Marian Smoluchowski
Institute of Physics

Jagiellonian University in Kraków

Diploma thesis

Polarization formalisms and quantum entanglement in the positronium system

Supervisor: dr Michał Silarski, dr Wojciech Krzemień

download

abstract

Defence year: 2022

Quantum entanglement of the group of particles, is a fascinating quantum mechanical phenomenon, without the classical analogy, which happens when the system state can be treated only as a whole, and the constituent particles cannot be described separately. The simplest example in which the quantum entanglement can be manifested is the polarized two -photon system.Indeed such a case was analyzed both theoretically and experimentally many times. However, most of the studies were concentrated on the optical photons regime. For higher-energetic photons, the polarization cannot be measured by using standard devices such as polarizers. However, the partial polarization estimation is possible by exploiting the Compton scatterings process. In this work the analysis of high-energetic, polarized two-photon system is considered, probed by the doubly Compton scattering process. The model is described using the quantum information theory formalism. In addition, the model is incorporated to the Monte Carlo C++ library. The simulations of the various quantum states are performed and the results are compared with the expectations from the theory.

Publications

ARTICLES POSTERS

1. Realistic Total-Body J-PET Geometry Optimization--Monte Carlo Study
   J. Baran, W. Krzemień, L. Raczyński, M. Bała, A. Coussat, S. Parzych, N. Chug, E. Czerwiński, C. Oana Curceanu, M. Dadgar, K. Dulski, K. Eliyan, J. Gajewski, A. Gajos, B. Hiesmayr, K. Kacprzak, Ł. Kapłon, K. Klimaszewski, G. Korcyl, T. Kozik, D. Kumar, S. Niedźwiecki, D. Panek, E. Perez del Rio, A. Ruciński, S. Sharma, Shivani, R.Y. Shopa, M. Skurzok, E. Stępień, F. Tayefiardebili, K. Tayefiardebili, W. Wiślicki, P. Moskal
   download

   abstract

   HEP: arXiv:2212.02285
   Total-Body PET imaging is one of the most promising newly introduced modalities in the medical diagnostics. State-of-the-art PET scanners use inorganic scintillators such as L(Y)SO or BGO, however, those technologies are very expensive, prohibitng the broad total-body PET applications. We present the comparative studies of performance characteristics of the cost-effective Total-Body PET scanners using Jagiellonian PET (J-PET) technology that is based on plastic scintillators. Here, we investigated in silico five realistic Total-Body scanner geometries, varying the number of rings, scanner radius, and distance between the neighbouring rings. Monte Carlo simulations of two NEMA phantoms (2-meter sensitivity line source and image quality) and the anthropomorphic XCAT phantom, were used to assess the performance of the tested geometries. We compared the sensitivity profiles and we performed the quantitative analysis of the reconstructed images by using the quality metrics such as contrast recovery coefficient, background variability and root mean squared error. The optimal scanner design was selected for the first Total-Body J-PET scanner configuration.
2. Advanced Monte Carlo simulations of emission tomography imaging systems with GATE
   D. Sarrut, M. Bała, M. Bardies, J. Bert, M. Chauvin, K. Chatzipapas, M. Dupont, A. Etxebeste, L.M. Fanchon, S. Jan, G. Kayal, A.S. Kirov, P. Kowalski, W. Krzemien, J. Labour, M. Lenz, G. Loudos, B. Mehadji, L. Ménard, C. Morel, P. Papadimitroulas, M. Rafecas, J. Salvadori, D. Seiter, M. Stockhoff, E. Testa, C. Trigila, U. Pietrzyk, S. Vandenberghe, M.A. Verdier, D. Visvikis, K. Ziemons, M. Zvolský, E. Roncali
   download

   abstract

   Phys. Med. Biol. 66 (2021) 10TR03
   Built on top of the Geant4 toolkit, GATE is collaboratively developed for more than 15 years to design Monte Carlo simulations of nuclear-based imaging systems. It is, in particular, used by researchers and industrials to design, optimize, understand and create innovative emission tomography systems. In this paper, we reviewed the recent developments that have been proposed to simulate modern detectors and provide a comprehensive report on imaging systems that have been simulated and evaluated in GATE. Additionally, some methodological developments that are not specific for imaging but that can improve detector modeling and provide computation time gains, such as Variance Reduction Techniques and Artificial Intelligence integration, are described and discussed.
3. 3D TOF-PET image reconstruction using total variation regularization
   L. Raczyński, W. Wiślicki, K. Klimaszewski, W. Krzemień, P. Kopka, P. Kowalski, R. Y. Shopa, M. Bała, J. Chhokar, C. Curceanu, E. Czerwinski, K. Dulski, J. Gajewski, A. Gajos, M. Gorgol, R. Del Grande, B. Hiesmayr, B. Jasińska, K. Kacprzak, L. Kapłon, D. Kisielewska, G. Korcyl, T. Kozik, N. Krawczyk, E. Kubicz, M. Mohammed, S. Niedźwiecki, M. Pałka, M. Pawlik-Niedźwiecka, J. Raj, K. Rakoczy, A. Ruciński, S. Sharma, S. Shivani, M. Silarski, M. Skurzok, E.Ł. Stepień, B. Zgardzińska, P. Moskal
   download

   abstract

   Physica Medica 80 (2020) 230-242
   In this paper we introduce a semi-analytic algorithm for 3-dimensional image reconstruction for positron emission tomography (PET). The method consists of the back-projection of the acquired data into the most likely image voxel according to time-of-flight (TOF) information, followed by the filtering step in the image space using an iterative optimization algorithm with a total variation (TV) regularization. TV regularization in image space is more computationally efficient than usual iterative optimization methods for PET reconstruction with a full system matrix that uses TV regularization. The efficiency comes from the one-time TOF back-projection step that might also be described as a reformatting of the acquired data. An important aspect of our work concerns the evaluation of the filter operator of the linear transform mapping an original radioactive tracer distribution into the TOF back-projected image. We obtain concise, closed-form analytical formula for the filter operator. The proposed method is validated with the Monte Carlo simulations of the NEMA IEC phantom using a one-layer, 50 cm-long cylindrical device called Jagiellonian PET scanner. The results show a better image quality compared with the reference TOF maximum likelihood expectation maximization algorithm.
4. Synchronisation and calibration of the 24-modules J-PET prototype with 300 mm axial field of view
   P. Moskal, T. Bednarski, Sz. Niedźwiecki, M. Silarski, E. Czerwiński, T. Kozik, J. Chhokar, M. Bała, C. Curceanu, R. Del Grande, M. Dadgar, K. Dulski, A. Gajos, M. Gorgol, N. Gupta-Sharma, B. C. Hiesmayr, B. Jasińska, K. Kacprzak, Ł. Kapłon, H. Karimi, D. Kisielewska, K.Klimaszewski, G. Korcyl, P. Kowalski, N. Krawczyk, W. Krzemień, E. Kubicz, M. Mohammed, M. Pawlik-Niedźwiecka, L. Raczyński, S. Sharma, Shivani, R. Y. Shopa, M. Skurzok, E. Stępień, W. Wiślicki, B. Zgardzińska
   download

   abstract

   IEEE Trans. Instrum. Meas. 70 (2020) 2000810

   HEP: arXiv:2008.10868
   Research conducted in the framework of the J-PET project aims to develop a cost-effective total-body positron emission tomography scanner. As a first step on the way to construct a full-scale J-PET tomograph from long strips of plastic scintillators, a 24-strip prototype was built and tested. The prototype consists of detection modules arranged axially forming a cylindrical diagnostic chamber with an inner diameter of 360 mm and an axial field-of-view of 300 mm. Promising perspectives for a low-cost construction of a total-body PET scanner are opened due to an axial arrangement of strips of plastic scintillators, which have a small light attenuation, superior timing properties, and the possibility of cost-effective increase of the axial field-of-view. The presented prototype comprises dedicated solely digital front-end electronic circuits and a triggerless data acquisition system which required development of new calibration methods including time, thresholds and gain synchronization. The system and elaborated calibration methods including first results of the 24-module J-PET prototype are presented and discussed. The achieved coincidence resolving time equals to CRT = 490 +- 9 ps. This value can be translated to the position reconstruction accuracy s(Dl) = 18 mm which is fairly position-independent Keywords: positron emission tomography, plastic scintillators, J-PET.
5. Feasibility studies of the polarization of photons beyond the optical wavelength regime with the J-PET detector
   P. Moskal, N. Krawczyk, B. C. Hiesmayr, M. Bała, C. Curceanu, E. Czerwinski, K. Dulski, A. Gajos, M. Gorgol, R. Del Grande, B. Jasinska, K. Kacprzak, L. Kapłon, D. Kisielewska, K. Klimaszewski, G. Korcyl, P. Kowalski, T. Kozik, W. Krzemien, E. Kubicz, M. Mohammed, Sz. Niedźwiecki, M. Pałka, M. Pawlik-Niedźwiecka, L. Raczynski, J. Raj, Z. Rudy, S. Sharma, M. Silarski, Shivani, R. Y. Shopa, M. Skurzok, W. Wislicki, B. Zgardzinska
   download

   abstract

   Eur. Phys. J. C 78 (2018) 970

   HEP: arXiv:1809.10397
   J-PET is a detector optimized for registration of photons from the electron-positron annihilation via plastic scintillators where photons interact predominantly via Compton scattering. Registration of both primary and scattered photons enables to determinate the linear polarization of the primary photon on the event by event basis with a certain probability. Here we present quantitative results on the feasibility of such polarization measurements of photons from the decay of positronium with the J-PET and explore the physical limitations for the resolution of the polarization determination of 511keV photons via Compton scattering. For scattering angles of about 82 degree (where the best contrast for polarization measurement is theoretically predicted) we find that the single event resolution for the determination of the polarization is about 40 degree (predominantly due to properties of the Compton effect). However, for samples larger than ten thousand events the J-PET is capable of determining relative average polarization of these photons with the precision of about few degrees. The obtained results open new perspectives for studies of various physics phenomena such as quantum entanglement and tests of discrete symmetries in decays of positronium and extend the energy range of polarization measurements by five orders of magnitude beyond the optical wavelength regime.
6. Processing optimization with parallel computing for the J-PET scanner
   W. Krzemień, M. Bała, T. Bednarski, P. Białas, E. Czerwiński, A. Gajos, M. Gorgol, B. Jasińska, D. Kamińska, Ł. Kapłon, G. Korcyl, P. Kowalski, T. Kozik, E. Kubicz, Sz. Niedźwiecki, M. Pałka, L. Raczyński, Z. Rudy, O. Rundel, N.G. Sharma, M. Silarski, A. Słomski, K. Stola, A. Strzelecki, D. Trybek, Anna Wieczorek, W. Wiślicki, M. Zieliński, B. K. Zgardzińska, P. Moskal
   download

   abstract

   NUKLEONIKA 60 (2015) 745-748

   HEP: arXiv:1508.02751
   The Jagiellonian-PET (J-PET) collaboration is developing a prototype TOF-PET detector based on long polymer scintillators. This novel approach exploits the excellent time properties of the plastic scintillators, which permit very precise time measurements. The very fast, FPGA-based front-end electronics and the data acquisition system, as well as, low- and high-level reconstruction algorithms were specially developed to be used with the J-PET scanner. The TOF-PET data processing and reconstruction are time and resource demanding operations, especially in case of a large acceptance detector, which works in triggerless data acquisition mode. In this article, we discuss the parallel computing methods applied to optimize the data processing for the J-PET detector. We begin with general concepts of parallel computing and then we discuss several applications of those techniques in the J-PET data processing.

1. Towards molecular in-vivo cancer imaging by means of positronium and the J-PET tomograph
   P. Moskal, M. Bała, Z. Bura, J.Chhokar, M. Dadgar, K. Dulski, K.Farbaniec, A. Gajos, B. Jasińska, H. Karimi, E. Kubicz, G. Korcyl, K. Rakoczy, S. Sharma, E.Stępień
   FNP IIIrd Inter Deciplinary Congress meeting, April 11, 2019, Warsaw, Poland

   download poster
2. Efficiency estimates for various e+e- system decays
   M. Bała
   Discrete symmetries in particle, nuclear and atomic physics and implications for our universe, October 8-12, 2018, Trento, Italy

   download poster