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SciPost Physics Proceedings

Wigner function analysis of finite matter-radiation systems

Eduardo Nahmad-Achar, Ramón López–Peña, Sergio Cordero, Octavio Castaños Garza

Published Nov 24, 2023• 0 citations
Publisher

Abstract

We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of minimum fidelity.

DOI
10.21468/scipostphysproc.14.039

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We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of minimum fidelity.
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The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of the Wigner function has been extended to quantum fields, scalar and electromagnetic. Then, one deals with the Wigner functional which gives a distribution of field and its conjugate momentum. We introduce here the Wigner functional of fermionic fields of the values in a Grassmann algebra. Properties of the functional are discussed and its equation of motion, which is of the Liouville form, is derived.
Abstract The ground state of 3-level atoms in the V -configuration interacting dipolarly with two modes of an electromagnetic field is determined. By means of the fidelity concept, the quantum crossovers, called also quantum phase diagrams for a finite number of particles, are obtained. The behaviour of light traversing these finite quantum phase diagrams is studied through the calculation of their corresponding Wigner and Husimi functions. This allows us to predict the unimodal and bimodal character of light when it is in the normal or superradiant regions.