Michelini, Ragazzon, Santi and Stefanel (2000), Scarani (2010), Malgieri, Onorato & De Ambrosis (GIREP 2014)
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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
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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)
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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
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Outline
Challenges of quantum mechanics instruction
Interactive simulations
Overview of the QuVis resources
Development process and evaluation outcomes
Conclusions and future plans
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“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
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“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
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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
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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
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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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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)
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Visualizing non-classical states
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)
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Visualizing non-classical states
Limitations: Small region of “parameter
space” explored Small number of interviews
(N=9)
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incorrect: Photon splits into two half-energy photons
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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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inter-rater reliability: Cohen's Kappa 0.62-1 𝜒2 4, 𝑁 = 104 = 15.9, exact 𝑝 = 0.003
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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.”
Observation sessions
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making predictions and testing them experimentally
Observation sessions
[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]”
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generalizing results to come up with general rules
Observation sessions
[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.”
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Observation sessions
[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?”
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Observation sessions
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.
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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)
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Do students achieve the learning goals?
assess success in completing challenges
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Superposition states and mixed states: success in completing challenges
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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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Pre-test Post-test
Superposition states and mixed states: pre- and post-test outcomes
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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
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p-value for t-test
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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
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Outline
Challenges of quantum mechanics instruction
Interactive simulations
Overview of the QuVis resources
Development process and evaluation outcomes
Conclusions and future plans
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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.
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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]