The Wigner functional of the electromagnetic field

M Levanda, V. Fleurov

Arthur S. Wightman

Wang Jian-hua

The Wigner functions play a significant role in quantum mechanics,quantum optics,thermodynamics and quantum statistics.Therefore,it has high research value to investigate the Wigner functions for neutral particles with structure that moving in an external electromagnetic field.In this paper,first,we introduce the properties and application of Wigner function.Then,we provide the Hamiltonian of the polarized atom using the symmetric gauge.At last,by using Bopp shift,we solve the energy eigenvalue equation with the Moyal-Weyl star product,and obtain the energy levels and Wigner functions of the neutral particles in an external electromagnetic field.

L. Davidovich, L. G. Lutterbach

We show that the technique of Ramsey interferometry may be used to completely determine the quantum state of an electromagnetic field in a cavity. Our method, which allows the direct measurement of the Wigner function of the field, is a useful tool for probing the quantum-classical transition and, in particular, the decoherence between coherent superpositions of distinguishable coherent states of the electromagnetic field in the cavity. We also show that the realization of a controlled-not gate within framework of cavity QED is a special case of our proposal, and leads to the measurement of a negative value for the Wigner function of an electromagnetic field.

Прохоров Лев Васильевич