A Study of q-Deformed Bosons, and Their Implications to Quantum Optics

Year 2024, Volume: 28 Issue: 5, 1093 - 1102, 25.10.2024

Mustafa Şenay

https://doi.org/10.16984/saufenbilder.1522962

Abstract

In this study, we investigate three types of q-deformed boson oscillators, focusing on their mathematical frameworks and thermodynamic properties. We calculate key thermodynamic quantities, such as internal energy and entropy, as functions of the deformation parameter q. Our results reveal that these oscillators are eigenstates of specific deformed boson annihilation operators. We also analyze their unique characteristics and implications in deformed quantum optics. Furthermore, we examine the impact of q-deformation on qutrit logic gates, including cycle, self-shift, controlled cycle, controlled self-shift, Feynman, ternary Toffoli, and Fredkin gates, highlighting their altered computational properties. This research contributes to a deeper understanding of q-deformed systems and their applications in quantum computing. Overall, it opens new avenues for exploring the interplay between deformation parameters and quantum information processing.

Keywords

q-deformed boson, Quantum statsitics, Quantum optics, Thermodynamics

References

• A. Blum, “From the Necessary to the Possible the Genesis of the Spin-Statistics Theorem,” The Euopean Physical Journal H, vol. 39, pp. 543-574, 2014.
• G. Gentile, M. Hechinger, “Osservazioni sopra le statistiche intermedie”, Nuovo Cimento, vol. 17, pp. 493-497,1940.
• H. S. Green, “A Generalized Method of Field Quantization,”, Physical Review, vol. 90, pp. 270, 1953.
• F. Wilczek, “Fractional Statistics and Anion Superconductivity,” World Scientific, Singapore, 1990.
• C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, vol. 52, pp. 479-487, 1988.
• M. Masi, “A step beyond Tsallis and Rényi entropies,” Physics Letters A, vol. 338, pp. 217-224, 2005.
• M. Arik, D. D. Coon, “Hilbert spaces of analytic functions and generalized coherent states,” Journal of Mathematical Physics, vol. 17, pp. 524-527, 1976.
• L. C. Biedenharn, “The quantum group SUq(2) and a q-analogue of the boson operators,” Journal of Physics A: Mathematical and General, vol. 22, pp. L873-L878, 1989.
• A. J. Macfarlane, “On q-analogues of the quantum harmonic oscillator and the quantum group SUq(2),” Journal of Physics A: Mathematical and General, vol. 22, pp. 4581-4588, 1989.
• K. S. Viswanathan, R. Parthasarathy, .R. Jagannathan, “Generalized q-fermion oscillators and q-coherent states,” Journal of Physics A: Mathematical and General, vol. 25, pp. L335-L339, 1992.
• M. Chaichian, R. Gonzalez Felipe, C. Montonen, “Statistics of q-oscillators quons and relations to fractional statistics,” Journal of Physics A: Mathematical and General, vol. 26, pp. 4017-4034, 1993.
• Y. J. Ng, “Comment on the q-analogues of the harmonic oscillator,” Journal of Physics A: Mathematical and Theoretical, vol. 23, no. 6, pp. 1023-1027, 1990.
• C. R. Lee, J. P. Yu, “On q-analogues of the statistical distribution,” Physics Letters A, vol. 150, no. 2, pp. 63-66, 1990.
• H. S. Song, S. X. Ding, I. An, “Statistical mechanical properties of the q-oscillator system,” Journal of Physics A: Mathematical and Theoretical, vol. 26, no. 20, pp. 5197-5205, 1993.
• A. Lavagno, P. Narayana Swamy, “Generalized thermodynamics of q-deformed bosons and fermions,” Physical Review E, vol. 65, pp. 036101-1-036101-5, 2002.
• G. Su, S. Cai, H. Chen, “Bose-Einstein condensation of a relativistic q-deformed Bose gas,” Journal of Physics A: Mathematical and Theoretical, vol. 41, pp. 045007, 2008.
• B. Mirza, H. Mohammadzadeh, “Thermodynamic geometry of deformed bosons and fermions,” Journal of Physics A: Mathematical and Theoretical, vol. 44, pp. 0475003, 2011.
• A. A. Marinho, F. A. Brito, C. Chesman, “Thermal properties of a solid through q-deformed algebra,” Physica A, vol. 391, pp. 3424-3434, 2012.
• E. Dil, “Q-Deformed Einstein equations, ”Canadian Journal of Physics, vol. 93, no. 11, pp. 1274-1278, 2015.
• M. Senay, S. Kibaroğlu, “Thermosize effects in a q-deformed fermion gas model,”Modern Physics Letters B, vol. 32, no. 20, pp. 1850230-1-1850230-9, 2018.
• A. Lavagno, P. Narayana Swamy, “Deformed Quantum Statistics in Two Dimensions,” International Journal of Modern Physics B, vol. 23, no. 2, pp. 235-250, 2009.
• M. Senay, “High temperature thermostatistical properties of deformed quantum gas in two dimensions,” Sakarya University Journal of Science, vol. 23, pp. 1273-1278, 2019.
• A. Algin, A. S. Arikan, “Thermostatistical properties of the blackbody radiation and Debye crystal model through Fibonacci oscillators,” The European Physical Journal Plus, vol. 137, pp. 1230, 2022.
• A. Algin, A. S. Arikan, E. Dil, “High temperature thermostatistics of fermionic Fibonacci oscillators with intermediate statistics,” Physica A: Statistical Mechanics and its Applications, vol. 416, pp. 499-517, 2014.
• M. Senay, “Entropic gravity corrected by q-statistics, and its implications to cosmology,” Physics Letters B, vol. 820, pp. 136536, 2021.
• M. Senay, S. Kibaroğlu, “q-deformed Einstein equations from entropic force,” International Journal of Modern Physics A, vol. 33, pp. 1850218, 2018.
• A. Algin, M. Senay, “Fermionic -deformation and its connection to thermal effective mass of a quasiparticle,” Physica A: Statistical Mechanics and its Applications, vol. 447, pp. 232-246, 2016.
• A. Algin, M. Senay, “High-temperature behavior of a deformed Fermi gas obeying interpolating statistics,” Physical Review E, vol. 85, pp. 041123, 2012.
• F. Ozaydin, O. E. Mustecaplıoğlu, T. Hakioğlu “Powering quantum Otto engines only with 𝑞-deformation of the working substance,” Physical Review E, vol. 108, pp. 054103, 2023.
• A. A. Altintas, F. Ozaydin, C. Yesilyurt, S. Bugu, M. Arik, “Constructing quantum logic gates using q-deformed harmonic oscillator algebras,” Quantum Information Processing, vol. 13, pp. 1035-1044, 2014.
• A. A. Altintas, F. Ozaydin, C. Bayındır, “q-Deformed three-level quantum logic,” Quantum Information Processing, vol. 19, No. 247, 2020.
• F. Nutku, K. D. Sen, E. Aydiner, “Complexity study of q-deformed quantum harmonic oscillator,” Physica A: Statistical Mechanics and its Applications, vol. 533, pp. 122041, 2019.
• S. Jalalzadeh, H. Moradpour, P. V. Moniz, “Modified cosmology from quantum deformed entropy,” Physics of the Dark Universe, vol. 42, pp. 101320, 2023.
• A. Guha, J. Selvaganapathy, P. K. Das, “𝑞-deformed statistics and the role of light fermionic dark matter in SN1987A cooling,” Physical Review D, vol. 95, pp. 015001, 2017.
• X. Y. Hou, H. Yan, G. Guo, “Thermostatistics of a q-deformed relativistic ideal Fermi gas,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2020, pp. 113402, 2020.
• A. Boumali, A. Bouzenada, S. Zare, H. Hassanabadi, “Thermal properties of the q-deformed spin-one DKP oscillator,” Physica A: Statistical Mechanics and its Applications, vol. 628, pp. 129134, 2023.
• A. M. Gavrilik, I. I. Kachurik, Yu. A. Mishchenko, “Quasibosons composed of two q-fermions: realization by deformed oscillators,” Journal of Physics A: Mathematical and Theoretical, vol. 44, pp. 475303, 2011.
• M. Maleki, Z. Ebadi, H. Mohammadzadeh, “q-deformed Bose statistics and the Gross-Pitaevskii equation,” International Journal of Geometric Methods in Modern Physics, vol. 21, pp. 2450121, 2024.
• H. Mohammadzadeh, Y. A. Kalandaragh, N. Cheraghpour, F. Adli, “Thermodynamic geometry, condensation and Debye model of two-parameter deformed statistics,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2017, pp. 083104, 2017.
• L. Tao, Z. Chen, Z. Li, J. Wang, X. Xu, J. B. Xu, “Enhancing light-matter interaction in 2D materials by optical micro/nano architectures for high-performance optoelectronic devices,” Infomat, vol. 3, pp. 36-60, 2021.
• M. Fleischhauer, A Imamoglu, J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Reviews of Modern Physics, vol. 77, pp. 633, 2005.
• Y. Ashida, A. İmamoğlu, E. Demler, “Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths,” Physical Review Letters, vol. 126, pp. 153603, 2021.
• N. Boutabba, S. Grira, H. Eleuch, “Analysis of a q‑deformed hyperbolic short laser pulse in a multi‑level atomic system,” Scientific Reports, vol. 12, pp. 9308, 2022.
• A. Lavagno, P. Narayana Swamy, “Thermostatistics of a q-deformed boson gas,” Physical Review E, vol. 61, pp. 1218-1226, 2000.
• K. Huang, “Statistical Mechanics,” John Wiley and Sons, New York 1987.
• C. Quesne, “New q-deformed coherent states with an explicitly known resolution of unity,” Journal of Physics A: Mathematical and General, vol.35, pp.9213-9226, (2002).
• M. N. Hounkonnou, E. B. Ngompe Nkouankam, “New (p, q;μ, ν, f)-deformed states,” Journal of Physics A: Mathematical and Theoretical, vol.40, pp.12113-12130, (2007).