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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Selective probing of electronic and nuclear coherences using time-resolved off-resonant excitation of Raman-active vibration modes

E. Gaižauskas

Published May 1, 2013• 0 citations
Publisher

Abstract

In this presentation the underlying theoretical analysis of the four wave mixing (FWM) efficiency is given for the resembling experiment of three-level quantum system (TLQS), where the transition from |1> to |3> correspond to a Raman active vibration mode and is forbidden in the dipole approximation. In this case quantum state |3> (vibration mode) is excited by combined resonance and, subsequently, quantum state |2> is driven by a (delayed) weak field. Notable, that during off-resonance FWM experiments significant excited state probability amplitude and, consequently, FWM exists only as long as the perturbing fields overlap. Actually, in this presentation we discuss efficiency of the FWM process, which exist for long (as compared to the pump and probe pulses) times, and appears dependent on the both electronic and nuclear excitations, stored in the TLQS. The induced material variables (coherences and populations) in the TLS were considered by means of the density matrix, and in order to account for Raman transition |1> → |3> we used an approach closely related to that exploited previously. Considerable impact of the created in TLQS electronic and nuclear coherences on the frequency conversion for specific (negative and positive) time delays will be demonstrated.

DOI
10.1109/cleoe-iqec.2013.6801982

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In this presentation the underlying theoretical analysis of the four wave mixing (FWM) efficiency is given for the resembling experiment of three-level quantum system (TLQS), where the transition from |1> to |3> correspond to a Raman active vibration mode and is forbidden in the dipole approximation. In this case quantum state |3> (vibration mode) is excited by combined resonance and, subsequently, quantum state |2> is driven by a (delayed) weak field. Notable, that during off-resonance FWM experiments significant excited state probability amplitude and, consequently, FWM exists only as long as the perturbing fields overlap. Actually, in this presentation we discuss efficiency of the FWM process, which exist for long (as compared to the pump and probe pulses) times, and appears dependent on the both electronic and nuclear excitations, stored in the TLQS. The induced material variables (coherences and populations) in the TLS were considered by means of the density matrix, and in order to account for Raman transition |1> → |3> we used an approach closely related to that exploited previously. Considerable impact of the created in TLQS electronic and nuclear coherences on the frequency conversion for specific (negative and positive) time delays will be demonstrated.
The delayed or time-domain four-wave-mixing experiment is treated in the regime of intense near-resonant pulses. The interaction with the radiation during both pump and probe pulses is considered to all powers of the electric field amplitude. Analytical results are obtained for an effective four-level system. These include the dependence of the coherence amplitudes on the ratio of the pump-field intensities when there is a large vibrational discrepancy between ground and excited electronic states and a general solution for the unitary time development during the probe pulse. For the first time, delayed coherent anti-Stokes Raman scattering is detected from highly dilute (10-ppm) guest molecules. Illustrative examples are presented for the system of pentacene in benzoic acid at low temperature. Vibronic-free induction decay and the effect of field inhomogeneity across the beam profile are found to be essential for understanding the observed intensity and spectral distribution of the signal beam in the region of optimum pulse intensity.
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.
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 predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.
The influence of nonlinear interference processes and of changes in populations in strong electromagnetic fields, and also of the Doppler broadening on resonant four-wave frequency mixing is investigated for a system of Raman-type transitions. The case in which a quantum system interacts with one weak field and two strong fields is considered. Each of the energy levels is assumed to be perturbed by just one strong field. It is shown that the Doppler broadening alters drastically the contributions of the populations of the various levels to the investigated process and that this can alter by several orders of magnitude and nonlinear susceptibilities averaged over the velocities and influence significantly the selection of optimal configurations of the transitions and of the experimental conditions for effective resonant four-wave conversion of the radiation frequencies. A numerical analysis of the derived expressions is used to account for the experimentally observed considerable differences between the spectral dependences of the output power and the conclusions drawn from perturbation theory.
An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.