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Journal of the Optical Society of America B

Ultrafast interferometric pump–probe correlation measurements in systems with broadened bands or continua

Miles J. Weida, Susumu Ogawa, H. Nagano, Hrvoje Petek

Published Aug 1, 2000• 58 citations
Publisher

Abstract

Ultrafast (femtosecond) interferometric pump–probe techniques can be used to measure rates of population and quantum phase decay in complicated media such as liquids and solids. However, the levels probed in such systems are often inhomogeneously broadened or are part of a continuum of states. The use of broadband ultrafast lasers thus results in multiple levels being excited and detected. The inherent averaging that is due to this effect can alter the measured coherent response, thus affecting the information that can be retrieved on the phase decay. The importance of these effects is considered for the representative case of two-photon photoemission from metals. The effects of (i) continuum excitation; (ii) excitation from the Fermi level, i.e., a spectral step function; (iii) excitation from broadened levels with a finite width; and (iv) photoelectron energy analyzer resolution are determined.

DOI
10.1364/josab.17.001443

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Ultrafast (femtosecond) interferometric pump–probe techniques can be used to measure rates of population and quantum phase decay in complicated media such as liquids and solids. However, the levels probed in such systems are often inhomogeneously broadened or are part of a continuum of states. The use of broadband ultrafast lasers thus results in multiple levels being excited and detected. The inherent averaging that is due to this effect can alter the measured coherent response, thus affecting the information that can be retrieved on the phase decay. The importance of these effects is considered for the representative case of two-photon photoemission from metals. The effects of (i) continuum excitation; (ii) excitation from the Fermi level, i.e., a spectral step function; (iii) excitation from broadened levels with a finite width; and (iv) photoelectron energy analyzer resolution are determined.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy.In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels.It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid.Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180" pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes.The role of pulse phase is extensively analyzed.Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters.The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem.Phys.Lett.48, 256 (1977); Orlowski et al., ibid.54, 197 (1978)).The relative merits offluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences.Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions.In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.
Ultrafast pump-probe spectroscopy with high temporal and spectral resolutions provides new insight into ultrafast nonequilibrium phenomena. We propose that transient interference between pump and probe pulses is realized in pump-probe spectroscopy of band and Mott insulators, which can be observed only after recent developments of ultrafast spectroscopic techniques. A continuum structure in the excitation spectrum of band insulators is found to act as a medium for storing the spectral information of the pump pulse, and the spectrum detected by the probe pulse is interfered with by the medium, generating the transient interference in the energy domain. We also demonstrate the transient interference in the presence of electron correlations in a one-dimensional half-filled Hubbard model. Furthermore, bosons coupled to electrons additively contribute to the interference. Our finding will provide an interpretation of probe-energy-dependent oscillations recently observed in the pump-probe spectrum for a two-dimensional Mott insulator.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem. Phys. Lett. 48, 256 (1977); Orlowski et al., ibid. 54, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.
Observation of pulsed superradiance from two-level systems under direct excitation is challenging because the much stronger excitation pulse overlaps with the emitted radiation in time, space, and spectrum. Previous demonstrations have therefore mostly relied on excitation via auxiliary levels or multiphoton excitation at different wavelengths, limiting applicability. Here we present an interferometric pump-probe technique that enables observation of picosecond superradiance from a moderately-dense-but-optically-thin ensemble of two-level atoms resonantly excited under substantial Doppler and collisional broadening. Sequential pump and probe pulses tuned to the 555.6-nm E1 transition of 174 Yb allowed us to reconstruct the temporal waveform of the superradiant field from time-averaged transverse fluorescence. The fluorescence displayed interference fringes as a function of the pump-probe delay, whose envelope corresponds to the superradiant polarization P ( t ); taking its time derivative yields the radiated electric field. Pulse widths extracted from the reconstructed field follow a power-law scaling of 1/N00.441/{N}_{0}^{0.44}1/N00.44​ , where N 0 is the number of atoms in the interaction volume. The measured temporal dynamics and scaling behavior are in good agreement with simulations based on the coupled Maxwell-Schrödinger equations. This technique provides direct access to ultrafast superradiant dynamics without requiring auxiliary transitions, multiphoton excitation, or ultrafast detectors.
We study theoretically ultrafast modulation spectroscopy in Doppler-broadened cascading three-level and four-level systems. The pump beams consist of two frequency components that drive two-pathway excitation. The four-wave mixing (FWM) signal exhibits damping oscillation as the relative time delay τ between the two pump beams is varied, from which the resonant frequencies between energy levels can be deduced. Furthermore, Doppler-free precision in the measurement of the resonant frequencies can be achieved when the pump beams have either narrow-band or broadband linewidths. We study two-photon resonant FWM induced by time-delayed correlated fluctuating fields in a Doppler-broadened cascading three-level system. It is related intrinsically to the sum-frequency trilevel echo when the pump beams have broadband linewidths. However, unlike the corresponding incoherent-light stimulated photon echo, the maximum of the FWM signal is shifted from τ≃0. If we consider the fluctuations of the pump beams, the FWM signal exhibits damping oscillation when the laser frequency is off resonant from the two-photon transition.
Recent femtosecond transmission-correlation measurements1 of large organic dye molecules revealed surprising details concerning the ultrafast relaxation dynamics of such dyes. Superposed on simple exponential decays, the observation of damped sinusoidal oscillations with a period of ~ 150 fs has been puzzling. We theoretically and numerically demonstrate that such oscillatory behavior could be due to quantum beats of closely spaced two levels, whose coherent superposition state is optically prepared and monitored by a pair of femtosecond pulses. Although studies of quantum beats have been developed in both fluorescence-type2 and nonfluorescence-type measurements, such as those based on photon echoes3 or polarization spectroscopy,4 this simple method gives a new approach to femtosecond time domain spectroscopy. The generalized perturbation theory5 of optical coherent transients is extended to the case of optical transmission-correlation or pump-probe-type experiments. The model used is a three-level system which has split levels in either the ground or optically excited states. Especially, if the ground state has sublevels, the system becomes quite similar to the case of coherent Raman beats. Both cases are shown to give quantum beats when the excitation pulses are short compared with the inverse sublevel splitting. The period and decay time of the damped sinusoid represent the separation energy and the dephasing time between the sublevels, respectively. Using third-order perturbation theory, the transmission-correlation signal STC(τ) as a function of the first-to-second pulse delay time Is derived for arbitrary-shaped excitation pulses and is given in the form of fourfold integrals with many terms.