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Physical Review A

Quantum beating in uv radiation generation by ultrashort laser pulses via four-wave mixing

Anahit L. Gogyan, Yu. P. Malakyan

Published Nov 3, 2008• 4 citations
Publisher

Abstract

We show that quantum beating appears in the intensity of Stokes and uv radiation generated via hyper-Raman scattering (HRS) and four-wave mixing (FWM), respectively, when a large number of close-lying upper states of atoms or molecules is excited by two-photon interaction with consecutive ultrashort laser pulses. The quantum beating at frequencies correlated with the energy difference between atomic states results from a Ramsey-like interference of atomic wave packets created by the pump and probe laser fields. We reveal that the destructive interference between HRS and FWM is superimposed on the wave packet interference, leading to substantial enhancement of the beating fringe visibility. We examine the effect of laser phase fluctuations and show that they strongly limit the number of beating modes. An analytical solution of transient Maxwell-Bloch equations is obtained, and the oscillatory dependence of uv emission on the delay between two laser pulses is revealed, allowing atomic wave packets to be detected optically. A comparison to available pump-probe experiments is made.

DOI
10.1103/physreva.78.053401

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We show that quantum beating appears in the intensity of Stokes and uv radiation generated via hyper-Raman scattering (HRS) and four-wave mixing (FWM), respectively, when a large number of close-lying upper states of atoms or molecules is excited by two-photon interaction with consecutive ultrashort laser pulses. The quantum beating at frequencies correlated with the energy difference between atomic states results from a Ramsey-like interference of atomic wave packets created by the pump and probe laser fields. We reveal that the destructive interference between HRS and FWM is superimposed on the wave packet interference, leading to substantial enhancement of the beating fringe visibility. We examine the effect of laser phase fluctuations and show that they strongly limit the number of beating modes. An analytical solution of transient Maxwell-Bloch equations is obtained, and the oscillatory dependence of uv emission on the delay between two laser pulses is revealed, allowing atomic wave packets to be detected optically. A comparison to available pump-probe experiments is made.
A theory of quantum beats in a Stokes signal observed in pump-probe experiments upon excitation of four-level atoms with two close upper lying levels by femtosecond laser pulses is developed. Quantum beats arise in the intensity of the Stokes field due to the interference of two atomic wave packets generated by ultrashort pump and probe pulses. An analytical solution of the non-steady-state Maxwell-Bloch equations is obtained, and the dependence of the Stokes radiation intensity on the delay time between two laser pulses is investigated. The theoretical results describe qualitatively well the observed features of quantum beats.
The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and (n-2)dstates (n=8 for K; n=11 , 12 for Rb) with red (~620-nm) , 80-100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp(2)P? (2)S(1/2) (7</=m</=12 for Rb; 5</=m</=7 for K) resonance transitions when a probe pulse is scattered by the wave packet established by the earlier (identical) pump pulse. The spatial and spectral characteristics of the UV emission are well described by axially phase-matched four-wave mixing, and all the prominent frequency components of the wave packets are associated with energy differences between pairs of excited states for which Diota=0 or Diota=2 . These results demonstrate that the wave packet modulates chi((3))of the medium, thus rendering the wave packet detectable.
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
A theoretical model of coupled four-wave mixing (FWM) processes comprising five atomic energy levels was proposed to investigate the coherent characteristics of atomic wave packets using perturbation theory. As several states in atoms are coherently excited by a two-photon transition, triple coupled FWM can be produced, and triple quantum beats associated with the atomic energy levels are embedded in the FWM signals. Triple coupled FWM processes were achieved experimentally in Rb vapor by two-photon excitation using broadband optical pulses. A pump–probe scheme was utilized to record the time-varying FWM signals, and Fourier transform was applied to retrieve the quantum beats. Furthermore, short-time Fourier transform was implemented to investigate the dynamics of quantum beats. The results show that the coherent characteristics of atomic wave packets, which are intimately related to the dynamics of quantum beats, can be probed by coupled nonlinear optical wave mixing.
Probing the interactions between a mode-locked laser pulse and saturated rubidium vapor with a pump–probe technique has resulted in observations of coherences within the atom that persist longer than 150 ps. Quantum beats due to the interference between the 7S and 5D_{5/2} energy states were observed by a four-wave mixing process. The difference frequency between the 5D–5P_{3/2} and the 5P_{3/2}–5S transitions was also observed for interpulse delays up to 180 ps. The temporal evolution of the beat amplitude indicates the existence of a superfluorescent process and a scattering process detected simultaneously with the four-wave mixing process. A model was developed to explain the processes and was used to predict the range of pulse parameters for which the scattering process and four-wave mixing could be simultaneously detected.
Two coupled axially phase matched parametric four-wave mixings have been achieved in Rb vapor by using broad bandwidth laser pulses. Coherent radiations at 420 nm produced by difference-frequency optical wave mixing processes were detected and a pump-probe scheme was employed to record time varying characteristics of the parametric four-wave mixing signals. Quantum beatings at 608 cm-1 and 70 cm-1 were retrieved from the time varying signals by Fourier transform. Moreover, time dependent Fourier transform was utilized to analyze the dynamics of quantum beatings. The results indicate that two wave packets associated with the two quantum beating frequency components interact strongly and the quantum beating dynamics can be controlled by adjusting Rb number density.