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Journal of Physics B Atomic Molecular and Optical Physics

Laser-induced resonant transitions with Gaussian switching conditions

Predrag Krstić, R K Janve, D. Fussen

Published Mar 28, 1991• 2 citations
Publisher

Abstract

A simple closed-form formula is obtained for the transition probability of a two-state atom in a Gaussian laser pulse. The validity of the formula is tested by comparison with numerical results. The analytic formula is applicable over a wide range of the laser intensities, detunings and pulse durations. Particularly, it can be used for calculation of excitation probability when the Rabi frequency is of the order of or larger than a frequency associated with the pulse duration.

DOI
10.1088/0953-4075/24/6/016

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A simple closed-form formula is obtained for the transition probability of a two-state atom in a Gaussian laser pulse. The validity of the formula is tested by comparison with numerical results. The analytic formula is applicable over a wide range of the laser intensities, detunings and pulse durations. Particularly, it can be used for calculation of excitation probability when the Rabi frequency is of the order of or larger than a frequency associated with the pulse duration.
We investigate the excitation of an atom or molecule via two-photon absorption induced by an ultrashort laser pulse in the perturbative intensity regime. We show that the probability for a resonant transition, i.e., with an intermediate state within the spectral width of the pulse, can be reduced to zero by pulses having a $\ensuremath{\theta}$-phase step at a certain detuning $\ensuremath{\delta}\ensuremath{\omega}$ from the central frequency. Our theoretical predictions are confirmed by numerical calculations for the $4s\ensuremath{\rightarrow}4d$ transition in the potassium atom.
Abstract We consider the interaction of atomic hydrogen, in its ground state, with an electromagnetic pulse whose duration is fixed in terms of the number of optical cycles. We study the probability of excitation of the atom in the static field limit i.e. for field frequencies going to zero. Despite the fact that the well-known Born–Fock adiabatic theorem is valid only for a system whose energy spectrum is discrete, we show that it is still possible to use this theorem to derive, in the low frequency limit, an analytical formula which gives the probability of transition to any excited state of the atom as a function of the field intensity, the carrier envelope phase and the number of optical cycles within the pulse. The results for the probability of excitation to low-lying excited states, obtained with this formula, agree with those we get by solving the time-dependent Schrödinger equation. The domain of validity is discussed in detail.
The authors treat a model for photoionisation in which the atom has many bound atomic levels and the laser may be either monochromatic or possess a finite bandwidth. The treatment is restricted to the case where the laser is not sufficiently intense to cause Stark splitting of the atomic energy levels. They obtain an expression for the two-photon ionisation probability as a function of time which covers both resonant and non-resonant excitation. They identify several time regimes where the probability takes on a particularly simple form. In particular they discuss the short time behaviour and the conditions under which a time-independent transition rate exists. Numerical plots of the ionisation probability against laser frequency for a wide range of pulse durations are given for the two-level model.
We consider the process of transition of a two-level system to the excited state with subsequent photon emission in the presence of a laser pulse with a high degree of unipolarity. Within the framework of quantum electrodynamics, we obtain analytical expressions for the differential probability of the process depending on the temporal scales of the problem: laser pulse duration, excited-state lifetime, inverse transition frequency, and inverse frequency of the photon emitted. Besides, we calculate the total absorption probability by integrating over the three-dimensional photon momentum and summing over polarizations. We compare the results obtained for unipolar and bipolar (many-cycle) pulses.
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A simple model with only three quantum states is used for an atom or molecule in which two transitions are driven by two overlapping laser pulses. The amplitudes of the two pulses are not proportional to the same function of time. The authors impose the 'two-photon resonance' condition, but the two pulses separately are not applied at the resonant frequencies. For pulse pairs having certain shapes, the wavefunctions are written in terms of generalised hypergeometric functions. Simple formulae for transition probabilities are then obtained, are are used to discuss transfer of the three-state system from its ground state to its highest state.