arXiv:quant-ph/9803043

On multiphoton absorption by molecules

Pedro F. González-Dı́az

Published Mar 17, 1998• 0 citations

Abstract

Rabi frequencies for multiphoton absorption by atoms or molecules that can be characterized as two- or three-level systems are obtained in the cases of single and double laser perturbations. If the ambiguity in the origin of absolute energy is conveniently gauged off in the three-level model, there appears an additional non linear frequency which is originated from the separate evolution of a relative-frequency component induced in the whole system by the simultaneous action of the two perturbations.

DOI: 10.48550/arxiv.quant-ph/9803043

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arXiv:quant-ph/9803043

On multiphoton absorption by molecules

Pedro F. González-Dı́az

Published Mar 17, 1998• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.quant-ph/9803043

Related papers

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The multiple-linear-time-scale method is used to construct a perturbation theory for

N

-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/

{\mathrm{cm}}^{2}

) 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/

{\mathrm{cm}}^{2}

), the approximate solution is valid for many thousands of Rabi cycles.

We show that a class of multiphoton-absorption problems has exact solutions. In these problems an

N

-level atom or molecule absorbs energy from near-resonance monochromatic laser fields, and one asks for the time-dependent populations of the energy levels of the absorber. We find that the equal-Rabi and the harmonic-Rabi

N

-level systems studied numerically in the preceding paper are associated with Chebyshev and Hermite polynomials. Using the exact solutions we find exact expressions for the time averages of occupation probabilities in terms of sums of squares of polynomials. In addition we find the first approximate analytic expression for the long-period population oscillations observed in numerical solutions; and we show that a steady-state population inversion between the highest and lowest levels may be maintained by multiphoton pumping.

{\mathrm{SF}}_{6}

transition has been determined from the relation between laser fluence and number of Rabi oscillations. For the two-color cases the detuning with the intermediate level is varied by tuning the respective laser frequencies while keeping the sum frequency constant. A dramatic change in the degree of excitation as a function of the intermediate detuning has been observed. \textcopyright{} 1996 The American Physical Society.

s

-photon absorption can be expressed by ${(4\ensuremath{\pi})}^{\frac{\ensuremath{-}1}{2(s\ensuremath{-}1)}}s!{s}^{\frac{1}{2}}{(\frac{{\ensuremath{\tau}}_{c}}{\ensuremath{\tau}})}^{s\ensuremath{-}1},$ where $\ensuremath{\tau}$ is the time during which the atomic system is illuminated by thermal radiation with coherence time ${\ensuremath{\tau}}_{c}$. This shows that multiphoton absorption processes depend on the statistical properties of the incident light, and that the probability induced by the laser packet is certainly greater than that induced by the thermal light if $s<\frac{\ensuremath{\tau}}{{\ensuremath{\tau}}_{c}}$.