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Physical Review A

Modifying H − resonance asymmetries with short light pulses

J. Bengtsson, Eva Lindroth

Published May 11, 2012• 2 citations
Publisher

Abstract

We present a method based on time-dependent perturbation theory and complex rotation to treat the interaction of a short light pulse with a correlated atomic system. The pulse is built from two short and weak pulses with Gaussian envelopes that are centered at two different frequencies. The method is applied to the negative hydrogen ion in the vicinity of a doubly excited resonance and it is shown that the two light pulses can be used to alter the Fano profile of a resonance.

DOI
10.1103/physreva.85.053413

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We present a method based on time-dependent perturbation theory and complex rotation to treat the interaction of a short light pulse with a correlated atomic system. The pulse is built from two short and weak pulses with Gaussian envelopes that are centered at two different frequencies. The method is applied to the negative hydrogen ion in the vicinity of a doubly excited resonance and it is shown that the two light pulses can be used to alter the Fano profile of a resonance.
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A theoretical analysis of the propagation of near resonant and linearly chirped light pulses through a resonant medium is presented under the restriction that the pulses are far enough off resonance or weak enough so that they do not significantly alter the atomic populations. If the pulses are of duration comparable to or less than the phase memory time T(2) of the atoms, it is found that the transient response of the medium gives rise to amplitude-and phase-modulating effects. Analytic solutions are presented to describe the propagation of an off-resonant pulse which is very short compared with T(2) and an off-resonant rectangular pulse. The evolution of a Gaussian pulse having a positive linear chirp is studied numerically.
The Fano resonance theory is modified to account for photoionization by ultrashort laser pulses where the probability definition due to the nonlinear dependence on time is no longer valid. We employ the exact integrals over the Fourier transform of the photoionization cross section including the Fano resonances and a corrected Gaussian pulse shape that has vanishing electric field for zero frequency. Numerical results are presented for neutral helium that allow us to deduce the spectral distribution of the Fano resonance for different parameters and to identify the cases where the linear regime is invalid. Analytical approximations are given that provide a clear understanding of the linear and nonlinear regime related to the Fano parameter qqq, the detuned carrier frequencies, and pulse durations.
The multiple-linear-time-scale method is used to construct a perturbation theory for NNN-level quantum systems subjected to time-dependent perturbations. The secular and small-denominator terms which plague conventional time-dependent perturbation theory are avoided; consequently, the theory is useful for treating long-term behavior and resonant interactions. The introduction of a self-energy operator allows the shifts in energy levels to be displayed explicitly. When the perturbation is the dipole interaction with an electromagnetic field, the successive approximations yield the well-known rotating-wave approximation, corrections due to counter rotating terms, and the Bloch-Siegert frequency shift. The formalism is applicable to arbitrary pulse shapes, provided that $\ensuremath{\parallel}{H}_{1}\ensuremath{\parallel}\ensuremath{\ll}\ensuremath{\hbar}\overline{\ensuremath{\omega}}$, where $\ensuremath{\parallel}{H}_{1}\ensuremath{\parallel}$ represents the inter-action strength and $\overline{\ensuremath{\omega}}$ is a characteristic frequency of the field. Rabi oscillations induced by multiphoton resonances are automatically included, and this effect is demonstrated in the case of a square pulse with frequency approximately one half the resonance frequency for a transition between two vibrational levels of a molecule. These calculations are compared to an exact numerical solution in order to find the limits of validity of the approximation. Even at high intensities ($I\ensuremath{\sim}{10}^{14}$ W/cm2{\mathrm{cm}}^{2}cm2) the shifted resonance frequency is quite accurate; however, the approximate and exact solutions are slightly out of phase, so that the approximate solution can only be trusted for a few Rabi cycles. For much lower intensities ($I\ensuremath{\sim}{10}^{10}$ W/cm2{\mathrm{cm}}^{2}cm2), the approximate solution is valid for many thousands of Rabi cycles.