Special States of the Electromagnetic Field

Jan Peřina

Xiong Zhi-bin, Zeng Gao-jian

The energy level decay terms are introduced into the Schrdinger equation of a three-level atom in an electromagnetic field of circular polarization. By means of modulating frequency of a circularly polarized electromagnetic field and approximation of a strong laser, three special states of three kinds of three-level atom are discovered. Based on these special states, we further study the atom-lifetime of three-level atom in a circularly polarized electromagnetic field.

Miguel Orszag

I.A. Malkin, Vladimir I. Man’ko, D. A. Trifonov

New time-dependent invariants for the $N$-dimensional nonstationary harmonic oscillator and for a charged particle in a varying axially symmetric classical electromagnetic field are found. For these quantum systems, coherent states are introduced, and the Green's functions are obtained in closed form. For a special type of electromagnetic field which is constant in the remote past and future, the transition amplitudes between both arbitrary coherent states and energy eigenstates are calculated and expressed in terms of classical polynomials. The adiabatic approximation and adiabatic invariants are discussed. In the special case of a particle with time-dependent mass, the solution of the Schr\"odinger equation is found. The symmetry of nonstationary Hamiltonians is discussed, and the noncompact group $U(N, 1)$ is shown to be the group of dynamical symmetry for the time-dependent $N$-dimensional oscillator.

Miguel Orszag

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.