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Physical Review A

Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences

A. Präkelt, M. Wollenhaupt, Cristian Sarpe, Thomas Baumert

Published Dec 13, 2004• 97 citations
Publisher

Abstract

Phase effects in a quantum control experiment on the two-photon transition $4s\phantom{\rule{0.3em}{0ex}}\ensuremath{\leftarrow}\ensuremath{\leftarrow}\phantom{\rule{0.3em}{0ex}}3s$ of atomic sodium are studied. In our experiment, we combine the generation of phase-locked interferometrically generated pulses with pulse-shaping techniques to study in detail the interplay of optical and quantum-mechanical phases. Subtle differences in the physical realization of the pulse sequences produce large difference in the control objective---the $4s$ population. The control mechanisms of more complex pulse sequences generated by periodic and discontinuous phase-modulation functions are investigated systematically and analyzed on the basis of quantum-mechanical interference.

DOI
10.1103/physreva.70.063407

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With femtosecond laser spectral phase shaping technique and polarization modulation technique,the coherent control of two-photon fluorescence(TPF)in Rhodamine B solution is studied.By shaping the femtosecond pulse with simple phase patterns(cosinusoidal andπphase step-function shape),two-photon fluorescence intensity of Rhodamine B can be controlled effectively.Theoretical simulation and calculation show that the variation of twophoton fluorescence intensity for Rhodamine B solution is ascribed to the constructive and destructive interference of various quantum paths in two-photon transitions.TPF of Rhodamine B solution displays periodical change by polarization modulation.TPF decreases when the laser polarization changes from linear through elliptical to circular.These experimental results are theoretically confirmed to be caused by the variation of laser polarization.

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Phase effects in a quantum control experiment on the two-photon transition 4s\ensuremath←\ensuremath←3s4s\phantom{\rule{0.3em}{0ex}}\ensuremath{\leftarrow}\ensuremath{\leftarrow}\phantom{\rule{0.3em}{0ex}}3s4s\ensuremath←\ensuremath←3s of atomic sodium are studied. In our experiment, we combine the generation of phase-locked interferometrically generated pulses with pulse-shaping techniques to study in detail the interplay of optical and quantum-mechanical phases. Subtle differences in the physical realization of the pulse sequences produce large difference in the control objective---the 4s4s4s population. The control mechanisms of more complex pulse sequences generated by periodic and discontinuous phase-modulation functions are investigated systematically and analyzed on the basis of quantum-mechanical interference.
Coherent control of femtosecond two-photon absorption in the intermediate-field regime is analyzed in detail in the powerful frequency domain using an extended 4th-order perturbative description. The corresponding absorption is coherently induced by the weak-field non-resonant two-photon transitions as well as by four-photon transitions involving three absorbed photons and one emitted photons. The interferences between these two groups of transitions lead to a difference between the intermediate-field and weak-field absorption dynamics. The corresponding interference nature (constructive or destructive) strongly depends on the detuning direction of the pulse spectrum from half the two-photon transition frequency. The model system of the study is atomic sodium, for which both experimental and theoretical results are obtained. The detailed understanding obtained here serves as a basis for coherent control with rationally-shaped femtosecond pulses in a regime of sizable absorption yields.
A femtosecond laser pulse can be tailored to control the two-photon transitions using the ultra-fast pulse-shaping technique. This paper theoretically and experimentally demonstrates that two-photon transitions in molecular system with broad absorption line can be effectively controlled by square phase-modulation in frequency domain, and the influence of all parameters characterizing the square phase-modulation on two-photon transitions is systemically investigated and discussed. The obtained results have potential application in nonlinear spectroscopy and molecular physics.
The experimental work in this thesis is divided into two distinct parts. In both parts, broadband femtosecond laser pulses are "shaped" by adjusting the relative phase and amplitude of spectral components. In the first set of experiments, time-dependent perturbation theory is used to show that the probability of a quantum transition in atomic rubidium can be substantially enhanced or suppressed using pulse shaping, compared to the probability of transition observed when a transform-limited or "flat phase" optical pulse is used. These enhancement or suppression effects are also demonstrated experimentally. As quantum interference (the material phase having been transferred from the optical phase) is used to enhance or diminish a particular final quantum state, this can be classified as a quantum coherent control experiment. In the second set of experiments, an optical pulse is scattered into a train of pulses by a layered structure. The layered structure is used to simulate the effect of optical pulses travelling through certain types of complex media. One consequence of the disruption of a single pulse into a train of pulses is lower per-pulse peak intensity, and thus a greatly diminished nonlinear signal. It is shown that spectral pulse shaping (in phase only) is sufficient to pre-compensate for the scattering structure, allowing a single transform-limited pulse to be obtained at the output.
We experimentally demonstrate a strong-field coherent control mechanism that combines the advantages of photon locking (PL) and rapid adiabatic passage (RAP). Unlike earlier implementations of PL and RAP by pulse sequences or chirped pulses, we use shaped pulses generated by phase modulation of the spectrum of a femtosecond laser pulse with a generalized phase discontinuity. The novel control scenario is characterized by a high degree of robustness achieved via adiabatic preparation of a state of maximum coherence. Subsequent phase control allows for efficient switching among different target states. We investigate both properties by photoelectron spectroscopy on potassium atoms interacting with the intense shaped light field.
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
With femtosecond laser spectral phase shaping technique and polarization modulation technique,the coherent control of two-photon fluorescence(TPF)in Rhodamine B solution is studied.By shaping the femtosecond pulse with simple phase patterns(cosinusoidal andπphase step-function shape),two-photon fluorescence intensity of Rhodamine B can be controlled effectively.Theoretical simulation and calculation show that the variation of twophoton fluorescence intensity for Rhodamine B solution is ascribed to the constructive and destructive interference of various quantum paths in two-photon transitions.TPF of Rhodamine B solution displays periodical change by polarization modulation.TPF decreases when the laser polarization changes from linear through elliptical to circular.These experimental results are theoretically confirmed to be caused by the variation of laser polarization.