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Physical Review A

Femtosecond-pulse two-photon resonant difference-frequency mixing in gases: A technique for tunable vacuum-ultraviolet femtosecond-pulse generation and a spectroscopic tool for studying atoms in strong laser fields

A. Nazarkin, G. Korn, Olaf Kittelmann, Jens Ringling, Ingolf Volker Hertel

Published Jul 1, 1997• 19 citations
Publisher

Abstract

Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time ${T}_{2}^{\ensuremath{'}}$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.

DOI
10.1103/physreva.56.671

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Quantum control of optical four-wave mixing with femtosecond !-3! laser pulses: coherent ac Stark nonlinear spectroscopy

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Near-resonant four-wave mixing of attosecond extreme-ultraviolet pulses with near-infrared pulses in neon: Detection of electronic coherences

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Coherent narrow-band extreme-ultraviolet (EUV) light is generated by a near-resonant four-wave mixing (FWM) process between attosecond pulse trains and near-infrared pulses in neon gas. The near-resonant FWM process involves one vacuum-ultraviolet (VUV) photon and two near-infrared (NIR) photons and produces new higher-energy frequency components corresponding to the $ns/nd$ to ground-state $(2{s}^{2}2{p}^{6})$ transitions in the neon atom. The EUV emission exhibits small angular divergence (2 mrad) and monotonically increasing intensity over a pressure range of 0.5--16 Torr, suggesting phase matching in the production of the narrow-bandwidth coherent EUV light. In addition, time-resolved scans of the NIR nonlinear mixing process reveal the detection of a persistent, ultrafast bound electronic wave packet based on a coherent superposition initiated by the VUV pulse in the neon atoms. This FWM process using attosecond pulses offers a means for both efficient narrow-band EUV source generation and time-resolved investigations of ultrafast dynamics.

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Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time T2\ensuremath′{T}_{2}^{\ensuremath{'}}T2\ensuremath′​ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.
Resonant and near-resonant two-photon excitations with ultrashort laser pulses of forbidden atomic transitions give access to a wide class of nonlinear-optical processes such as two-photon absorption, stimulated Raman scattering, four-wave sum- and difference-frequency mixing. The latter has proofed to be a powerful tool for efficient femtosecond pulse generation in the VUV-spectral range [1]. Nevertheless, up to now only few experimental results have been obtained which allow the direct observation of the coherent dynamics in two-photon induced radiation-matter interactions (see experimental papers [2-5] and monograph [6]).
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
We present experimental data on the coherent control of frequency conversion toward the vacuum-ultraviolet regime in xenon atoms, applying intense ultrashort picoseconds (ps) radiation pulses. We report on quantum interference between two resonantly enhanced frequency conversion processes (i.e., fifth harmonic generation and four-wave mixing). The conversion processes are driven by a fundamental (ps) laser pulse at 530 nm and the phase-locked second harmonic at 265 nm. Both fifth harmonic generation and four-wave mixing yield vacuum-ultraviolet radiation at 106 nm. The two frequency conversion pathways interfere with each other---either constructively or destructively, depending on the relative phase of the driving laser pulses. Thus, by variation of the relative phase, we substantially enhance or reduce the conversion efficiency (i.e., the yield of generated vacuum-ultraviolet radiation).
We present experimental data on adiabatically driven frequency conversion with ultrashort (picosecond) laser pulses towards the vacuum-ultraviolet regime, enhanced by coherent population return and preparation of maximal atomic coherences. We generate the sum frequency of an intense pump pulse and a probe pulse via a two-photon resonance in xenon. When we slightly detune the pump laser from two-photon resonance, the atomic populations are adiabatically driven forth and back from the atomic ground state to an excited state. This coherent population return (CPR) prepares the medium in a transient state of maximal atomic coherence, which enhances frequency mixing with a probe laser. We thoroughly study the variation of CPR-enhanced frequency conversion with experimental parameters and compare CPR with conventional, resonantly enhanced frequency conversion. In particular, we investigate the temporal evolution of the atomic coherence and the effect of inevitable ac Stark shifts. We find that ac Stark shifts induce an asymmetry in the spectral characteristics of CPR, which nevertheless permits enhanced frequency conversion. For the case of resonantly enhanced frequency conversion, we show that the atomic coherences are maintained for several tens of picoseconds after the pump pulse, which permits time-delayed frequency conversion. Moreover, we analyze the pressure dependence of the atomic coherence' lifetime and observe a free induction decay at the two-photon coherence with the generation of a second harmonic field. These findings shall push applications of adiabatic light-matter interactions also to the regime of nonlinear optics, driven by intense laser pulses.
Coherent narrow-band extreme-ultraviolet (EUV) light is generated by a near-resonant four-wave mixing (FWM) process between attosecond pulse trains and near-infrared pulses in neon gas. The near-resonant FWM process involves one vacuum-ultraviolet (VUV) photon and two near-infrared (NIR) photons and produces new higher-energy frequency components corresponding to the ns/ndns/ndns/nd to ground-state (2s22p6)(2{s}^{2}2{p}^{6})(2s22p6) transitions in the neon atom. The EUV emission exhibits small angular divergence (2 mrad) and monotonically increasing intensity over a pressure range of 0.5--16 Torr, suggesting phase matching in the production of the narrow-bandwidth coherent EUV light. In addition, time-resolved scans of the NIR nonlinear mixing process reveal the detection of a persistent, ultrafast bound electronic wave packet based on a coherent superposition initiated by the VUV pulse in the neon atoms. This FWM process using attosecond pulses offers a means for both efficient narrow-band EUV source generation and time-resolved investigations of ultrafast dynamics.