HW Set#3 Due Sept 6 Abraham-Minkowski comments (Extra Credit!)
Aug. 29
Information & Operations/Processing:
In-class discussion of HW Set #1, from Beck Ch. 1 pre-term reading (Any questions?)
Useful Formalisms versus Truth: Probability (crime waves, pandemic waves; an average family might have 2.5 children) versus Reality (the localized nature of events: each robbery occurs at a place, each threshold of contagion occurs within an individual; children within each family are counted in integer units); before a robbery takes place, it does not have a location (even if there is some expectation, on the part of the robbers, about where things will go down).
Beck Ch. 1, a prerequisite to starting the term (!)
Pre-labs
Before tonight's lab, you need to read Ch 1-2 of Laboratory Optics, by Peter Beyersdorf ("Before You Begin" and "Setting Things Up"). Be sure you watch videos in Beyersdorf's book: they appear as little black squares until you click on them.
In lab, you'll remind yourself of some "Wave Physics" you've seen in earlier coursework: compare the diffraction pattern due to a single slit with what is produced by two slits of equivalent width.
Also in lab, you'll want to use a couple of irises, as shown in Beyersdorf's Sect. 3.1, to make sure that your laser is parallel to the optical table, and to a line of holes on that table. This is really quite difficult to accomplish UNLESS you have paid attention to the advice that Beyersdorf gives! Once that is accomplished, you should be in good position to build a "beam expander" (i.e., two lenses separated by the sum of their focal lengths), and test the output using Beyersdorf's Sect. 3.2
Again, in preparation, read Ch 1-2 of Laboratory Optics, by Peter Beyersdorf ("Before You Begin" and "Setting Things Up")
Is Energy itself a statistical construct?
Where's the energy go when there is destructive interference?
Useful notes on opto-mechanics or on lenses?
Whatever you see, say what you saw
(and whatever meaning you can extract)
HW Set# 4 Due Sept 7 Beck 2.A.1
HW Set# 5 Due Sept 11 Beck 3.4
Sept. 5
All information must be physically held.
Differing rubrics may be applied to the bookkeeping, yielding, e.g., the Abraham-Minkowski "paradox" for Ray-Optic Momentum What is the momentum "of the photon" inside a transparent material? (Your comments are due on Wednesday!)
In-class, at-the-board, discussion of HW problems due so far
To directly observe the action of (a small) optical momentum transfer to optical components, it makes sense to use microscopic components, ...but you may still want components large enough that you can resolve their details under a microscope. Today, we discuss Ray Optics vs. Physical Optics: we consider the difference between the momentum transferred via reflection and absorption, and then break optical forces into components along the optic axis and perpendicular to that axis. When might we care about Numerical Aperture?
For most labs subsequent to this week's, you'll need more careful alignment than you will for this week, so please, this week, also read Ch 3 of Laboratory Optics ("Aligning Things")
Today, we kill time while waiting for you to begin annotating Beck Ch 3
Questions re: Beck Section 2.5? (e.g., p. 37 on coherence length)
Beck Problem 2.14?
Beck's Complement to Ch. 2?
Over the weekend:
Begin annotating Beck thru Sect 3.5 (Quantum States)
Beck's Complement to Ch. 2
Measuring the Polarization of Light:
Are the angular settings on your polarizers consistently calibrated?
When do you need a transparent wave plate, rather than an inexpensive absorbing polarizer?
HW Set# 5 Due Sept 11 Beck 3.4
HW Set# 6 Due Sept 13 Beck 3.10, 3.11, 3.13, 3.14
HW Set# 7 Due Sept 15 Beck 4.1, 4.6
Sept. 12
Representation of Quantum States
With the start of Beck Ch 3, you've begun your trip "down the rabbit hole, Alice!" (or "Bob," ...or whomever you claim to be):
Be prepared to discuss Beck p. 59, Experiment 6:
How does the photon "know"...?
In lab, you'll either work on:
Further exploration of waveplates & polarization, or...
Return of the droplet lens, and its characterization!
(Division of labor can help you to move forward!)
Review of crime waves, pandemic waves, etc.: before a robbery takes place, it does not have a location (even if there is some expectation, on the part of the robbers, about where things will go down), even though measured events such as a robbery each occur at a place, and each threshold of contagion occurs within a localized individual
Waves, in general, don't have 'a' position:
So, what does it mean to speak of the velocity of a wave?
Therein lies the origin of the Operator Structure of quantum mechanics.
Look ahead towards our next class!
Beck thru 4.4
Extend your work from previous lab meetings
HW Set# 8 Due Sept 20 Beck 4.7, 4.8
HW Set# 9 Due Sept 22 Beck 4.14, 4.19, 4.20
Sept. 19
EXAMINATION I covers through
Beck Ch. 3 and Basics of Optical Trapping
Your review will surely benefit from supplemental readings: find a couple of references that you like! Is it better to search within the American Journal of Physics, or to use Web of Science, or Google Scholar, or just a basic browser search? Import your favorite references into Zotero
Have you watched all videos from Ch. 1-4 of Laboratory Optics?
BE PREPARED TO ANSWER QUESTIONS IN LAB!
Read this week's
Lab Procedural noting that, to minimize aberrations, the optic axis of each lens can be aligned with the grid of the optical breadboard, as a fiducial reference (i.e., a "guide to the eye"). Key methods introduced involve "walking" a laser through "cloned" apertures, and beam expansion & collimation. Having mastered these, you can apply your methods towards calibrating the retardance of a programmable waveplate that you will need for later labs
CAUTION: Our
405nm blue-ray lasers should never be allowed to impinge upon an SLM, as it could cause crosslinking of the liquid crystal, destroying the SLM! Please use lower-energy photons when working with an SLM
Review of Jones Vectors from Ref. Sheet, my handout on Matrices, HW Sets #7-9
Changing Bases & Measurement
We will later use 405nm blue-ray lasers as the pump beam for a non-linear process called "Spontaneous Parametric Downconversion" (SPDC), where (rarely generated) degenerate entangled photons are produced at 810nm. (This is our key to working with TRUE single photons!) It is safe to use an SLM at 810nm, as these are lower-energy photons. ...Based upon your measurements of this week, which were made using visible light, predict the maximum "phase throw" expected when using your particular SLM at 810nm (at the same angle of incidence): in preparation for next week's Lab Practicum, think about the wavelength dependence of the retardance of a waveplate, which depends upon the ratio of its physical thickness to the wavelength of the light used, and therefore upon how the index of refraction varies as a function of frequency.
Beck thru 4.6
Beck Complement
to Ch 4
Beck thru Sect 5.4
Lab Part 1: Expanding & Collimating a beam
Lab Part 2: The SLM as a Variable Waveplate (or "Retarder")
HW Set# 10 Due Sept 25 Beck 5.1, 5.2, 5.6
HW Set# 11 Due Sept 27 Beck 5.7, 5.12
HW Set# 12 Due Sept 29 Beck 5.23
Sept. 26
In class today, you will have the opportunity to work with others on homework
Commutation, Indeterminacy, and Complementarity
We started our discussion with the simple case of photon polarization was because that can be described with just two basis states; in general quantum systems may require a much larger (perhaps infinite) set of basis states. These slides illustrate that simple fact. Supplemental slides consider the physicality of
Information (and its destruction)
Read the materials linked at left, then TEST YOUR UNDERSTANDING IN THE LAB!
Sept. 28
To reinforce concepts encountered so far, consider a problem
analogous to photon polarization: Electron Angular Momentum States. In Chapter 6 of Beck's text, we now consider performing the kinds of "Gradient Force experiments" that I also use in the context of Optical Tweezers, except that while my Optical Tweezers act on polarized microparticles (which are still large enough to behave classically), Beck considers what happens when we perform "Gradient Force experiments" on quantum particles:
Spin States as a Paradigm: "Toto, I don't think we're in Kansas anymore"
Over the weekend, read up to (but not including) Sect. 1.3 of our own notes prepared during previous work at IWU! I tried to go over the same material in the final four and a half pages of my Igor Pro Tutorial (i.e., Sect. 9.3-9.4)
Beck thru Sect. 6.4
The Future of Optics is Programmable
HW Set# 13 Due Oct 4: Beck 6.8, Read the next HW
HW Set# 14 Due Oct 6: Beck 6.13, 6.19, 6.20, 6.23
Oct. 3
Discussion of your required "weekend reading:" Spontaneous parametric down-conversion versus Classical Second-Harmonic Generation
On the matter of "pure" states and "mudbloods," once in a great while an energetic photon (call her "Hermione") will give her energy to "Harry" & "Ron," who are INSEPARABLE: their futures are said to be irrevocably entangled, which will (later) lead us to discussion of the strange language of the Klyshko Advanced Wave picture, a phrasing sometimes used to predict the outcomes of experiments, by saying it is AS IF something went backwards in time:
(A similar picture could be applied to describe Fermat's Principle of Least Time, if you wish.)
Summary of the formalism associated with Spin States
How would you create your own Optical Logic Gates?
The local "time lags" you program into the SLM skew the local Poynting vector
Oct. 12
The weirdness of "Particle Interference" necessarily leads us into discussion of various (disputed!!) notions of what's "really" going on here:
Is it possible that our experiments can "rule out" any of these models?
Over the weekend, read Beck Ch 7-8, together:
Following up our discussion of the irreality of the wave function (and of probability waves in general), we will be taking up the notion of "Compatible Observables," in the context of Angular Momentum (& Rotation of "things") in Quantum Mechanics, and describing a Single Photon in terms of a vector field
Team B Optimize Amplitude Modulation:
Using any drawing program
(or presentation software)
Explore Two Slits (one of variable transmissivity).
Project these onto a far screen
"Mrs. Weasley's Connundrum," wherein the essential principles of Multi-particle Wavefunctions are revealed via discussion of two non-interacting particles using, as a simple example, two teenage brothers (call them "Fred" and "George").
Is the universe becoming more & more entangled? What limits entanglement?
If there are limits on entanglement, what are the consequences for Snape & Dumbledore's Secure Communications (a next-generation occlumency protocol intended for avoiding eavesdropping by He-Who-Must-Not-Be-Named).
Statistical Mechanics of Small Systems
Beck text Ch 7-8
Pre-labs
You might say that something is particle-like if it is countable — e.g., by (very carefully analyzing the statistics of) an avalanche detector. Begin by reviewing (cheap) low-efficiency SPAD detectors:
Over the weekend: Consider your next lab: read Beck p. 435-448, and Complete your
"Lab Ticket" before Lab!
As a Visiting Professor at IWU, Robert Wagner gave a Nat. Sci. Colloquium, entitled "But It's a Wave Equation! Finding the Particles in Quantum Mechanics." Before discussing this perspective, read this article, which could have been entitled, "But it's a PARTICLE detected! Finding the waves in quantum mechanics."
Understand the plan: your BBO crystal should be as far as is practical from your collection optics!
1) Use cloned iris apertures to align your 405-nm laser parallel to a line of holes running along the middle of your workspace: remember Peter Beyersdorf's advice to place your 2nd mirror as close as is practical to the first aperture; that mirror's post holder should be on a slotted base
2) Use a tip-tilt ("kinematic") mount to align your BBO crystal such that the beam is normal to it (and back-reflections return towards the source
3) Assemble your collection optics (without the long-pass filter), and place those as far from the BBO as is practical, at the angles specified by your lab ticket calculation
4) Use a long-wavelength laser to "back-propagate" light through your collection optics, to ensure that they are pointing towards your BBO. (Ideally, back-propagated light from one collector will go to the other, and vice-versa.)
5) Add your long-pass filter (RG780 glass) to protect the expensive SPADs from room light
6) Connect the fiber coupling to your expensive SPADS
Read Beck p. 435-448
Complete your
"Lab Ticket" before Lab!
Oct. 26
What might you explore, regarding
Wavefront Engineering?!!
Observed phenomena of these sorts demand revision of your mental model of what a "particle" is!
Over the weekend, read Andy Ding's thesis, Sect. 1.3-1.4
Hermione is a RARE photon!
The 810-nm paired photons will be too rare to see with your eyes
(which are not sensitive at 810nm)
It's time to set up some high-quality detectors!
HW Set# 20: Write in your OneNote!
Oct. 31
"But It's a Wave Equation! Finding the Particles in Quantum Mechanics."
Understand the coincidence counter software, expected count levels and, critically, from Sect. 1.4 of Andy Ding's thesis, the statistical metric used to determine whether the source exhibits "photon bunching" (or "anti-bunching")
Andy Ding's thesis
Sect. 1.3-1.4
Nov. 2
CLASSICAL Fields: mode expansion solution to Maxwell's wave equation
A prequel to further discussion about Time Evolution in quantum physics
...We can discuss the
Violence of the NanoWorld, dissipation of information, and how the Arrow of Time emerges (and how you can use an optical trap to explore its emergence) [Did time exist before the Big Bang? Did time exist 'right after'?]
Over the weekend: Consider your next lab: read Beck p. 449-462, and Complete your
"Lab Ticket," Q1 & Q2, before Lab!
Even More Stats
Work towards SPONTANEOUS (i.e., non-classical) Parametric Down-Conversion (SPDC) for creation of (entangled) SINGLE photons
HW Set# 21: Lab!
Nov. 7
Number States, Coherent States, and Thermal Sources
Further discussion of Thermal Sources, Coherent States, Number States and Discretization of the Field. Did you, in the lab, prove the existence of the photon? How did your work go beyond what the PhotoElectric Effect proved? What do we mean when we speak of The Momentum of The Photon, its Spin Angular Momentum, and its Orbital Angular Momentum? In the end, what have we learned, and what outstanding questions remain?
