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Physical Review A

Theory for direct frequency-comb spectroscopy

D. Felinto, Carlos E. E. López

Published Jul 29, 2009• 23 citations
Publisher

Abstract

Direct frequency-comb spectroscopy is a technique that employs a train of well-stabilized ultrashort pulses to study the spectral properties of atomic or molecular systems. In this way, it opens the possibility of incorporating various coherent-control techniques for such spectral investigations. Here we introduce a theory for the interaction of a multilevel atom with such pulse trains, which is general enough to take into account an arbitrarily shaped frequency comb. We illustrate its application by studying the interaction of $^{87}\text{R}\text{b}$ atoms with trains of pulses of various shapes, resonant with the $5S\text{\ensuremath{-}}5D$ two-photon transition of rubidium. More specifically, we treat the interaction with hyperbolic-secant pulses, chirped pulses, and 0-$\ensuremath{\pi}$ pulses, respectively. The theory is designed to work at an arbitrary perturbation order. For the results presented here, we mostly used a 12th-order perturbation series at the pulse's electric field. Due to the large number of levels involved, such modeling may be quite complex computationally, and an important point of the present work is then to introduce the required numerical approach to treat this problem efficiently.

DOI
10.1103/physreva.80.013419

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•Jan 1, 2013•1 citation
Direct frequency-comb spectroscopy is a technique that employs a train of well-stabilized ultrashort pulses to study the spectral properties of atomic or molecular systems. In this way, it opens the possibility of incorporating various coherent-control techniques for such spectral investigations. Here we introduce a theory for the interaction of a multilevel atom with such pulse trains, which is general enough to take into account an arbitrarily shaped frequency comb. We illustrate its application by studying the interaction of 87Rb^{87}\text{R}\text{b}87Rb atoms with trains of pulses of various shapes, resonant with the 5S\ensuremath-5D5S\text{\ensuremath{-}}5D5S\ensuremath-5D two-photon transition of rubidium. More specifically, we treat the interaction with hyperbolic-secant pulses, chirped pulses, and 0-\ensuremathπ\ensuremath{\pi}\ensuremathπ pulses, respectively. The theory is designed to work at an arbitrary perturbation order. For the results presented here, we mostly used a 12th-order perturbation series at the pulse's electric field. Due to the large number of levels involved, such modeling may be quite complex computationally, and an important point of the present work is then to introduce the required numerical approach to treat this problem efficiently.
A theoretical analysis is carried out for the recently developed three-pulse photon echo spectroscopy employing dual frequency combs (DFC) as the light sources. In this method, the molecular sample interacts with three pulse trains derived from the DFC, and the generated third-order signal is displayed as a two-dimensional (2D) spectrum that depends on the waiting time introduced by employing the asynchronous optical sampling method. Through the analysis of the heterodyne-detected signal interferogram using a local oscillator derived from one of the optical frequency combs, we show that the 2D spectrum closely matches the spectrum expected from a conventional approach with four pulses derived from a single femtosecond laser pulse, and the waiting time between the second and third field-matter interactions is given by the down-converted detection time of the interferogram. The theoretical result is applied to a two-level model system with solvation effect described by solvatochromic spectral density. The model 2D spectrum reproduces spectral features such as the loss of frequency correlation, dephasing, and spectral shift as a function of the population time. We anticipate that the present theory will be the general framework for quantitative descriptions of DFC-based nonlinear optical spectroscopy.
The main goal of this PhD work is an experimental study of coherent excitation of atomic and molecular wavepackets, i.e. superpositions of many quantum eigenstates, by shaped femtosecond pulses. Approaches allowing nearly complete population transfer between quantum eigenstates were well studied in the past within the two level approximation. In this work we focus on adiabatic and non-adiabatic methods of population transfer beyond the two-level approximation. Excitation of multi-level target states is possible due to broad spectrum of an ultrashort pulse which contains frequencies needed for multiple transitions to different states in the final superposition. At the same time, the spectrum of an ultrashort pulse can be modified, or ``shaped'', in order to affect the excitation process and control the amplitudes in the final superposition. Both non-adiabatic and quasi-adiabatic methods were first implemented and studied in electronic wavepackets in alkali atoms. The non-adiabatic approach revealed features linked to the strong-field perturbations of the energy level structure of the quantum system. An adiabatic method was implemented for the first time on a femtosecond time scale, and was thoroughly characterized. The control over complex amplitudes in the target superposition was demonstrated as well as completeness of the population transfer. In the second part of this work, we focused on coherent control of rotational wavepackets in diatomic molecules. Rotational excitation by a periodic train of femtosecond pulses was investigated in the context of ``delta-kicked'' rotor - a paradigm system for studying quantum chaos, and the effect of quantum resonance was demonstrated for the first time in a system of true quantum rotors. Control of uni-directional molecular rotation was proposed and demonstrated with a novel ``chiral pulse train'' - a sequence of femtosecond pulses with polarization rotating from pulse to pulse by a predefined angle. All the developed techniques offer new tools in coherent control of atomic and molecular wavepackets on an ultrashort time scale.
The direct and optical control of x-ray transitions is studied theoretically by investigating the spectra of resonance fluorescence and absorption. The work is motivated by the rapid advances in x-ray science, enabling the application of quantum-control schemes at short wavelengths. In a two-level system we study Rabi oscillations of atomic inner-shell electrons, induced by intense x-ray pulses and competing with Auger decay, and their signature in the spectrum of resonance fluorescence. Subsequently, optical manipulation of x-ray transitions is examined, by employing an optical frequency comb coupling nearby excited levels to control their spontaneous decay. First, narrow-bandwidth x rays are adopted, giving rise to the periodic shaping of the atomic dynamic variables and the imprinting of a comb onto the x-ray resonance fluorescence spectrum. A more realistic model for an immediate experimental implementation is then provided, by developing a scheme to imprint a comb onto the absorption spectrum of an ultrashort x-ray pulse. An experimental realization of the predicted comb structures is anticipated to transfer the accuracy of optical frequency combs into the x-ray regime