The morning started off with working on Shor’s Algorithm, as usual. I was writing a new section on the Controlled-U gate. There was an excellent question, “What is a logic gate?” I took off explaining how binary works, which lead to how binary addition works. At which point another student wandered over and asked, “Have you ever build an adder circuit?” Which lead to quite an excited discussion about the plan to build an optical Turing machine that became a project to build an optical AND gate and reprised the difficulty of actually creating one. Then it was time for the lunch meeting.
The lunch meeting was on heat conductivity, and I had the chance to hold a diamond chip and ‘cut’ ice. It went right through the chuck of ice, but it quickly cooled down to. One thing that stuck with me is that solids are really gases, except they are composed of two different gases. Phonons and Electrons. Fascinating point of view.
When we came back from lunch I was talking with another student about circular polarization of light. We did a miniature experiment, where we verticality polarized light, and then measured the intensity. Next we added a quarter-wave plate and measured the intensity. It remained the same, except for a small drop due to reflection off the wave-plate. Next we inserted a horizontal polarizer, and the intensity continued to remain the same. As we rotated the polarized it continued to remain nearly the same, except for some minor oscillations, which we attributed to reflections from the polarizer.
This is the beginning of the fourth week of the REU program, and I believe it is time for me to pick a topic for the summer and begin to narrow my focus. I think my focus is narrowing into non-linear optics. There is the LiNbO3 crystal in the lab. That crystal is very interesting.
I think what I want to experiment on with this crystal is frequency doubling. In general, the final goal is to successfully achieve frequency doubling, using a non-linear medium. I don’t really care what sort of non-linear medium I use.
The second interest, but the one I think is less applicable is the optical logic gate.
There was a talk about buying a new laser in the AM. In the afternoon I was reading about solar pumped lasers. Overall it (solar pumped laser) sounds impractical.
This morning’s talk about buying a laser involved a discussion about the thermal properties of a crystal, which starts to act as a lens when heated. This reminded me of the LiNbO3 crystal in the LTC. If I were to rank my idea’s so far I think studying the properties of nonlinear optics is quite high. I drew a schematic for an AND gate based on polarization of light and one of the things I want to do is modulate the amplitude of the output light. Maybe I could use the LiNbO3 crystal for this. Then I could combine two of my interests into one project.
On the train I wrote a java program for adding two numbers together. It required the class Scanner.
Scanner input = new Scanner ( System.in );
That statement creates an object, input of the class Scanner.
number1 = input.nextInt();
nextInt() is a method of the class Scanner. It expects the input to be an integer and throws an exception if it’s not.
Does it effect the polarization of light?
Does it have nonlinear properties?
What happens if I put in it an electric field?
Is it photorefractive?
How to make it:
Could I suspend other elements in the aerogel?
Today was the completion of the Shor’s algorithm paper, section 2, "Classical Factoring Algorithm’s". Writing this paper is quite a time consuming process, and the method I use for writing is shifting as I begin to learn how to write a paper about a scientific process. Each sentence needs to be carefully thought about, and as I write it I need to know what source inspired each thought. This is a different approach to writing and it is producing a better final product, where each line can be explained in greater detail. Each word becomes important and that is a new experience to me.
The last lecture in the machine learning series was today. It was on hidden marklov chains. The lecturer introduced the problem as: "You are at a casino, and you record the results of a series of dice rolls. On each roll the casino could switch between one of two loaded dice. Based on just the values of the rolled dice, what was the probability one or the other loaded dice being rolled".
In the early morning I set up a package to use in eclipse, but I think now I am not going to use this ‘learning’ package. I’m just going to start writing a program (OO). Maybe the bank account program I did at the end of C++ course, but in java instead. Or maybe something to implement the idea’s from the machine learning series.
Another excellent day has passed. The morning began in a most productive way, with a through investigation of the general number field sieve algorithm for classical factoring of numbers greater than 100 digits. To understand how this method of factoring works it was necessary to investigate number fields. This was a new concept to me. A number field, is a group of numbers and the addition/subtraction operators. The smallest number field is rational numbers. Irrational numbers are an expanded field of rational numbers, and complex numbers are an expanded field of irrational numbers. This investigation was a continuation of the Shor’s Algorithm paper. It is still being written.
The third lecture in the machine learning series was today. The lecture was on how to tell apart nerve signal ‘spikes’, on an electrode. This is because an electrode might (most likely does…) receive impulses from several different neurons. Each neuron has a preferred spike pattern. It might be short and fat, or wide and tall, or tall and narrow… There are many different characteristics we can look at. So, now we have these spikes with different characteristics and we want to cluster them together and say "This spike belongs to this neuron.". Or rather we want the computer to cluster them together. So at first a rather simple approach is taken. Simply pick a center to each cluster and then assign each point to the closest neighbor. But this method leaves questions about the boundaries.
We want an approach that weights the probability of each point falling within a certain cluster. To do this hidden variables are used. Each point is assumed to fall in some cluster, and a hidden variable of the probability of it falling in that point is used. At this point it became quite complicated, but the general idea was that we were maximizing the probability of each point falling in some particular location based on the influence of some hidden variables. The speaker mentioned how this is commonly used in modeling the stock markets, and it reminded me of the "risk factors" that I used to work with at my old job. This was the math behind them.
Immediately after was another talk, this time on BEC. I arrived late and missed the introduction, but I thought the discussion on optical lattices being used to contain atom’s was promising. I am going to read more of this later. At the end was a lab tour, and we walked through the optics setup for the BEC experiment. I was interested in the CCD camera, I’m going to read more about how they work.
Finally, after the BEC talk, but before the BEC lab tour, I overheard a portion of a conversation and it gave me the idea about a sun powered laser. When I googled it I did find some information on laser sam’s website about how to do this, but he said there is trouble getting a coherent beam.
I spent the day sorting optical elements. I kept Thor labs website up and looked for the names of the different elements, then placed them in labeled bag’s. It was a fun break day, and I learned the names of many different things.
For the past few days I have been deep into my project on an optical Turing machine. My notebook is full of drawings of various component layouts to produce different effects, and I have been creating charts like this:
R W M
1 1 L
0 0 L
Read a 1
Move one element left
Write a 1.
Read a 0
Move one element left
Write a 0.
I’ve been putting together various combinations like this, and trying out different arrangements of elements. An element is one RWM chart for a 1/0 combination. I’m working on a google sketch-up model of an element. I think the RW components and the M component will be separable, so I can combine various RW instructions with different M instructions, making it easier to ‘program’ the computer.
This does mean my Turing machine operates differently than the idealized machine, of the infinite tape, read/write head and table of instructions. The table of instructions is really the core of my Turing machine. This means to change the program a different table of instructions needs to be assembled. Because of this I’m not sure if this machine is actually a Turing machine. It is more like Charles Babbage’s difference engine.
While thinking of different elements for my Turing machine, I have been reading about optical elements in greater detail. It also occurred to me that instead of arranging mirrors to move the light around, I could use fiber optic cable to send light from one element to the next. To do this I need a single mode fiber, and putting together fiber optic cable is apparently quite a tricky skill to acquire. I also learned about neutral density filters. This could be useful for adjusting the intensity of the output.
Programmable optical processor based on symbolic substitution
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