Quantum theory of atoms and radiation

Albert Einstein

Dipankar Bhattacharyya, Jyotirmoy Guha

Xie Li-Jun, Deng-Yu Zhang

The interaction between radiation and two-level atom was investigated by semi-classical theory and quantum theory respectively.The fidelity of the two-level atom's quantum state was written out, The influences of the radiation intensity in the case of semi-classical theory and the photon number of the radiation in the case of quantum theory on the fidelity were discussed for different atomic initial states.It is found that the fidelity of quantum state is independent of radiation intensity when the atom is initially in a superposition state and the atom interacts resonantly with the radiation field in semi-classical theory. The atom's quantum fidelity evolves periodically with time,and its frequency is modulated by radiation intensity.Furthermore,it can effectively change quantum information fidelity when the appropriate detuning is selected.

P. A. M. Dirac

Abstract The new quantum mechanics could at first be used to answer questions concerning radiation only through analogies with the classical theory. In Heisenberg’s original matrix theory, for instance, it is assumed that the matrix elements of the polarisation of an atom determine the emission and absorption of radiation analogously to the Fourier components in the classical theory. In more recent theories a certain expression for the electric density obtained from the quantum mechanics is used to determine the emitted radiation by the same formulæ as in the classical theory. These methods give satisfactory results in many cases, but cannot even be applied to problems where the classical analogies are obscure or non-existent, such as resonance radiation and the breadths of spectral lines. A theory of radiation has been given by the author which rests on a more definite basis. It appears that one can treat a field of radiation as a dynamical system, whose interaction with an ordinary atomic system may be described by a Hamiltonian function. The dynamical variables specifying the field are the energies and phases of its various harmonic conrponents, each of which is effectively a simple harmonic oscillator. One must, of course, in the quantum theory take these variables to be q-numbers satisfying the proper quantum conditions. One finds then that the Hamiltonian for the interaction of the field with an atom is of the same form as that for the interaction of an assembly of light-quanta with the atom. There is thus a complete formal reconciliation between the wave and light-quantum points of view.

B. A. Veklenko

The scattering of resonant radiation on an excited atom is considered. It is shown that the scattering cross section calculated with the help of quantum theory of radiation is five times larger than the one calculated using semi-classical theory. The quantum theory predicts, in general, the change in internal quantum statistical properties of light due to the scattering processes on excited atoms.

Alberto Galindo, P. Pascual