To conduct the theoretical mod
elling of the quantum field interaction of light with nonlinear optical crystal.
To carry out the numerical modelling of the spontaneous parametric down-conversion process to generate entangled photon pair.
Entangled States
Entangled states or Einstein-Podolsky-Rosen (EPR) states is a states such that measurement of an observable of either particle determines the value of the obervable for the other particle. Meaning that, there are correlation(or anti correlation) between both particle(idler and signal). Spontaneous Parametric Down Conversion(SPDC) is one of the tool to generate this kind of states.[a2]
This decay process obeys (phase matching laws) to energy conservation and momentum conservation[c6]
The down-conversion is said to be of type I or type II[a2]
About Nonlinear Crystal
In this project we will use β-BARIUM BORATE (BBO) crystal as the nonlinear crystal. There are two types of Nonlinear crystal which is uniaxial and biaxial nonlinear crystal. BBO is uniaxial type.
Type indices of refraction for uniaxial crytal :-
ordinary (o)
extraordinary (e)
*for negatif uniaxial crystal, the ordinary ray travels slower than extraordinary ray
The orientation of BBO crystal will lead to what type of phase matching the photon will have[c6]
Phase Matching
Phase matching can be achieve if the frequency and momentum of photons agree with the equation above. Combination between ordinary and extraordinary ray will the determines the type of SPDC can have.[c6]
(a) type I SPDC; (b)collinear type II SPDC; (c)non collinear type II SPDC
Condition for type I is
kpump(o) = ksignal(e) +kidler(e).
The signal and idler have parallel polarization
Condition for type II iskpump(o) =ksignal(o) +kidler(e) , |
|
kpump(o) =ksignal(e) +kidler(o) | |
The signal and idler photon have orthogonal polarization. If photon pair come out from crystal were same direction with the photon from pump, the process is collinear type II SPDC and if photon pair come out in different direction with the photon pump, the process known as non collinear type II SPDC. The photon pair from non collinear type II SPDC is much easier to differentiate between the idler and signal photon.[c6]
Simple Configuration of SPDC experiment
A birefringent crystal converts the pump beam into a pair of collinear down-conversion beams. BS is a polarization dependent beam splitter which transmits the o ray and reflects the e ray. D1 and D2 are photodectors and C is the coincidence counter.[a2]
Program for Calculating Non-Colinear Phase Matching
(http://physics.nist.gov/Divisions/Div844/facilities/cprad/PMProgram.html)
Briefly this computational techniques being build so that it can provide preliminary answers to a variety of questions that must be asked about a particular down-conversion source before it is constructed in the laboratory, such as "Over what range of wavelengths is down-conversion possible? What should the 'cut' of the crystal's optical axis be? At what angles can we expect to find certain wavelengths emitted from the crystal?" and so on. The method presented on[c6](documentation of NIST Phasematch Program) can calculate both collinear and non-collinear phase matching that allows experimental configuration including uniaxial or biaxial crystal to be modeled in detail.
There are several research work on this source code. One of it is thesis by Dustin Shipp. From his research using the the fotran source code from NIST(freely distributed) on Non Collinear Parametric Down Conversion, he compared the down-conversion ring from the program and the experimental result and both of it agree of predicting the location of the down-conversion ring with only 0.2 degree of error on the program.[d0]
Kyle J. Arnold working by using the numerical data produced by NIST Phasematch Program, he making a model of a downconversion source in ASAP( Breult Inc.)[c0]
List Of Problem
The NIST Phase Matching program not a dynamic model of spdc process. It is much more on mathematical model.
The program no stated on how to determine the pair photon we get were entangle(only on how to produce pair photon of SPDC source).
Recommendation of Sotware
Kyle J. Arnold have prove that he can get the down conversion source in ASAP using numerical data produced by NIST Phasematch program. Below is ASAP features :
Model optical and mechanical system components
Model imaging systems, illumination systems, and light-concentrating devices
Model visible, ultraviolet, and infrared radiation in optical systems
Model radiometry of complex systems, including radiance
Model surface (BRDF) and volume scatter (pre-defined or custom)
Build system models requiring large numbers of objects and sources
Render system geometry, raytraces, and light sources
Perform numerical and graphical CIE/Chromaticity analyses
Optimize optical systems with the ASAP Optimization interface
Tolerance optical systems in the ASAP Builder interface or scripts
Import measured source data such as Radiant Sources™
Use the SolidWorks Parts Only 3D Modeling Engine (license included)
Write ASAP-specific GTX files from within SolidWorks
Assign object and layer names in SolidWorks
Write ASAP-specific IGES files from within Rhinoceros®
Import/Export IGES files using the ASAP smartIGES translator
Import geometry and optical properties using the XML file format
Integrate scripts in Python, VBscript, Jscript, and other languages
Use pre-defined LED, CCFL, incandescent, and arc sources
Drag-and-drop sources, lenses, glasses, scatter models, and coatings
Begin your simulation with one of 600+ example files
Use distributed processing to spawn up to 5 ASAP sessions on networked computers
Create your own custom workspace within ASAP
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after 1 1/2 hours we end the session and we conclude that, our next job should focus on [c6] and maybe we will convert the fotran source code on [c6] to become C code. Hopefully we can model this SPDC.
But still in question is that how we want to show that the spdc source we get from mathematical model that propose by [c6] were entangled???
