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Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians |
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| Authors: | Julio A. Ló pez-Saldí var,Margarita A. Man’ ko,Vladimir I. Man’ ko |
| Affiliation: | 1.Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, Ciudad de México 04510, Mexico;2.Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow 141700, Russia;3.Russian Quantum Center, Skolkovo, Moscow 143025, Russia;4.Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia; |
| Abstract: | 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. |
| Keywords: | Wigner function tomogram Gaussian states temperature thermal states coupled harmonic oscillators |