Analytic solution of the two-state problem

An exact solution of the time-dependent Schrodinger equation is obtained for a simple model with only two quantum states. The calculated transition probability involves only exponential and hyperbolic functions

Analytic solutions for three-state systems with overlapping pulses

Two classes of analytic solutions for three-state systems involving two overlapping laser pulses of different shapes, or of similar shapes but with their centers displaced, are presented. We find a remarkable connection between the order of arrival of the two overlapping pulses and the effectiveness of transfer from the ground state to the third state, and we find remarkable results for the maximum occupation probability of the intermediate state. The approach of these analytic solutions to the adiabatic-following process is also demonstrated

Selective excitation via the continuum and suppression of ionization

Two laser pulses that overlap in time have been successfully used for coherent excitation of a molecule or atom to a desired state. An intermediate state that is at or near resonance with the laser frequencies has been used in past experiments and calculations. Here we replace this intermediate state by a continuum of intermediate states. An analytic solution of a simple model suggests that the continuum can be used in such an excitation scheme, provided that the laser pulses are arranged in the so-called counter intuitive order. %\u27e use a special case of this solution to relate this work to ionization suppression and coherent population trapping

Coherent Population Transfer via the Continuum

We present a remarkable analytic result which suggests that a continuum can be used as an intermediary for a significant transfer of population from one discrete state to another discrete state in a stimulated Raman transition. the population transfer is accomplished by employing two laser pulses that overlap in time, arranged in the so-called counterintuitive order. That a continuum can be used for population transfer is shown here for the first time. It promises to open up more channels for selective coherent excitation of atoms or molecules

Selective excitation and structure in the continuum

We show that efficient transfer of molecules or atoms from one bound state to another is possible via the continuum in some cases, using two overlapping laser pulses. The structure of the continuum determines the pulse delay, laser frequencies, and laser intensities that should be used. We present simple formulas that relate the optimum values of pulse intensities, pulse separation, and detuning; these estimates can be used as a guide. More detailed calculations give quantitative results for two specific potentials

Solitary waves and atomic population transfer via the continuum

Exact analytic results are presented that represent a pair of solitary waves that can propagate through an atomic medium with their shapes invariant while producing transfer of atoms or molecules from one bound state to another via a continuum. The speed of the waves and the amount of population transfer are given in terms of the wave amplitudes. A general ~not solitary wave! solution for the case of a single wave is presented, together with a nonlinear Beer’s law of absorption

Three-state model driven by two laser beams

We use a three-state model for an atom or molecule in which two transitions are simultaneously driven by the oscillating electric fields of two laser beams. The amplitudes and detunings of the applied oscillating fields vary during the optical pulse, which can cause transitions from one state to another. For some special cases not previously known, the transition probabilities and probabilities of no transition are obtained analytically. We give conditions for complete transfer of the atomic population from one state to another, and for complete return to the initial state

Three-state systems driven by resonant optical pulses of different shapes

New analytic solutions to the problem of a three-state system driven simultaneously by resonant optical pulses of different shapes are presented. The solutions are useful for prescribing the conditions for complete population transfer from one state to another or for complete population return

Coherent population trapping in N-level quantum systems

A multilevel quantum system interacting with an intense laser Seld is shown to exhibit many invariants, or constants of evolution, under various conditions. Our results also apply to other similar physical problems

Analytic calculation of nonadiabatic transition probabilities from monodromy of differential equations

The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2x2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy approach. The application of this method to multi-level systems is also discussed.Comment: 13 pages, 2 figure