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Physical Review A

Observation of ac Stark-effect-enhanced four-wave mixing in a near-resonant four-level system

Chen-Yu Tai, Charles C. Kim, Robert T. Deck, Yet-Ta Wu

Published Jun 1, 1986• 6 citations
Publisher

Abstract

Two laser beams at frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ are used to produce nonlinear scattering (wave mixing) in ${\mathrm{I}}_{2}$ vapor at frequency 2${\ensuremath{\nu}}_{1}$+${\ensuremath{\nu}}_{2}$. The scattering results from near-resonant allowed transitions in ${\mathrm{I}}_{2}$ molecules and is observed to be anomalously strong when both laser beam frequencies are detuned in the same direction from frequencies corresponding to resonance in the free molecule. The strong scattering is interpreted in terms of a resonantly enhanced ac Stark shift caused by a configuration interaction between the ``dressed molecular levels.'' By tuning the two pulses simultaneously, a tuning range of approximately 2 A\r{} (50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) is achieved in the mixed wave. The scattering process should therefore have practical application in the efficient generation of tunable coherent radiation in the ultraviolet and vacuum-ultraviolet range of the spectrum. Some of the spectroscopic properties of the three-quantum state at E\ensuremath{\sim}53 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are studied.

DOI
10.1103/physreva.33.3970

Related papers

ac-Stark-effect-enhanced four-wave mixing in a near-resonant four-level system

Chen-Yu Tai, Robert T. Deck, Charles Kim

We report on an ac-Stark-effect-enhanced wave-mixing experiment in ${\mathrm{I}}_{2}$ vapor in which an output uv signal at frequency 2${\ensuremath{\omega}}_{1}$+${\ensuremath{\omega}}_{2}$ is maximized when the input frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are both detuned in the same direction from the resonance frequencies of the free molecule. A theory based on a configuration interaction between the ``dressed molecular levels'' is presented to explain the strong enhancement of the uv signal under these conditions. The data presented demonstrate that tunable coherent radiation at ultraviolet and vacuum-ultraviolet frequencies can be generated by the wave-mixing process we describe.

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AC Stark-effect-enhanced near-resonant wave mixing in a four-level system. 1: Experiment

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Two laser beams at frequencies v(1) and v(2) are used to produce nonlinear scattering (wave mixing) in I2 vapor at frequency 2v(1) + v(2). The scattering results from near resonance allowed transitions in I2 molecules and is observed to be resonantly enhanced when neither the one-, two-, nor three-quantum transitions are in resonance.

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arXiv:physics/0507061•Jul 7, 2005•0 citations
Two laser beams at frequencies \ensuremathν1{\ensuremath{\nu}}_{1}\ensuremathν1​ and \ensuremathν2{\ensuremath{\nu}}_{2}\ensuremathν2​ are used to produce nonlinear scattering (wave mixing) in I2{\mathrm{I}}_{2}I2​ vapor at frequency 2\ensuremathν1{\ensuremath{\nu}}_{1}\ensuremathν1​+\ensuremathν2{\ensuremath{\nu}}_{2}\ensuremathν2​. The scattering results from near-resonant allowed transitions in I2{\mathrm{I}}_{2}I2​ molecules and is observed to be anomalously strong when both laser beam frequencies are detuned in the same direction from frequencies corresponding to resonance in the free molecule. The strong scattering is interpreted in terms of a resonantly enhanced ac Stark shift caused by a configuration interaction between the ``dressed molecular levels.'' By tuning the two pulses simultaneously, a tuning range of approximately 2 A\r{} (50 cm\ensuremath−1{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}cm\ensuremath−1) is achieved in the mixed wave. The scattering process should therefore have practical application in the efficient generation of tunable coherent radiation in the ultraviolet and vacuum-ultraviolet range of the spectrum. Some of the spectroscopic properties of the three-quantum state at E\ensuremath{\sim}53 000 cm\ensuremath−1{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}cm\ensuremath−1 are studied.
We report on an ac-Stark-effect-enhanced wave-mixing experiment in I2{\mathrm{I}}_{2}I2​ vapor in which an output uv signal at frequency 2${\ensuremath{\omega}}_{1}$+${\ensuremath{\omega}}_{2}$ is maximized when the input frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are both detuned in the same direction from the resonance frequencies of the free molecule. A theory based on a configuration interaction between the ``dressed molecular levels'' is presented to explain the strong enhancement of the uv signal under these conditions. The data presented demonstrate that tunable coherent radiation at ultraviolet and vacuum-ultraviolet frequencies can be generated by the wave-mixing process we describe.
It is observed that when an intense, nearly resonant laser beam propagates through a dilute ($N<5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) vapor of sodium atoms, a four-wave-mixing process occurs, leading to the generation of strong, coherent radiation in the forward direction at frequencies symmetrically detuned from that of the exciting laser by the generalized Rabi frequency. This phenomenon is explained as resulting from a nearly phase-matched mixing process utilizing the nonlinear response of the sodium atom. Our analysis is based on a solution of the density-matrix equations of motion that includes the effect of level shifts induced by the ac Stark effect, which can be as great as 10 \AA{} for our experimental conditions, and which leads to gain due to the stimulated three-photon effect at one Rabi sideband and to strong coupling due to a parametric mixing process between radiation at the two sideband frequencies. It is also observed that at larger sodium densities ($N\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency $\ensuremath{\Omega}$ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance $\ensuremath{\Delta}$ and we explain this result as a consequence of strong saturation of the refractive index that occurs for $\ensuremath{\Omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$. Four-wave mixing is found to occur within these self-trapped filaments. The high-frequency sideband thus generated is trapped within the filament, whereas the lower-frequency sideband is ejected as a consequence of Snell's law and forms a cone surrounding the transmitted laser beam.
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
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.
The four-wave mixing produced with two ultrashort phase-locked w-3w 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 5w 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.