Title: Quantum Socks and Photon Polarization Revision: July 29, 2005 Authors: Appropriate Level: Abstract: Time Required: Equipment: Acknowledgement: Lisa Larrimore, Saikat Ghosh, and George Wolf AP or Honors Regents This lab gives students a quick and fun introduction to the quantum world. Students will experiment with a model system that simulates the discrete and probabilistic nature of quantum objects. Using a Javascript program that models quantum socks, students are introduced to concepts such as superposition and the role of probability. A parallel is then drawn between the fictitious quantum socks and the real polarization of photons, and students will use what they have learned to predict the result of shining light through polarizing filters at various orientations. They will then perform this experiment and find that real photons behave in the same way as the photons modeled by the box. One 45-minute period Students need access to the Internet, where they can use Javascript-based quantum sock boxes (available at http://www.physics.cornell.edu/~larrimore/socks/). Each student group will need 3 polarizing filters and a light source (either a window or a laser pointer). Quantum Socks is a kit available through the CIPT equipment lending library. We would like to thank Professor Amy Bug of Swarthmore College for the idea of using quantum socks to introduce students to the quantum world. Center for Nanoscale Systems Institute for Physics Teachers 632 Clark Hall, Cornell University, Ithaca, NY 14853 ph: (607) 255-9434; fax: (607) 255-5579 www.cns.cornell.edu/cipt cipt_contact@cornell.edu
TEACHER SECTION Objectives: The take home message from this lab is that small (quantum) objects behave differently from the large (classical) objects that we are familiar with, so we must throw our physical intuition out the window and learn a new set of rules for how quantum objects behave. In particular: Some characteristics cannot be exactly known at the same time. For example: o Color and material of fictitious quantum socks o Vertical vs horizontal and +45 vs -45 degree polarization of photons o Position and momentum of electrons A quantum object can be in a superposition of different states. For example: o A red sock is a superposition of a cotton sock and a wool sock o A vertically polarized photon is a superposition of a +45 degree polarized photon and a -45 degree polarized photon o An electron can be in a superposition of all the positions around a nucleus Although you do not always know the outcome of a specific quantum measurement, you can know the exact probabilities of the different outcomes. The role of the scientist goes from determining exactly which number will come up to determining how often a number shows up on a die. Knowing the probabilities of different outcomes allows us to predict the results of experiments involving quantum objects accurately, such as shining photons through polarizing filters. Teacher preparation time required: 5 minutes to get out materials and load websites. Background information students need before starting this lab: Some knowledge of polarization would allow students to get more out of this lab, but it is not necessary. Background information for the teacher: The key to helping your students understand quantum mechanics is that they must throw away all their physical intuition. You cannot relate quantum behavior to things we are used to or come up with a straightforward model that explains everything. You just have to accept that there is a new set of rules to describe the behavior of objects that are as small as atoms. And these rules work: it is only using these rules that scientists have been able to explain the behavior of particles like electrons, protons, neutrons, and photons. Most physicists have to use quantum mechanics to understand their research. It is okay if your students are somewhat confused at the end of the experiment. Quantum mechanics is confusing! Neils Bohr, one of the founders of quantum mechanics, has said, Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it. And physicist Richard Feynman said, I think it is safe to say that no one understands quantum mechanics. The important point is that it works: it has been tested over and over, and has successfully predicted some startling results. And your students should be left with some taste of what quantum mechanics is all about.
Teacher Section Practical applications of quantum mechanics include lasers, magnetic resonance imaging, electron microscopes, and modern electronics. Some of your students may have also heard of quantum computers, in which information is not only stored as 1 s and 0 s, but also as any superposition of the two. A practical quantum computer is still far from being realized, but it could quickly solve problems like factoring large numbers that normal computers find difficult. Since the difficulty of factoring large numbers is currently used to secure most digital data, many people are very interested in developing a quantum computer that could break this encryption method. A question teachers have asked about this lab is whether they should think of the light in the polarizing filter experiment as a wave or a particle. I would say that it is neither. A photon, just like an electron or a proton, is a quantum mechanical object that has some wave-like characteristics and some particle-like characteristics, but the wave and particle pictures are only models to help you understand certain behaviors. I think that in the context of this exercise, it is best to think about the photons as individual objects, and to tell your students that each individual photon has a 50-50 chance of making it through a given polarizing filter. Here you can see one way of thinking about this in terms of vectors. (Note that this is also just a model, and it has its own limitations. To accurately describe the system you need some more complicated math.) A model of the path of 8 photons through 3 polarizing filters: This is probabilistic, so the number of photons might be 8, 5, 3, 2 or 8, 3, 1, 1 instead of 8, 4, 2, 1. Finally, a note about polarizing filters. Many people have the impression that if you have a filter with vertical wires (or a plastic polarizer, with polymer chains stretched in the vertical direction), then vertically polarized light will pass through. This is frequently explained by the picket fence model by saying that you can only wiggle a rope if the wiggles are in the same direction as the fence slats. But this is incorrect: only the light that is perpendicular to the wires or polymer chains will pass through. The energy of the light polarized in the same direction as the wires will be dissipated by the filter, and it will be blocked. To avoid confusion, I just draw filter with one arrow that shows the direction of transmitted light.
Teacher Section Quantum Socks and Photon Polarization: ANSWER KEY Introduction: This quick and fun exercise will introduce you to some of the differences between the large objects you are used to dealing with, which we refer to as classical, and tiny objects such as atoms, which we refer to as quantum. You are very familiar with the way classical objects, such as your socks, behave, but you will find that if you were able to shrink your socks down to the size of atoms, they can act very strangely! But once you understand the rules of the quantum world, you will see that you can predict some cool stuff, like how photons will behave when you pass them through polarizing filters. Sock and Photon Measurement Box Website: Begin by loading the website http://www.physics.cornell.edu/~larrimore/socks Measurements with the sock box: Start with your sock measurement box switched to classical socks. Any property of an object that you can measure, like the color or material of a sock, is known as an observable. What color is your sock to start out (red or blue) Everyone starts with a red sock. Now measure the material of your sock. Is it cotton or wool Everyone starts with a cotton sock. What do you think will happen if you measure the color again Try it were you right Still red. Now try measuring the material again has it changed No, it is still cotton, and still red. Has the sock in your box behaved any differently than you expected No (unless they had some strange expectations )
Teacher Section Now switch to measuring quantum socks, which makes the sock in your box shrink down to the size of atoms. What color is your sock to start out Assuming they switch to quantum after measuring color, the socks should all still be red. Now measure the material of your sock. Is it cotton or wool Half will be cotton, half will be wool. What do you think will happen if you measure the color again Try it were you right Spend some time making different measurements on your sock and recording your results. Is there any rationale to how your sock behaves Once you have some ideas, you can discuss them with your classmates and with your teacher. This should be the most time consuming part of the exercise, and students may find different ways of recording their data. For instance, here are two examples of what a student s data might look like: Each measurement will have a 50-50 chance of either outcome, no matter what the student measured before. So a sock that was red can later be measured as blue. The important point is that although you do not know the outcome of a given measurement, you can find out the probability of either result. (A good analogy is knowing how often a number shows up on a die, but not knowing which side of the die will come up when you roll it.) To get better statistics, the teacher may want to get students to combine their results. Measurements with photon polarization box: Now that you have a better understanding of how the quantum world works, you can look at some real quantum objects. As you know, we cannot make a sock so small that it acts quantum mechanically, but there are plenty of things that are already really tiny. For example, a photon is a single particle of light. Each photon has a property called polarization, which you can think of as a little two-sided arrow associated with each photon. (You may have seen polarizing sunglasses, which work by filtering out photons with certain polarizations.) Polarization is an observable for a photon, just like color and material are observables for socks. We can describe photons by which way their polarization arrow is pointing, like this: Vertically polarized: Polarized at +45 degrees: Horizontally polarized: Polarized at -45 degrees:
Teacher Section Photon polarization works the same way as the color and material of your socks: Just like you can measure to see if a sock is red or blue, you can measure to see if a sock is vertically or horizontally polarized. And just as a red sock is a superposition of a cotton sock and a wool sock, a vertically polarized photon is a superposition of a photon polarized at +45 degrees and one polarized at -45 degrees. You can try this out. Switch your box from a sock measurement box to a photon measurement box, and record some measurements of the polarization. What do you observe Students should find exactly the same results that they did for socks. If the photon is vertically polarized, then there is a 50-50 chance that it will be +45 or -45 degree polarized, etc. Experiment with Polarizing Filters: A polarizing filter is designed to only let through photons with a certain polarization. The double-sided arrows on your filters indicate which photons are able to get through. What do you expect to happen if you send photons through a vertical polarizing filter followed by a horizontal polarizing filter (Hint: This is like starting with a vertically polarized photon and then measuring whether it is vertically or horizontally polarized what does your photon box tell you) They should expect that none of the photons get through. If they use their box to start with a vertically polarized photon and then measure whether it is vertically or horizontally polarized, it will always still be vertically polarized. Try this using the polarizing filters and a light source, like a window or a laser pointer. Do any photons get through Is this what you expected No photons should get through. What do you expect to happen if you now put a filter in the middle at +45 degrees, so that you have a vertical filter, then a +45 degree filter, and then a horizontal filter This is like starting with a vertically polarized photon, then measuring whether it is +45 degree polarized (half of them should be), and then measuring whether it is horizontally polarized (half of the +45 degree polarized photons will be). So some photons (1/4 of the ones that get through the first filter, or 1/8 of the original photons) should get through. Try doing this experiment. Do any photons get through How does this compare to the amount that get through just one filter Yes, 1/4 of the photons that get through one filter should get through the third.
STUDENT SECTION Introduction: This quick and fun exercise will introduce you to some of the differences between the large objects you are used to dealing with, which we refer to as classical, and tiny objects such as atoms, which we refer to as quantum. You are very familiar with the way classical objects, such as your socks, behave, but you will find that if you were able to shrink your socks down to the size of atoms, they can act very strangely! But once you understand the rules of the quantum world, you will see that you can predict some cool stuff, like how photons will behave when you pass them through polarizing filters. Sock and Photon Measurement Box Website: Begin by loading the website http://www.physics.cornell.edu/~larrimore/socks Measurements with the sock box: Start with your sock measurement box switched to classical socks. Any property of an object that you can measure, like the color or material of a sock, is known as an observable. What color is your sock to start out (red or blue) Now measure the material of your sock. Is it cotton or wool What do you think will happen if you measure the color again Try it were you right Now try measuring the material again has it changed Has the sock in your box behaved any differently than you expected
Student Section Now switch to measuring quantum socks, which makes the sock in your box shrink down to the size of atoms. What color is your sock to start out Now measure the material of your sock. Is it cotton or wool What do you think will happen if you measure the color again Try it were you right Spend some time making different measurements on your sock and recording your results. Is there any rationale to how your sock behaves Once you have some ideas, you can discuss them with your classmates and with your teacher. Measurements with photon polarization box: Now that you have a better understanding of how the quantum world works, you can look at some real quantum objects. As you know, we cannot make a sock so small that it acts quantum mechanically, but there are plenty of things that are already really tiny. For example, a photon is a single particle of light. Each photon has a property called polarization, which you can think of as a little two-sided arrow associated with each photon. (You may have seen polarizing sunglasses, which work by filtering out photons with certain polarizations.) Polarization is an observable for a photon, just like color and material are observables for socks. We can describe photons by which way their polarization arrow is pointing, like this: Vertically polarized: Polarized at +45 degrees: Horizontally polarized: Polarized at -45 degrees:
Student Section Photon polarization works the same way as the color and material of your socks: Just like you can measure to see if a sock is red or blue, you can measure to see if a sock is vertically or horizontally polarized. And just as a red sock is a superposition of a cotton sock and a wool sock, a vertically polarized photon is a superposition of a photon polarized at +45 degrees and one polarized at -45 degrees. You can try this out. Switch your box from a sock measurement box to a photon measurement box, and record some measurements of the polarization. What do you observe Experiment with Polarizing Filters: A polarizing filter is designed to only let through photons with a certain polarization. The double-sided arrows on your filters indicate which photons are able to get through. What do you expect to happen if you send photons through a vertical polarizing filter followed by a horizontal polarizing filter (Hint: This is like starting with a vertically polarized photon and then measuring whether it is vertically or horizontally polarized what does your photon box tell you) Try this using the polarizing filters and a light source, like a window or a laser pointer. Do any photons get through Is this what you expected What do you expect to happen if you now put a filter in the middle at +45 degrees, so that you have a vertical filter, then a +45 degree filter, and then a horizontal filter Try doing this experiment. Do any photons get through What fraction of the original number of photons do you end up with