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The Journal of Chemical Physics

Broadband population inversion by a frequency-swept pulse beyond the adiabatic approximation

Lorenz Mitschang, Herbert H. Rinneberg

Published Mar 13, 2003• 2 citations

Abstract

Frequency swept pulses are used to invert population over a broad band of transition frequencies without the need for a precise calibration of the pulse amplitude. As long as the adiabatic approximation is valid, population is adiabatically inverted at each individual transition frequency of the swept range. Even though this picture fails to be true when the adiabatic approximation breaks down, population inversion can still be achieved for an appreciable range of transition frequencies and field amplitudes. We discuss population inversion in an ensemble of two-level systems by a frequency-swept pulse, the so-called constant adiabaticity pulse, without invoking the adiabatic approximation. The equations of motion are integrated by a seminumerical method to analyze population inversion in the regime where usually the adiabatic approximation is applied. The effects of resonance offset and variable pulse amplitude are described by an average Hamiltonian expansion to discuss pulse performance beyond the validity of the adiabatic approximation. As a function of the adiabaticity parameter (reciprocal of the pulse area), the inversion bandwidth increases in a stepwise fashion due to the consecutive cancellation of average Hamiltonians. The first inversion over a finite range of transition frequencies and pulse amplitudes is shown to occur for an adiabaticity parameter of 1/15.

DOI: 10.1063/1.1554737

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Frequency swept pulses are used to invert population over a broad band of transition frequencies without the need for a precise calibration of the pulse amplitude. As long as the adiabatic approximation is valid, population is adiabatically inverted at each individual transition frequency of the swept range. Even though this picture fails to be true when the adiabatic approximation breaks down, population inversion can still be achieved for an appreciable range of transition frequencies and field amplitudes. We discuss population inversion in an ensemble of two-level systems by a frequency-swept pulse, the so-called constant adiabaticity pulse, without invoking the adiabatic approximation. The equations of motion are integrated by a seminumerical method to analyze population inversion in the regime where usually the adiabatic approximation is applied. The effects of resonance offset and variable pulse amplitude are described by an average Hamiltonian expansion to discuss pulse performance beyond the validity of the adiabatic approximation. As a function of the adiabaticity parameter (reciprocal of the pulse area), the inversion bandwidth increases in a stepwise fashion due to the consecutive cancellation of average Hamiltonians. The first inversion over a finite range of transition frequencies and pulse amplitudes is shown to occur for an adiabaticity parameter of 1/15.

We describe a class of continuously phase-modulated radiation pulses that result in coherent population inversion on resonance as well as over a large range of transition frequencies and radiation field strengths. This is a population-inversion analogy to self-induced transparency. Simulations of the inversion properties of the modulated inversion pulse (MIP) are presented. It is shown that the inversion behavior can be explained by treating the MIP as a highly efficient adiabatic sweep. Criteria for establishing adiabaticity are discussed in detail. Finally, a method is presented for generating a sequence of phase-shifted radio-frequency pulses, from the continuously modulated pulse, which can be implemented on modern NMR and coherent optical spectrometers; experimental confirmation is given.

A theoretical analysis is made of the interaction between a two-level quantum-mechanical system and an electromagnetic field which is frequency- and amplitude-modulated. Attention is drawn to the fact that, subject to certain general assumptions, the usual methods for population inversion in such a system—(2 n + l)π pulses and adiabatic inversion methods—apply also if the pump field is of the wide-band type. Exact solutions are obtained for the nature of the time dependence of the instantaneous field frequency at which a population inversion occurs under nonadiabatic conditions.

A numerical analysis is presented of several potential pulsed-laser applications of adiabatic population inversion in atoms or molecules. A simple numerical method is demonstrated for evaluating adiabatic processes in multilevel systems for both swept-frequency and resonant, time-delayed pulses. Adiabatic inversion with time-delayed pulses is generalized to systems with any number of levels. The effect of Doppler broadening on time-delayed adiabatic pumping of a three-level system is investigated.

Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s\ensuremath{\rightarrow}5p\ensuremath{\rightarrow}5d of the rubidium atom by frequency-swept ultrashort laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s\ensuremath{\rightarrow}5p transition, and later with the 5p\ensuremath{\rightarrow}5d transition. With this ``intuitive'' scheme it is possible to achive complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a ``counterintuitive'' direction of the frequency sweep, in which case population of the intermediate level during the pulse is strongly reduced.

We propose a technique for coherent population inversion of a two-state system, which uses an amplitude-modulated pulse. In the modulation-free adiabatic basis, the modulation introduces oscillating interaction between the adiabatic states. In a second rotating-wave approximation picture, this oscillating interaction induces a pair of level crossings between the energies of the adiabatic states if the modulation frequency is chosen appropriately. By suitably offsetting the modulation with respect to the center of the pulse, one can make the modulation act only in the vicinity of one of these crossings. In a higher-order adiabatic basis, this crossing shows up as an avoided crossing between the energies of the higher-order adiabatic states. As a result robust and efficient population transfer can be achieved between the adiabatic states, and hence, between the original bare states. We derive analytically the conditions on the interaction parameters for this technique and verify them with numerical simulations. Possible experimental implementations are discussed.