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A Simplified Wave Function for Dressed Atoms

Li Shu

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

A wave function for laser dressed atom is derived as a perturbative solution of the timedependent Schrdinger equation in the velocity gauge. With the use of the average excitation energy approximation and the closure approximation, the solution is reduced to a timedependent operator acting on the bare atomic state. In softphoton approximation, the average excitation energy only appears in the first and second order terms of field frequency. Such a simplified dressed wave function is useful in the calculation of laserassisted scattering, especially in the laserassisted rearrangement collisions.

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A wave function for laser dressed atom is derived as a perturbative solution of the timedependent Schrdinger equation in the velocity gauge. With the use of the average excitation energy approximation and the closure approximation, the solution is reduced to a timedependent operator acting on the bare atomic state. In softphoton approximation, the average excitation energy only appears in the first and second order terms of field frequency. Such a simplified dressed wave function is useful in the calculation of laserassisted scattering, especially in the laserassisted rearrangement collisions.
A wave function for laser dressed atom is derived as a perturbative solution of the time-dependent Schrodinger equation in the velocity gauge. With the use of the average excitation energy approximation and the closure approximation, the solution is reduced to a time-dependent operator acting on the ”bare” atomic state. In soft-photon approximation, the average excitation energy only appears in the first and second order terms of field frequency. Such a simplified dressed wave function is useful in the calculation of laser-assisted scattering, especially in the laser-assisted rearrangement collisions.
Dressed states of an atom in a classical laser field of frequency close to an atomic transition frequency are obtained, which are a considerable improvement over the usual two-level rotating-wave approximation. These wave functions are used in a calculation of the cross section for elastic electron-atom scattering in a laser field. Numerical calculations for electron-hydrogen scattering demonstrate that scattering involving absorption or emission of photons can be strongly influenced by coupling to the nonresonant states, regardless of the field strength. Inclusion of the counter-rotating terms in the calculation is shown to be essential for extending the applicability of the theory to scattering in nonresonant fields, where a first-order perturbation-theoretic treatment of the atom-field interaction would be expected to be quite justified.
A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a ``soft-pair'' approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.
In this chapter,we shall analyze the particular case of an atom interacting with a laser pulse whose duration is sufficiently long, so that the evolution of the atom in the laser field is adiabatic. When this condition is fulfilled, the atom can be considered to interact with a monochromatic laser field. As a consequence, the Hamiltonian of the system is periodic in time, and the Floquet theory [1] can be used to solve the time-dependent Schrödinger equation (TDSE) non-perturbatively. We begin in Section 4.1 by considering the Hermitian Floquet theory. We first derive the Floquet theorem for a monochromatic, spatially homogeneous laser field and show that the solutions of the TDSE correspond to dressed states having real quasi-energies , which can be obtained by solving an infinite system of time-independent coupled equations. We then generalize the Floquet theory to multicolor laser fields and to “non-dipole” laser fields which are not spatially homogeneous. In Section 4.2, the Floquet theory is applied to study the dynamics of a model atom having M discrete levels interacting with a monochromatic laser field. In this case, the coupling between the bound and continuum atomic states is neglected.We analyze the relationship between the Floquet theory and the rotating wave approximation, and examine the perturbative limit of the Floquet theory. We also consider the population transfer between Floquet dressed states.
Theory relevant to the treatment of resonance collisions between two-level dressed atoms has been extended to the three-level case in a self-contained calculation of field-dependent collision rates. With the laser field tuned close to the \ensuremath{\Vert}e1{\mathit{e}}_{1}e1​〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}e2{\mathit{e}}_{2}e2​〉 transition, dressing of the upper two-level system is achieved. We solve coupled equations of motion for two-atom states that describe one atom in the ground state and the other in one of two dressed states. Dressed-state collision rates are calculated within the impact approximation using S-matrix theory. The coupled equations of motion are simplified in the limit of intense field. We have applied the theory to describe approximately collisions between Ne atoms in fields intense enough to dress the collision complex.
Resonance fluorescence consists of photon absorption and photon reemission by an atom interacting with a monochromatic, resonant and intense laser wave. The aim of this paper is to show that all fluorescence signals can be quantitatively calculated through the dressed atom method and that simple physical pictures can be associated to the results obtained in this manner. In such a method, the compound system «atom plus laser photons interacting together» (atom dressed by the laser photons) is first considered and the emission of fluorescence photons is then included as a radiative relaxation of this new quantum system. Emission frequencies thus appear as allowed Bohr frequencies of the dressed atom and Rabi nutation appears as a quantum beat signal between dressed states. Photon correlation and photon counting signals are well understood when fluorescence is considered as a radiative cascade of the dressed atom downwards its energy diagram. Mixed analysis time-frequency, for example study of temporal correlations between photons emitted in some sidebands of the fluorescence spectrum, is suggested by the dressed atom approach. Finally, when compared with the well known optical Bloch equations method, the dressed atom is shown to have a larger validity domain for the Markov approximation On montre que la methode de l'atome habille permet un calcul quantitatif de tous les signaux de fluorescence et associe les resultats a des interpretations physiques simples. Discussion des resultats et presentation des avantages de cette methode