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Physical Review A

Efficient selective optical excitation for isotope separation, using short laser pulses

Jean‐Claude Diels

Published Apr 1, 1976• 21 citations
Publisher

Abstract

Propagation of short ($\ensuremath{\lesssim}{T}_{2}$, where ${T}_{2}$ is the phase relaxation time) light pulses through absorbing media consisting of two ensembles of two-level systems of slightly different transition frequency is considered here. It is shown that one group of absorbers can be totally excited (inverted) while the other is returned to ground state. The effect of inhomogeneous broadening is illustrated by examples of propagation (numerical simulation) of properly shaped pulses through media having a linewidth equal to 1/5 of the frequency separation between the two transitions. The initial proportion of the two-level mixture is: 5% of the element to be excited, 95% of the element to be kept in ground state. The selective excitation capabilities of a Gaussian pulse and a zero-area pulse are compared.

DOI
10.1103/physreva.13.1520

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arXiv:quant-ph/0103130•Physical Review A•Oct 12, 2001•20 citations
Propagation of short (\ensuremath≲T2\ensuremath{\lesssim}{T}_{2}\ensuremath≲T2​, where T2{T}_{2}T2​ is the phase relaxation time) light pulses through absorbing media consisting of two ensembles of two-level systems of slightly different transition frequency is considered here. It is shown that one group of absorbers can be totally excited (inverted) while the other is returned to ground state. The effect of inhomogeneous broadening is illustrated by examples of propagation (numerical simulation) of properly shaped pulses through media having a linewidth equal to 1/5 of the frequency separation between the two transitions. The initial proportion of the two-level mixture is: 5% of the element to be excited, 95% of the element to be kept in ground state. The selective excitation capabilities of a Gaussian pulse and a zero-area pulse are compared.
A theoretical investigation is made of the photoionisation of a three-level medium intended for laser isotope separation. The results show that the highest ionisation efficiency can be achieved by dividing the process into two stages: coherent population inversion and photoionisation. A study is made of the possibility of inversion of three-level systems for various detunings of the laser frequencies from the radiative transition frequencies. It is shown that there are detunings for which the population of the third level is maximal for any a priori selected parameters of the medium and field. Such detunings lie near a two-photon resonance and depend on the energy density and duration of the laser pulses, and also on the dipole moments of the transitions. The suitability of this method in the case of inhomogeneously broadened optically dense media is considered. It is shown that the method is most efficient in the case of counterpropagating laser pulses. The efficiency of the method is demonstrated for ytterbium.
By the time-domain method this article deals with the interaction between a three-level quantum system (vibrational energy level of the molecule of a dilute gas) and the infrared electric field of CO2 laser. The semiclassical Bloch-Maxwell's equations have been changed into the equivalent differential equations of real function using the rotating wave approximation. This article studies their solutions of the rate-equations approach under the condition of long pulse and short pulse. The area theorem of coherent short pulses which is propagating through a three-level system of equal spacing is obtained. The article contains the derivations of the formula of separate coefficient, the conditions of the selective optical excitation and the excited rate for isotope separation as an actual application.
We propose a method of laser isotope separation based on the phenomenon of adiabatic inversion and illustrate the method in a multilevel system consisting of a single ground state and multiplet excited states. In this model, population may be transferred from the ground state to one of the excited manifolds with nearly 100% efficiency by using laser pulses, the envelope of which rises slowly and then decays rapidly on an internal time scale that can be precisely calculated. Adiabatic inversion in this model is strongly dependent on the laser frequency, thus permitting separation of isotopes by faking advantage of small shifts in molecular or atomic energy level spacings. The criterion that determines whether a laser pulse is adiabatic also depends strongly on the laser frequency and thereby enhances the separation. We demonstrate the effectiveness of the method with a solution of the time-dependent Schroedinger equation for a specific model of two isotopes.
Transmission characteristics in an excited absorbing medium are discussed on the basis of the photon transport-equation and the rate equations. An increasing power of the C W laser beam passing through the medium is considered when this medium is excited at the same time by a different pulse of radiation. A typical example of a square excitation-pulse states that the transmittance recovers to its original value after it once reaches a maximum value. The time response of the medium depends upon the total number of absorbing centers M, the absorption cross-section σ, and the relaxation time τ as well as the intensity of radiation sources I. The decay time of the increased transmittance is proportional to τ/σM if the quantity (1-M/2τI) is kept constant. As a numerical example the relaxation time of SF6 is estimated to be 2×10-6 s at a pressure of 3.7 Torr in comparison with an experimental result.
We show that pulses of electromagnetic radiation with a hyperbolic-secant envelope and a hyperbolic-tangent frequency sweep are capable of exciting an inversion line shape in a collection of two-level absorbers that is highly insensitive to optical density. This is not true of the hyperbolic-secant \ensuremath{\pi} pulse (with no frequency modulation) which undergoes significant reshaping as it propagates. The analysis is based on numerical solutions of the coupled Maxwell-Bloch equations in both the plane-wave and paraxial approximations. We also show an additional insensitivity of the inversion profile to finite relaxation times (T2{T}_{2}T2​) that approach the pulse width.
The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level \ensuremath{\Lambda}-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse T1,2(T2>T1){T}_{1,2} {(T}_{2}>{T}_{1})T1,2​(T2​>T1​) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"odinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].