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Fano profiles in two-photon photoassociation spectra

M. Portier, Michèle Leduc, Claude N. Cohen-Tannoudji

Published Jan 1, 2009• 3 citations
Publisher

Abstract

In this article we derive the lineshapes observed in two-photon photoassociation spectrocopy of molecules using an effective Hamiltonian adapted from previous work in atomic physics. The lineshape is decomposed in terms of sums and products of Breit-Wigner and Fano profiles, which we associate with physical absorption and emission processes, and to quantum interferences between transition amplitudes. We emphasize the specific features which do not exist in the atomic case, linked to the dissociation width of the photoassociated molecules in the electronic ground state.

DOI
10.1039/b819470j

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In this article we derive the lineshapes observed in two-photon photoassociation spectrocopy of molecules using an effective Hamiltonian adapted from previous work in atomic physics. The lineshape is decomposed in terms of sums and products of Breit-Wigner and Fano profiles, which we associate with physical absorption and emission processes, and to quantum interferences between transition amplitudes. We emphasize the specific features which do not exist in the atomic case, linked to the dissociation width of the photoassociated molecules in the electronic ground state.
The Fano resonance, with a unique asymmetric line shape, is a well-known manifestation of quantum interference with numerous promising applications for light-harvesting devices. Here we report an experimental observation of the Fano effect in an ultracold atom-molecule coupled system realized by photoassociation near a magnetically tunable ddd-wave Feshbach resonance. Our result shows that, compared to ubiquitous single-peak Fano-type line shapes, the coupled Fano resonances feature a two-peak profile. We develop a theory of coupled Fano resonances which agrees very well with the experimental results. This work may open a new perspective for tuning ultracold collisional interaction using the Fano resonance and studying bound states in continuum.
Recently, the method of Lu-Fano plots was extended to potentials with general ${R}^{\ensuremath{-}n}$ asymptotic behavior. The aim of this paper is to discuss the efficiency of this method for the interpretation of experimental vibrational spectra of long-range diatomic molecules when two channels are coupled. A Lu-Fano analysis is implemented on experimental data for the Cs20u+(6S+6P1/2,3/2){\mathrm{Cs}}_{2}{0}_{u}^{+}{(6S+6P}_{1/2,3/2})Cs2​0u+​(6S+6P1/2,3/2​) photoassociation spectra below the 6S+P1/2{6S+P}_{1/2}6S+P1/2​ and 6S+P3/2{6S+P}_{3/2}6S+P3/2​ dissociation limits. The parameters are fitted on level energies and predissociation widths, giving information about the asymptotic coefficients C3{C}_{3}C3​ for both channels and about a coupling parameter which determines the variation of predissociation widths as a function of detuning. This parameter can be extrapolated above the 6S+P3/2{6S+P}_{3/2}6S+P3/2​ threshold to yield the fine-structure transition cross section between the two channels. The probability for such a transition in a model where hyperfine structure effects are neglected is found to be 0.54.
Photoassociation, the bound←free absorption of a photon by a colliding pair of atoms, has been studied experimentally in the Kr–F and Xe–I systems and is demonstrated to be an effective tool for deducing molecular interaction potentials and for determining the dependence of the relative electronic transition moment on internuclear separation (R) in small molecules having dissociative ground states. Specifically, the excitation (‘‘action’’) spectrum for the photoassociation of thermalized Kr(4p6 1S0)–F(2p5 2P) collision pairs, measured at 300 K in the 208–250 nm wavelength region, reveals deeply modulated Franck–Condon structure associated with transitions of Kr–F pairs from the ground state’s thermal and vibrational continua to the lowest 27 bound vibrational states (v′=0–26) of the KrF(B 2Σ) excited state. Under these conditions, photoassociation occurs in a narrow (ΔR=0.7–0.8 Å) Franck–Condon region in which the difference potential is a single valued function of R. Similar spectra have been observed for Xe(1S0)–I(2P) pairs in the 208–258 nm spectral region that arise from bound←free transitions to the lowest ∼40 vibrational levels of the XeI(B) state. Since the Kr–F and Xe–I collision pairs are photoexcited from the vibrational continuum of the ground state, the atomic pair energy distribution is thermalized and the envelope of the excitation spectrum can be interpreted directly in terms of the relative B–X transition moment, μ(R). Consequently, the behavior of μ(R) has been determined over a limited range in R and, for XeI, μ is found to fall by a factor of 2 in the ∼0.4 Å region extending from R−ReB≊0.25–0.62 Å. The XeI ground state (X 2Σ1/2+) potential in the 3.0≤R≤5.0 Å interval, derived from photoassociation spectra, is similar to that deduced from scattering experiments. Excited and ground state structural constants derived from numerical quantum simulations of the experimental spectra are presented.
In this paper we apply the T matrix formalism of scattering theory to derive general expressions for the absorption cross sections, the cross sections for resonance fluorescence and the emission quantum yields from large molecules in the statistical limit. In the simple case of an isolated molecular resonance both the absorption line shape and the photon scattering cross section exhibit a Lorentzian distribution on the photon energy, the emission quantum yields are distributed among the ground state vibronic levels according to their radiative widths and, most important, the emission quantum yields are independent of the photon energy and of the spectral width of the exciting light. We were able to derive general expressions for the resonance scattering from a pair of overlapping resonances, including radiative corrections to infinite order. The absorption cross section does not vanish in the region of destructive interference but assumes a finite value which depends on the radiative widths. A sharp maximum in the partial and in the total emission quantum yields is exhibited in the destructive interference regions. This general scheme was applied to a pair of zero order discrete states, one of which is optically active, which interact with an optically inactive quasicontinuum. The energy dependent quantum yield depends on the total width of the radiatively impotent state and may exhibit a minimum. We have demonstrated that when interference effects are involved the decay characteristics of this system will differ for coherent and for narrow band excitation. The general formalism was utilized to derive approximate relations for the resonance fluorescence cross sections and for the quantum yield in the case of a Fano absorption line shape which are valid away from the interference region. Finally, we have applied the general theoretical scheme to the case of the direct photodissociation spectrum of molecules. We have demonstrated that a finite energy dependent emission quantum yield will be observed when a molecule is optically pumped into a dissociative continuum.
Photon absorption spectroscopy is a powerful tool for uncovering the structure of atoms, molecules, and solids. Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures related to the structural and dynamical properties. Recently, Ott et al. [Science 340, 716 (2013)] successfully transferred Fano profile into Lorentzian line shape using an intense infrared laser, after excitation of autoionizing states in helium by attosecond XUV pulse. This is a very important step forward in quantum phase control. However, here we show experimentally that an autoionizing state can have both Fano and Lorentzian behavior naturally, depending on the process involved. This study utilized the inverse process of photon absorption ionization, i.e., electron ion recombination with photon emission, making sure the resonant autoionizing state is not modified or decorated by the laser fields. Our result implies that excitation of the state through different paths---for example, one photon versus multiphoton excitation, or even one step versus multistep excitation---can lead to different Fano profiles for the same resonant state. We also report an experimental determination of the energy shifts in the recombination photon-intensity peaks due to the interference between the resonant and nonresonant processes.