Monthly Archives: June 2011

Readings on Optical Gates

Programmable optical processor based on symbolic substitution
Karl-Heinz Brenner
Applied Optics, Vol. 27, Issue 9, pp. 1687-1691 (1988) doi:10.1364/AO.27.001687

Digital optical computing with symbolic substitution
Karl-Heinz Brenner, Alan Huang, and Norbert Streibl
Applied Optics, Vol. 25, Issue 18, pp. 3054-3060 (1986)

A scheme for efficient quantum computation with linear optics
E. Knill1, R. Laflamme & G. J. Milburn
Nature 409, 46-52 (4 January 2001) | doi:10.1038/35051009; Received 24 July 2000; Accepted 13 November 2000

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Day 3 Week 2 REU

Yesterday was a most exciting day. The morning was spent on Shor’s Algorithm again.  The final part I am working on is the classical algorithm for continuous fraction expansion. In Shor’s Algorithm the quantum circuit outputs a phase shift of the form s/r where r is an unknown variable. To determine r, continuous fraction expansion is used. How exactly this works I am not yet certain.

Next there was a talk (part 1 of 4) on machine learning as applied to neural networks. The talk covered how to determine the probabilities of various patterns of nerve signals firing. Of particular interest was the importance placed on the discrete vs continuous choice. For example, each firing of a signal could be viewed as a discrete event occurring at some point t in a continuous time. Or time could be partitioned into discrete quantities, with a probability of some number of events occurring per time.

In the afternoon there was a talk by the owner of an optical consulting firm. He talked about some of the practical projects the company has worked on, like a vein imager, barcode scanners and barcode auto-focusing. One project involved using a mask with a UPN pattern on it. I feel like I have seen these patterns around but I have not known there origin before. The practical applications reminded me of the reactivision table (computer vision system) and the ARToolkit (for augmented reality).

Finally on the way home I was toying with the idea of an optical Turing machine, both to increase my understanding of Turing machines and understand how light could be used to (Classically) compute. At home I was investigating this and did not find much information on how an optical Turing machine might work. This is in a way good because it gives me plenty of freedom in thinking of how I would like one to work. At the same time I am wondering if this might be impractical? Along the way I began investigating optical logic gates. I thought I would try and build a simple AND gate from optical components, and this proved much more difficult than I initially thought. I was hoping to use as my two states Horizontal |0> and Vertical |1>. This did not go well. The best I could come up with was

0 0 0
0 1 0
1 0 0
11 Empty

The big problem is that 1 1 is giving me ‘Empty’. Empty wasen’t even one of my states! That’s like if instead of my gate saying yes/no it just stares at me in silence. So after this disappointment I began investigating various ideas for quantum logic gates. I found some information on them, and that’s where I left off for the night. The plan for today is to continue reading about experimental quantum gates.

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Day 2 Week 2 REU

Tour of the Van De Graf Accelerator. Orbital Angular Momentum.

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Day 1 Week 2 REU

This morning I was continuing to study the phase estimation algorithm used in Shor’s algorithm. Eventually I will post the paper, but until then I am not going to post journal entries about it. All of the writing I do about Shor’s algorithm is kept in my notebook, because the entries are quite mathematical.

While reading CQIT (Classical and Quantum Information Theory) I came across a section describing how optical elements like half-wave plates, quarter wave plates and polarizing beam splitters act like the quantum gates I learned about like X, Y, Z and H. This was a very exciting discovery.

In the afternoon we had a group meeting. I talked about my plans for either an electro-optical modulator or studying optical memory through the photorefractive effect. Dr Noe recommended I continue researching photorefraction even though we are uncertain of the availability of a crystal.

I continued trying to learn how to use "Notebook" and the new stylus for taking notes on my laptop. It still dosen’t feel quite like paper and I find myself switching back to my lovely bound notebook, but at the same time wishing I could read a note I made months ago in an old notebook I no longer carry. By the end of last semester I was carrying around quite a good deal of paper print outs too. I might need to give up on the idea of electronic notes again.

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Poincare Sphere

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Day 5 REU Notes

On Friday I spent a good portion of the day reading more about LiNbO3. Later in the day I switched to working on revisions of a paper I am writing on Shor’s Algorithm. For the weekend I renewed the book "Classical and Quantum Information Theory" and re-read the sections on Shor’s Algorithm. There were many small details I had missed before. This time I was trying to thoroughly understand the path of the qubits through the quantum gates.

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LaTeXiT test

LaTeXiT is a utility for mac that lets you enter LaTeX anywhere. Once you enter the code, right click, select "Services" and convert your LaTeX code into the formatted image.

Unfourtunately it does not work with my blog editor, but my desktop notes application "Notebook" has no trouble with it.

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Article of Interest

Silicon waveguide that converts polarization mode of light could speed up photonic circuits operation

Silicon is the dominant material for the fabrication of integrated circuits and is also becoming a popular material for making photonics circuits — miniaturized circuits that use light instead of electronic signals for processing information. One of the challenges in the field, however, has been silicon’s intrinsic sensitivity to the polarization of light, which can limit the rate of information transmission. Jing Zhang, Tsung-Yang Liow and co-workers at the A*STAR Institute of Microelectronics have now developed a novel solution to this problem.

***Note to Self***

transverse electric and transverse magnetic polarization

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Day 4 REU Notes

The fourth day of REU was an introduction to the linux computers. I printed out a nice cheat sheet of linux commands. I decided to quickly investigate how to build an Android app while everyone was learning linux. I used Google’s App Builder for this, and while it does require no programming I’d rather just program an app instead of learning a new weird interface based on dropping puzzle shaped blocks of code together. Not having an Android phone to try it out on took away some of the fun as well.

I tried looking at the interference pattern in a crystal. I didn’t have the two orthonormal beams set up yet, so I just used the fringe pattern from the quantum eraser experiment and a muddy calcite crystal. (By muddy I mean it was full of impurities so even though it was  transparent there were many imperfections for the light to reflect off of.) I could see the interference pattern in the crystal, but I think it would be better to set up an interferometer with the othonormal beams.

I was also looking for a LiNbO3 crystal. I didn’t find one, but I did learn that BK7 is a type of optical glass. Previously I had not bothered to consider the glass used in lenses. Now I realize that different types of glass have different properties and depending on what you are doing you can select types of glass.

For the afternoon we went to the library, where I had good intentions to look for books on photorefractive optics. I found four books, three which I liked. One was called Quantum Optics, and the author is Scully, one of the first people to perform a quantum eraser experiment. I put this book back for now, but it looks like a classic and eventually I will probably need to buy it for a class, or just to have it close at hand.

The second book was called "Building Scientific Apparatus", and right now it is the most useful book. It has clear explanations of what things are, how to build them, how to find the supplies and what they are useful for. There are about 160 pages of optics apparatus including charts for different types of glass. Then it has a bunch of information about building vacuum systems, information on pumps, and another 200 pages on electronics, with titles like "how to build a power supply for your laser".

The third book is called "Introduction to Artificial Life". I picked this one up on a whim and so far I’ve read about 1/3rd of it. About four years ago, I was reading an economics book and it was talking about a simulated environment of sugar farmers. Reading this book on AL (or CA as the book calls it, for Cellular Automata) is combining several interests of mine. It is talking about CPU’s from a completely different approach. Assembly language seems to be referred to as the rule set of the life and biology is talked about as the result of the ruleset. This book is more of a side project for me, but I intend to get the computer software used in the book for simulating life, and write a ruleset to simulate a life.

For today, I might put together the orthonormal interferometer, or perhaps go to the library and successfully come back with a book on photorefractive optics. I’m also planning on talking to the machine shop about taking the shop course.

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Photorefractive Effect

The photorefractive effect is incredible. When light from a split beam is shone in through the orthonormal sides of a photorefractive material the interference pattern creates dark and light zones throughout the crystal.  The electrons become excited in the bright areas and concentrate in the dark zones. This pattern becomes fixed in place and the refractive index changes depending on the concentration of the electrons throughout the crystal. This forms a 3D diffraction grating. Shining a two new lights through the crystal recreates the original pattern of light.

There are several things I had not known here. I did not know that shining two beams from a single source through a crystal would form an interference pattern. Of course I can understand why this would happen, I’m just not sure why I never thought to try it out.

The electrons gathering in certain areas changes the refractive index. I hadn’t thought about how the refractive index of a material works on the atomic level.

An internal space charge field develops! This means the electrons are trapped in the new formation!

It is a type of memory. And I could erase it and do it over and over again to the crystal. I need a special type of crystal. LiNbO3. Lithium Niobate.

Tomorrow I’m going to try observing interference in a material.

Just in case I need this link later, 3D light sculpting system out of MIT (Like a 3D graphics tablet) w/ force feedback)

Does it matter what sides(s) I shine the new lights through to recreate the effect? If I shine a blue, red and green lasers through different sides will I create color? Could I put polarizing filters over the front? What if I put the polarizing filters used in LCD screens? Could I change the saturation levels then?

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