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Physical Review A

Time-delayed probe spectroscopy in two-photon–pumped systems

A. Guzman de Garcia, Pierre Meystre, Rainer Salomaa

Published Sep 1, 1985• 18 citations
Publisher

Abstract

We study transients in resonantly coupled three-level systems. Two of the levels are coupled by intense two-photon pumping, and the third one provides a probing level. Adiabatically eliminated levels appear in effective system parameters. Experimentally, this model is applicable, e.g., in resonantly enhanced parametric and harmonic generation in atomic vapors. A distinguishing feature in the system is the appearance of ac Stark shifts in the probe spectra when pumping at the two-photon resonance. The nutation signal is shown to give information on the effective two-photon Rabi frequency and on the decay rate of the dipole-forbidden two-photon coherence. Free-induction decay is strongly dominated by population-induced effects; Raman-like peaks introduced by Stark shifts may show large instantaneous gain. Gaussian pump pulses are investigated to investigate effects arising from the temporal sweeping of the two-photon Rabi flipping and the modulation of the Stark shifts. The results also provide relevant information on the gain dynamics of coherently pumped lasers.

DOI
10.1103/physreva.32.1531

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•Oct 25, 2000•0 citations
We study transients in resonantly coupled three-level systems. Two of the levels are coupled by intense two-photon pumping, and the third one provides a probing level. Adiabatically eliminated levels appear in effective system parameters. Experimentally, this model is applicable, e.g., in resonantly enhanced parametric and harmonic generation in atomic vapors. A distinguishing feature in the system is the appearance of ac Stark shifts in the probe spectra when pumping at the two-photon resonance. The nutation signal is shown to give information on the effective two-photon Rabi frequency and on the decay rate of the dipole-forbidden two-photon coherence. Free-induction decay is strongly dominated by population-induced effects; Raman-like peaks introduced by Stark shifts may show large instantaneous gain. Gaussian pump pulses are investigated to investigate effects arising from the temporal sweeping of the two-photon Rabi flipping and the modulation of the Stark shifts. The results also provide relevant information on the gain dynamics of coherently pumped lasers.
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.
Wave mixing in a three-level quantum system induced by two-photon resonant pump and one-photon resonant coupling at lower transition has been studied theoretically and experimentally. Resonantly enhanced difference-frequency generation efficiency was observed clearly dependent on the time delay and its sign between the femtosecond pump and probe. The role of the atomic coherences on the amplification without inversion during different sequences of interaction in a closed three-level system has been also stressed. These findings were confirmed experimentally in atomic potassium, where strong parametric amplification, induced by the pump delayed with respect to the probe, has been observed for the first time.
Abstract We demonstrate how strong-field multiphoton transitions between dynamically shifted atomic levels can be traced in the energy spectra of emitted photoelectrons. Applying an ultrafast and intense laser pulse, two-photon Rabi oscillations are induced between two bound states of an atom. A third photon from the same pulse directly ionizes the atom, thus the emitted photoelectrons coherently probe the underlying dynamics. As the instantaneous energy of photoelectrons follows the pulse intensity envelope, modulated by the ac Stark shifts, electrons emitted with the same energy but at different times—at the rising and falling edge of the pulse—will interfere leading to pronounced dynamic interference pattern in the spectra. We investigate this phenomenon both numerically and analytically by developing a minimal three-state model that incorporates two-photon coupling and dynamically shifted atomic levels. On the example of atomic lithium (2 s → → 4 s → continuum) we show how the individual ac Stark shifts and the two-photon Rabi frequency are reflected through the asymmetry, shifting and splitting of the interference structure of the computed photopeaks.
We analyze the transient response induced by a resonant, weak probe laser in a three-level V-type system driven by a strong, resonant coupling laser. The Rabi oscillation of the probe transition contains two frequencies determined by the coupling laser, and the ratio of the two-frequency components can be controlled by a time delay between the probe and the coupling laser. In particular, when both lasers are turned on simultaneously, the optical nutation with the frequency approximately equal to the Rabi frequency of the coupling laser is dominant; when the probe laser is turned on well after the steady state is reached for the coupling transition, the Rabi oscillation of the probe transition still occurs, and the oscillatory frequency is approximately equal to half of the Rabi frequency of the coupling laser. When both the probe and the coupling lasers are strong, the mutual interaction of the two fields and the atomic system may revive the optical nutation with each other.
The quantum dynamics of a system of Rb atoms, modeled by a V-type three-level system interacting with intense probe and pump pulses, are studied. The time-delay-dependent transient-absorption spectrum of an intense probe pulse is thus predicted, when this is preceded or followed by a strong pump pulse. Numerical results are interpreted in terms of an analytical model, which allows us to quantify the oscillating features of the resulting transient-absorption spectra in terms of the atomic populations and phases generated by the intense pulses. Strong-field-induced phases and their influence on the resulting transient-absorption spectra are thereby investigated for different values of pump and probe intensities and frequencies, focusing on the atomic properties which are encoded in the absorption line shapes for positive and negative time delays.
The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.