Emulating the Wigner function of an odd cat state by means of classical light fields
The undergraduate physics thesis presents an optical implementation of the Wigner distribution function of a one dimensional electric field. Then, it is compared with the Wigner distribution function of an odd cat state in quantum mechanics.
- Autores:
-
Piñeros Lourenco, Pedro Enrique
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2023
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/67936
- Acceso en línea:
- http://hdl.handle.net/1992/67936
- Palabra clave:
- Fractional Fourier transform
Wigner distribution function
Cat state
Fourier optics
Inverse Radon transform
Física
- Rights
- openAccess
- License
- Attribution-NoDerivatives 4.0 Internacional
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Emulating the Wigner function of an odd cat state by means of classical light fields |
| dc.title.alternative.none.fl_str_mv |
Emulando la función de Wigner de un estado de gato impar por medio de campos de luz clásicos |
| title |
Emulating the Wigner function of an odd cat state by means of classical light fields |
| spellingShingle |
Emulating the Wigner function of an odd cat state by means of classical light fields Fractional Fourier transform Wigner distribution function Cat state Fourier optics Inverse Radon transform Física |
| title_short |
Emulating the Wigner function of an odd cat state by means of classical light fields |
| title_full |
Emulating the Wigner function of an odd cat state by means of classical light fields |
| title_fullStr |
Emulating the Wigner function of an odd cat state by means of classical light fields |
| title_full_unstemmed |
Emulating the Wigner function of an odd cat state by means of classical light fields |
| title_sort |
Emulating the Wigner function of an odd cat state by means of classical light fields |
| dc.creator.fl_str_mv |
Piñeros Lourenco, Pedro Enrique |
| dc.contributor.advisor.none.fl_str_mv |
Valencia González, Alejandra Catalina |
| dc.contributor.author.none.fl_str_mv |
Piñeros Lourenco, Pedro Enrique |
| dc.contributor.jury.none.fl_str_mv |
Quiroga Puello, Luis |
| dc.contributor.researchgroup.es_CO.fl_str_mv |
Óptica Cuántica |
| dc.subject.keyword.none.fl_str_mv |
Fractional Fourier transform Wigner distribution function Cat state Fourier optics Inverse Radon transform |
| topic |
Fractional Fourier transform Wigner distribution function Cat state Fourier optics Inverse Radon transform Física |
| dc.subject.themes.es_CO.fl_str_mv |
Física |
| description |
The undergraduate physics thesis presents an optical implementation of the Wigner distribution function of a one dimensional electric field. Then, it is compared with the Wigner distribution function of an odd cat state in quantum mechanics. |
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2023 |
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2023-06-27T19:56:41Z |
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2023-06-27T19:56:41Z |
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2023-06-27 |
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Trabajo de grado - Pregrado |
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eng |
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| dc.relation.references.es_CO.fl_str_mv |
M. Tse and N. Kijbunchoo. Quantum-Enhanced Advanced LIGO Detectors in the Era of Gravitational-Wave Astronomy. Phys. Rev. 123, (23): 231107, (2019). G. Milburn P. Cochrane and W. Munro. Macroscopically distinct quantumsuperposition states as a bosonic code for amplitude damping. Phys.Rev. A 59, 2631, (1999) E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749, (1932). A. Martinez. Characterization of quantum states of light by means of homodyne detection and reconstruction of Wigner functions. Monografía de pregrado: Universidad de los Andes. Bogotá, Colombia, (2020). U. Leonhardt. Measuring the quantum state of light. Cambridge University Press, (1997). A. Furusawa. Quantum states of light. Springer, (2015). C. Gerry and P. Knight. Introductory Quantum Optics. Cambridge University Press, (2004). M. Fox. Quantum Optics an introduction. Oxford University Press Inc, (2006). E. Condón. Immersion of the Fourier transform in a continuous group of functional transformations. Proc. Natl. Acad. Sci. 23, (3): 158-164, (1937). V. Namias. The fractional order Fourier transform and its application to quantum mechanics. IMA Journal of Applied Mathematics 25, (3): 241-265, (1980). H. Ozaktas and M. Kutay. The Fractional Fourier Transform. European Control Conference, (2001). V. Christlein A. Maier S. Steidl and J. Hornegger. Medical Imaging Systems. Springer International Publishing, (2018). G. Arfken and H. Weber. Mathematical Methods for Physicists. Academic Press, 4ta edición, (1995). I. Hoover. Introducing the Fractional Fourier Transform. (2013). D. Mendlovic A. Lohmann and Z. Zalevsky. Fractional transformations in Optics. Elsevier sciencie B.V., (1998). J. Ville. Théorie et Applications de la Notion de Signal Analytique. Cables et Transmission, 2, 61-74, (1948). L. Cohen. Time-frequency distributions-a review. Proceedings of the IEEE 77, 941, (1989). M. Scully M. Hilley E. O'Cornell and E. Wigner. Distributions functions in physics: fundamentals. Physics Reports 106, 121-167, (1984). B. Diu C. Cohen-Tannoudji and F. Laloe. Quantum Mechanics. John Wiley Sons, Vol. I, (1977). J. Radon. Über die bestimmung von funktionen durch ihre integralwerte längs gewisser manngfaltigkeiten. (1983). J. Radon and P. Parks. On the determination of functions from their integral values along certain manifols. IEEE transactions on Medical Imaging, 5 (4): 170-176, (1986). V. Velázquez E. Barrios-Barocio and S. Cruz. Design and Construction of Homodyne Detectors for the Study of Quantum Optical States. J. Phys.: Conf. Ser. 1540, 012030, (2020). A. Lohmann and B. Soffer. Relationships between the Radon-Wigner and fractional Fourier transforms. J. Opt. Soc. Am. A 11, pp. 1798-1801, (1994). H. Yuen and V. Chan. Noise in homodyne and heterodyne detection. Opt. Lett. 8, pp. 177179, (1983). K. Banaszek and K. Wódkiewicz. Direct Probing of Quantum Phase Space by Photon Counting. Phys. Rev. Lett. 76, 23, pp. 4344-4347, (1996). N. Sridhar and et al. Direct measurement of the Wigner function by photonnumber-resolving detection. J. Opt. Soc. Am. B 31, 10, (2014). L. Lutterbach and L. Davidovich. Method for Direct Measurement of the Wigner Function in Cavity QED and Ion Traps. Phys. Rev. Lett. 78, 13, (1997). G. Molina-Terriza N. Gonzalez and J. Torres. Properties of the spatial Wigner function of entangled photon pairs. Phys. Review. A80, 043804, (2009). T. Douce and et al. Direct measurement of the biphoton Wigner function through two-photon interference. Sci. Rep. 3, 3530, (2013). A. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Am. A 10, 10 (1993). J. Goodman. Introduction to Fourier optics. The McGraw-Hill Companies. Second edition, (1996). R. Guenther. Modern Optics. Duke University, (1990). V. Arnold. Mathematical Methods of Classical Mechanics. Springer, second edition, (1989). F. Lin and et al. Geometry for Computer Graphics. Student Notes, ITTI Gravigs Project, (1995). K. Izuka. Elements of photonics. Wiley-Interscience, (2002). |
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56 páginas |
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Universidad de los Andes |
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Física |
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Facultad de Ciencias |
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Departamento de Física |
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Attribution-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Valencia González, Alejandra Catalinavirtual::10433-1Piñeros Lourenco, Pedro Enrique310e476d-c243-4072-abdd-4987cff751dc600Quiroga Puello, LuisÓptica Cuántica2023-06-27T19:56:41Z2023-06-27T19:56:41Z2023-06-27http://hdl.handle.net/1992/67936instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/The undergraduate physics thesis presents an optical implementation of the Wigner distribution function of a one dimensional electric field. Then, it is compared with the Wigner distribution function of an odd cat state in quantum mechanics.The Wigner distribution function is a very useful tool in signal analysis because it provides a representation of a signal in the conjugate variables across phase space. In the context of quantum mechanics, this function represents a quasi-probability distribution in phase space for a quantum state. On the other hand, in signal processing, the Fourier transform and its generalization, the fractional Fourier transform (FFT), play an important role in time and frequency analysis. Moreover, research conducted in the late 1990s found that reconstruction of the Wigner function could be obtained from the collection of different fractional Fourier transforms. In this project, the Wigner function of a quantum state, called a cat state, was emulated by obtaining the fractional Fourier transforms in the spatial frequency variables of two Gaussian beams separated by "2d" distance. This will respond to the problem of generating lower cost methods that obtain properties of quantum states through their Wigner function, since, to generate, for example, a cat state, much more sophisticated and expensive equipment is needed.FísicoPregradoÓptica cuántica y clásica56 páginasapplication/pdfengUniversidad de los AndesFísicaFacultad de CienciasDepartamento de FísicaEmulating the Wigner function of an odd cat state by means of classical light fieldsEmulando la función de Wigner de un estado de gato impar por medio de campos de luz clásicosTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPFractional Fourier transformWigner distribution functionCat stateFourier opticsInverse Radon transformFísicaM. Tse and N. Kijbunchoo. Quantum-Enhanced Advanced LIGO Detectors in the Era of Gravitational-Wave Astronomy. Phys. Rev. 123, (23): 231107, (2019).G. Milburn P. Cochrane and W. Munro. Macroscopically distinct quantumsuperposition states as a bosonic code for amplitude damping. Phys.Rev. A 59, 2631, (1999)E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749, (1932).A. Martinez. Characterization of quantum states of light by means of homodyne detection and reconstruction of Wigner functions. Monografía de pregrado: Universidad de los Andes. Bogotá, Colombia, (2020).U. Leonhardt. Measuring the quantum state of light. Cambridge University Press, (1997).A. Furusawa. Quantum states of light. Springer, (2015).C. Gerry and P. Knight. Introductory Quantum Optics. Cambridge University Press, (2004).M. Fox. Quantum Optics an introduction. Oxford University Press Inc, (2006).E. Condón. Immersion of the Fourier transform in a continuous group of functional transformations. Proc. Natl. Acad. Sci. 23, (3): 158-164, (1937).V. Namias. The fractional order Fourier transform and its application to quantum mechanics. IMA Journal of Applied Mathematics 25, (3): 241-265, (1980).H. Ozaktas and M. Kutay. The Fractional Fourier Transform. European Control Conference, (2001).V. Christlein A. Maier S. Steidl and J. Hornegger. Medical Imaging Systems. Springer International Publishing, (2018).G. Arfken and H. Weber. Mathematical Methods for Physicists. Academic Press, 4ta edición, (1995).I. Hoover. Introducing the Fractional Fourier Transform. (2013).D. Mendlovic A. Lohmann and Z. Zalevsky. Fractional transformations in Optics. Elsevier sciencie B.V., (1998).J. Ville. Théorie et Applications de la Notion de Signal Analytique. Cables et Transmission, 2, 61-74, (1948).L. Cohen. Time-frequency distributions-a review. Proceedings of the IEEE 77, 941, (1989).M. Scully M. Hilley E. O'Cornell and E. Wigner. Distributions functions in physics: fundamentals. Physics Reports 106, 121-167, (1984).B. Diu C. Cohen-Tannoudji and F. Laloe. Quantum Mechanics. John Wiley Sons, Vol. I, (1977).J. Radon. Über die bestimmung von funktionen durch ihre integralwerte längs gewisser manngfaltigkeiten. (1983).J. Radon and P. Parks. On the determination of functions from their integral values along certain manifols. IEEE transactions on Medical Imaging, 5 (4): 170-176, (1986).V. Velázquez E. Barrios-Barocio and S. Cruz. Design and Construction of Homodyne Detectors for the Study of Quantum Optical States. J. Phys.: Conf. Ser. 1540, 012030, (2020).A. Lohmann and B. Soffer. Relationships between the Radon-Wigner and fractional Fourier transforms. J. Opt. Soc. Am. A 11, pp. 1798-1801, (1994).H. Yuen and V. Chan. Noise in homodyne and heterodyne detection. Opt. Lett. 8, pp. 177179, (1983).K. Banaszek and K. Wódkiewicz. Direct Probing of Quantum Phase Space by Photon Counting. Phys. Rev. Lett. 76, 23, pp. 4344-4347, (1996).N. Sridhar and et al. Direct measurement of the Wigner function by photonnumber-resolving detection. J. Opt. Soc. Am. B 31, 10, (2014).L. Lutterbach and L. Davidovich. Method for Direct Measurement of the Wigner Function in Cavity QED and Ion Traps. Phys. Rev. Lett. 78, 13, (1997).G. Molina-Terriza N. Gonzalez and J. Torres. Properties of the spatial Wigner function of entangled photon pairs. Phys. Review. A80, 043804, (2009).T. Douce and et al. Direct measurement of the biphoton Wigner function through two-photon interference. Sci. Rep. 3, 3530, (2013).A. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Am. A 10, 10 (1993).J. Goodman. Introduction to Fourier optics. The McGraw-Hill Companies. Second edition, (1996).R. Guenther. Modern Optics. Duke University, (1990).V. Arnold. Mathematical Methods of Classical Mechanics. Springer, second edition, (1989).F. Lin and et al. Geometry for Computer Graphics. Student Notes, ITTI Gravigs Project, (1995).K. Izuka. Elements of photonics. 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