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.
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.
A wave function for laser dressed atom is derived as a perturbative solution of the timedependent Schrdinger equation in the velocity gauge. With the use of the average excitation energy approximation and the closure approximation, the solution is reduced to a timedependent operator acting on the bare atomic state. In softphoton 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 laserassisted scattering, especially in the laserassisted rearrangement collisions.
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.
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.
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.
The time-dependent Schrodinger for an atom in a radiation field has a very special form, at least within the dipole approximation: The time-dependence of the Hamiltonian is contained entirely in a c-number which appears as a factor in the interaction, V(t), of the atom with the radiation field. In the velocity gauge this factor is the vector potential, A(t), of the field — we have V(t)= − (e/µc)A (t) • p, where e, µ, and p are the charge, reduced mass, and canonical momentum (in the center of mass frame) of the electron — while in the length gauge this factor is the electric field vector F(t) — we have V(t) = –eF(t) • x, where x is the position coordinate. To our knowledge, this factorization property has not been fully exploited in previous approaches to solving the timedependent Schrodinger equation1. As we show here, in an application to multiphoton ionization of atomic hydrogen, it is an extremely useful property; and although at first sight it would seem to be a unique feature of the atom-radiation system, this is not so, for, as Solov’ev2 has pointed out, the time-dependent Schrödinger equation for colliding atoms or ions can be transformed into a form in which a scaled time-dependence also appears only in c-number factors of the (transformed) interactions.
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〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}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.