Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum sy...

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Autores principales:	Julio A. López-Saldívar, Margarita A. Man’ko, Vladimir I. Man’ko
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Wigner function tomogram Gaussian states temperature thermal states coupled harmonic oscillators Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/d8c88d3ab53b41fbb5d29ea7b39b0d8c
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spelling	oai:doaj.org-article:d8c88d3ab53b41fbb5d29ea7b39b0d8c2021-11-25T17:29:43ZMeasurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians10.3390/e231114451099-4300https://doaj.org/article/d8c88d3ab53b41fbb5d29ea7b39b0d8c2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1445https://doaj.org/toc/1099-4300The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.Julio A. López-SaldívarMargarita A. Man’koVladimir I. Man’koMDPI AGarticleWigner functiontomogramGaussian statestemperaturethermal statescoupled harmonic oscillatorsScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1445, p 1445 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Wigner function tomogram Gaussian states temperature thermal states coupled harmonic oscillators Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	Wigner function tomogram Gaussian states temperature thermal states coupled harmonic oscillators Science Q Astrophysics QB460-466 Physics QC1-999 Julio A. López-Saldívar Margarita A. Man’ko Vladimir I. Man’ko Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians
description	The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.
format	article
author	Julio A. López-Saldívar Margarita A. Man’ko Vladimir I. Man’ko
author_facet	Julio A. López-Saldívar Margarita A. Man’ko Vladimir I. Man’ko
author_sort	Julio A. López-Saldívar
title	Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians
title_short	Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians
title_full	Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians
title_fullStr	Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians
title_full_unstemmed	Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians
title_sort	measurement of the temperature using the tomographic representation of thermal states for quadratic hamiltonians
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d8c88d3ab53b41fbb5d29ea7b39b0d8c
work_keys_str_mv	AT julioalopezsaldivar measurementofthetemperatureusingthetomographicrepresentationofthermalstatesforquadratichamiltonians AT margaritaamanko measurementofthetemperatureusingthetomographicrepresentationofthermalstatesforquadratichamiltonians AT vladimirimanko measurementofthetemperatureusingthetomographicrepresentationofthermalstatesforquadratichamiltonians
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Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

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