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Physical Review Letters

Coherent Control over Liouville-Space Pathways Interference in Transient Four-Wave Mixing Spectroscopy

Maxim S. Pshenichnikov, Wim P. de Boeij, Douwe A. Wiersma

Published Jun 17, 1996• 41 citations
Publisher

Abstract

A novel interference effect in transient four-wave mixing is demonstrated. The phenomenon is based on phase-controlled Liouville-space pathways interference and observed in the heterodyne-detected stimulated photon echo. Changing the phase difference between the first two excitation pulses from $\ensuremath{\pi}/2$ to 0 leads from no signal to maximum echo signal. A Brownian oscillator dynamical model is successfully used to analyze the effect and simulate the experimental data. The relation between this time-domain interference effect and dephasing-induced resonance in four-wave mixing spectroscopy is elaborated.

DOI
10.1103/physrevlett.76.4701

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Advances in multi-photon processes and spectroscopy•Dec 1, 2000•3 citations
A novel interference effect in transient four-wave mixing is demonstrated. The phenomenon is based on phase-controlled Liouville-space pathways interference and observed in the heterodyne-detected stimulated photon echo. Changing the phase difference between the first two excitation pulses from \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 to 0 leads from no signal to maximum echo signal. A Brownian oscillator dynamical model is successfully used to analyze the effect and simulate the experimental data. The relation between this time-domain interference effect and dephasing-induced resonance in four-wave mixing spectroscopy is elaborated.
We demonstrate coherent control over interference between different Liouville-space pathways that describe the generation of the nonlinear optical polarization in a stimulated photon echo. This control was exercised by phase-locking of the excitation pulses and observed in the heterodyne detected echo signal. A theoretical analysis of the effect is presented and found to be in good agreement with the obtained results. The relation between this novel time-domain interference effect and the pressure-induced extra resonance in four-wave mixing spectroscopy is discussed.
Dephasing-induced resonances, arising from interference between different excitation pathways, are well-known in frequency-domain spectroscopy.[1] It is generally thought that the time-domain analog of this phenomena is difficult to achieve due to the explicit time ordering of the interaction fields.[2,3] In this contribution we report on the observation of time-domain interference in phase-locked stimulated photon echo. We also show how complete control over the interference effect can be exercised.
Diagrammatic perturbation theory and the spherical tensor formalism are used to model the signal observed in time-resolved, two-colour resonant four-wave mixing (TC-RFWM). An analysis using the Liouville formalism illustrates how TC-RFWM can be used to perform state-selective quantum beat spectroscopy in three-level systems by suitably designing three experimental features: the excitation scheme for the matter-field interaction, the time ordering of the laser pulses and the polarization of the incident laser beams. In contrast to traditional fluorescence quantum beat spectroscopy, time-resolved TC-RFWM results in a background-free, coherent signal that allows for high-resolution detection of the spectrally unresolved energy structure within a selected material state of the three-level system. The beats are shown to result from the quantum interference between different Liouville-space pathways in the laser-induced evolution of the material density operator and appear as a temporal modulation in the amplitude of the light beam emerging as the output of the mixing process. This type of control of a coherent optical field, based on the selective preparation of superposition states, is reminiscent of other recently developed optical techniques such as coherent population trapping and lasing without inversion.
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.
Coherent signals induced by fundamentally incoherent phenomena through a four-wave mixing process are among the most intriguing and subtle effects in nonlinear spectroscopy. These effects were initially observed by Bloembergen and his co-workers in the form of pressure-induced extra resonances in four-wave mixing. Using standard perturbance techniques based on the optical Bloch equations, they suggested that these collision induced resonances were the result of a destruction of the destructive interference existent between two alternate time-ordered pathways. Subsequently, Prior et al realised that fluctuations in the incident radiation fields could play essentially the same role as the collisionally induced dephasing. In practice, of course, both collisional dephasing and field fluctuations are present in a typical atomic vapor pulsed four-wave mixing experiment. If the timescales governing these two effects approach one another, one can expect to gain valuable new insight into this fascinating process of incoherently inducing a coherent signal
The role of four-wave mixing (FWM) techniques in coherent control is considered from the point of view of some of the most important developments in this field over the past years, namely multiphoton excitation, pump-dump methods, interference between coherent pulses, chirped laser pulses, and optimal control. FWM techniques provide a powerful platform for combining coherently multiple laser pulses. We explore the effectiveness of these techniques in controlling chemical reactions. The phase relationship between the pulses is maintained by detecting the signal in a phase-matching direction. The results presented show control over the observed dynamics from ground and excited state populations. The FWM signal results from the polarization of the sample following three different electric field interactions. The virtual echo sequence is achieved by the interactions of the sample with three consecutive electric fields characterized by exp[i(kx-w t)], exp[-i(kx-w t)] and exp[i(kx-w t)]. This sequence allows control over the observed ground or excited state dynamics. With the photon echo pulse sequence, characterized by interactions with exp[-i(kx-w t)], exp[i(kx-w t)], and exp[i(kx-w t)], we find that control of ground and excited state populations is not achieved.