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Communications in Theoretical Physics

Non-integer Quantum Transition, a True Non-perturbation Effect in Laser-Atom Interaction

Qiren Zhang

Published Jun 1, 2007• 6 citations
Publisher

Abstract

We show that in the quantum transition of an atom interacting with an intense laser of circular frequency ω, the energy difference between the initial and the final states of the atom is not necessarily an integer multiple of the quantum energy ℏω. This kind of non-integer transition is a true non-perturbation effect in laser-atom interaction.

DOI
10.1088/0253-6102/47/6/010

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We show that in the quantum transition of an atom interacting with an intense laser of circular frequency ω, the energy difference between the initial and the final states of the atom is not necessarily an integer multiple of the quantum energy ℏω. This kind of non-integer transition is a true non-perturbation effect in laser-atom interaction.
We show that in the quantum transition of a system induced by the interaction with an intense laser of circular frequency ωωω, the energy difference between the initial and the final states of the system is not necessarily being an integer multiple of the quantum energy ℏω\hbarωℏω.
We discuss the interaction of an atom subject to an intense driving laser field with its own radiation field. In contrast to the states of bare atoms, the energy difference between some dressed states with the same total angular momentum, its projection and parity may be very small. The self-interaction of a combined atom–laser system associated with nonradiative transitions between such states is effectively strong. We show that the contribution to the radiative shift of the sidebands of the Mollow spectrum, which comes from such processes, is very significant and may be much larger than the trivial Lamb shift, which is the simple redistribution of the Lamb shifts of the corresponding bare states. In the final part, we discuss the possibility that in the Mollow spectrum nonlocality of electromagnetic interaction, which in other cases is hidden in the regularization and renormalization procedures, can manifest itself explicitly.
A small parameter is used to identify the orders of perturbation. The unperturbed Hamiltonian is assumed time-independent and can be diagonalized. The interaction of an electron with an applied electromagnetic field is governed by the gauge-invariant Hamiltonian. If both the initial and final energy levels are discretized, the delta function indicates that the transition happens only when the energy difference between the two levels matches the frequency of the perturbation. The delta function suggests that the absorption or stimulated emission happens only when the energy difference between the final and initial states matches precisely the frequency of the applied electromagnetic wave. The quantum transition induced by a monochromatic perturbation is determined by the matrix element between the initial and final states.
Perturbation theory for the interaction of light with a binary collisional system is applied to the calculation of line profiles, spontaneous emission rates and absorption or stimulated emission coefficients. For the usual radiation fields are perturber densities, this approximation is valid at all detunings Delta omega except the very narrow resonance region. Appropriate expansions of the total binary system wavefunctions give the emission and absorption profiles or rates, for atom-electron systems as well as for atom-atom systems, from the impact regime at small Delta omega up to the Born-Oppenheimer regime at very large Delta omega in collision-induced radiative transitions, the transitions being asymptotically allowed or forbidden. Emphasis is given to the proper averages and sums over initial and final states of the binary system which give rise to non-adiabatic effects. One shows that it is of crucial importance to include all dynamical effects during one collisional event before undertaking any calculation at small Delta omega where simultaneous collisions may occur.
Energy Approach to Atoms in a Laser Field and Quantum Dynamics with Laser Pulses of Different Shapes 161 strong nonlinear coupling of radiation with atoms which can not fully explained by the modern theoretical models.In any case the problem requires a consistent quantum electrodynamic approach.Another important topic is a problem of governing and control of non-linear processes in a stochastic, multi-mode laser field (Grance, 1981;Lompre et al, 1981;Zoller, 1982; Glushkov & Ivanov, 1992).The principal aim of quantum coherent control is to steer a quantum system towards a desired final state through interaction with light while simultaneously inhibiting paths leading to undesirable outcomes.This type of quantum interference is inherent in non-linear multiphoton processes.Controlling mechanisms have been proposed and demonstrated for atomic, molecular and solid-state systems (Goldansky-Letokhov, 1974, Letokhov, 1977;Delone-Kraynov, 1984).Theoretical studies of the laser-atom nonlinear interactions are often based on solving the time-dependent Schrödinger equation or using the time-independent Floquet formalism or special perturbation theories (Brändas &