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arXiv:1105.5402 · Physical Review A

Interaction of strongly chirped pulses with two-level atoms

Sara Ibañez, A. Peralta Conde, David Guéry-Odelin, Juan Gonzalo Muga

Published Jul 29, 2011• 24 citations
arXivHTMLPDF

Abstract

We study the effect of ultrachirped pulses on the population inversion of two-level atoms. Ultrachirped pulses are defined as those for which the frequency chirp is of the order of the transition frequency of the two-level atom. When the chirp is large enough, the resonance may be crossed twice, for positive and negative frequencies. In fact the decomposition of the field into amplitude and phase factors, and the corresponding definition of the instantaneous frequency, are not unique. The interaction pictures for different decomposition are strictly equivalent, but only as long as approximations are not applied. The domain of validity of the formal rotating wave approximation is dramatically enhanced by a suitable choice, the so-called analytic signal representation.

DOI
10.1103/physreva.84.013428

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We study the effect of ultrachirped pulses on the population inversion of two-level atoms. Ultrachirped pulses are defined as those for which the frequency chirp is of the order of the transition frequency of the two-level atom. When the chirp is large enough, the resonance may be crossed twice, for positive and negative frequencies. In fact the decomposition of the field into amplitude and phase factors, and the corresponding definition of the instantaneous frequency, are not unique. The interaction pictures for different decomposition are strictly equivalent, but only as long as approximations are not applied. The domain of validity of the formal rotating wave approximation is dramatically enhanced by a suitable choice, the so-called analytic signal representation.
We investigate the behavior of 85Rb{}^{85}\mathrm{Rb}85Rb atoms in the field of a sequence of frequency-chirped short laser pulses. The analysis is based on a numerical solution of equations for the probability amplitudes of the hyperfine levels of the ${5S}_{1/2}{\ensuremath{-}5P}_{3/2}$ transition in the 85Rb{}^{85}\mathrm{Rb}85Rb atom and the dressed-states analysis. We analyze different regimes of interaction, including relatively short laser pulses (when the width of the pulse envelope spectrum is of the order of or exceeds the frequency interval between the hyperfine levels resulting in effective mixing of them) and relatively long ones (when the ground hyperfine levels are resolved but the excited ones are not resolved). In the latter case dependence of the population transfer efficiency on the initial coherence of the ground states is analyzed. The case of long laser pulses when all working hyperfine levels are resolved is also discussed using numerical simulations and a dressed-states analysis. We show that in all regimes considered, the interaction of a frequency-chirped laser pulse with the multilevel 85Rb{}^{85}\mathrm{Rb}85Rb system is similar to the interaction with an effective two-level atom at sufficiently large peak intensities of the pulses. It allows us to perform efficient excitation of the multilevel atom by transferring populations of two hyperfine ground states to the excited ones and back to the ground states using a pair of frequency-chirped laser pulses. We propose to utilize this scheme of population transfer for the coherent manipulation of a beam of 85Rb{}^{85}\mathrm{Rb}85Rb atoms using sequences of counterpropagating frequency-chirped short laser pulses.
Detailed theoretical analysis and numerical simulation indicate that nearly complete electronic population inversion of molecular systems can be achieved with intense positively chirped broadband laser pulses. To provide a simple physical picture, a two-level model is used to examine the condition for the so-called π pulses and a four-level model is designed to demonstrate for molecular systems the correlation between the sign of the chirp and the excited state population. The proposed molecular π pulse is the combined result of vibrational coherence in the femtosecond regime and adiabatic inversion in the picosecond regime. Numerical results for a displaced oscillator, for LiH and for I2, show that the proposed molecular π pulse scheme is robust with respect to changes in field parameters such as the linear positive chirp rate, field intensity, bandwidth, and carrier frequency, and is stable with respect to thermal and condensed phase conditions including molecular rotation, rovibronic coupling, and electronic dephasing.
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A coherent mechanism of robust population inversion in atomic and molecular systems by a chirped field is presented. It is demonstrated that a field of sufficiently high chirp rate imposes a certain relative phase between a ground and excited state wavefunction of a two-level system. The value of the relative phase angle is thus restricted to be negative and close to 0 or −pi-\\pi−pi for positive and negative chirp, respectively. This explains the unidirectionality of the population transfer from the ground to the excited state. In a molecular system composed of a ground and excited potential energy surface the symmetry between the action of a pulse with a large positive and negative chirp is broken. The same framwork of the coherent mechanism can explain the symmetry breaking and the population inversion due to a positive chirped field.
A coherent mechanism of robust population inversion in atomic and molecular systems by a chirped field is presented. It is demonstrated that a field of sufficiently high chirp rate imposes a certain relative phase between a ground and excited state wavefunction of a two-level system. The value of the relative phase angle is thus restricted to be negative and close to 0 or - pi for positive and negative chirp, respectively. This explains the unidirectionality of the population transfer from the ground to the excited state.In a molecular system composed of a ground and excited potential energy surface the symmetry between the action of a pulse with a large positive and negative chirp is broken. The same framwork of the coherent mechanism can explain the symmetry breaking and the population inversion due to a positive chirped field.
According to the semi-classical theory of light-matter interaction,the Bloch equations with chirped terms were established in a dense two-level medium,and an accurate and efficient fourth-order Runge-Kutta method was applied for solving the equations.After numerical simulation,the interactions between a chirped ultra-short pulse and dense resonant two-level medium were investigated,and the influences of local-field effects and chirp on Bloch vectors were gained.The numerical results show that,the evolutions of Bloch vectors and the final state of inversion are strongly modulated by the local-field effects correction coefficient and chirp parameter,which provides a method to achieve stable population inversion of control by adjusting the linear chirp parameter and local-field correction coefficient.