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Journal of Physics B Atomic Molecular and Optical Physics

State-selective quantum beat spectroscopy via coherent control of Liouville-pathway interference in two-colour resonant four-wave mixing

Fabio Di Teodoro, Elizabeth F. McCormack

Published Sep 1, 1999• 9 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/18/301

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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 present a combined theoretical and experimental study of the effects of laser polarization on optical coherences produced in two-color, resonant four-wave mixing (TC-RFWM). A time-dependent model incorporating diagrammatic perturbation theory and spherical tensor formalism is used to interpret observations of quantum beats due to molecular hyperfine structure in time-resolved TC-RFWM in nitric oxide. Good agreement is found between the model and the observed time-resolved signals for two distinct excitation schemes and a variety of polarization configurations including both polarization and population gratings. Measured hyperfine energy intervals are reported for the $X{}^{2}{\ensuremath{\Pi}}_{1/2},$ v=0v=0v=0 ground state and the $A{}^{2}{\ensuremath{\Sigma}}^{+},$ v=0v=0v=0 excited state of NO. The experimental results demonstrate that 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.
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.
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.
Applying a recently developed ns Two-Colour Resonant Four-Wave Mixing (TC-RFWM) technique, a number of resonance lines forbidden by conventional three-level schemes are observed. A theoretical frequency-domain picture is developed with the help of exact (off-diagonal) relaxation matrices and general four-level schemes. The newly observed extra resonances are induced by collisional transfer of rotational energy. The role of the population, orientation and alignment gratings that are formed in both electronic states coupled by laser fields is elucidated. Relaxation models using the fast-collision approximation are elaborated for Hund's cases a and b giving quantitative arguments for the proposed interpretation. The potential of the TC-RFWM technique to study state-to-state transfer rates is emphasized.
A theory is developed and applied to the study of opportunities and specific features of coherent control of four-wave mixing as well as of the accompanying processes in the continuous-wave regime, which involve transitions between bound and free quantum states. Such opportunities become feasible through constructive and destructive interference of quantum pathways. Two coupling schemes of practical importance are investigated. In the first, a ladder energy level scheme, fully-resonant sum-frequency nonlinear-optical generation of short-wavelength radiation driven by several strong fields is investigated. The relaxation processes as well as absorption of the fundamental and generated radiations, which play an important role, are taken into consideration. It is shown that the generation output can be considerably increased through the appropriate adjustment of several laser-induced continuum structures. In the second, a folded scheme, a possible control of two-photon dissociation (Lambda-scheme) using auxiliary laser radiation applied to the adjacent bound-free transition (V-configuration) is investigated. Besides dissociation, the proposed method enables one to control population transfer between two upper discreet levels via the lower-energy dissociation continuum, while direct transition between these states is not allowed. The opportunities of manipulating these processes as well as of four-wave-mixing-based spectroscopy are explored both analytically and through a numerical simulation for Na_2 dimers.
The recent evolution toward resonant conditions of the two-color resonant four-wave-mixing (TC-RFWM) spectroscopy has been dictated by the high sensitivity required experimentally. While some models have been used in different contexts such as light pressure forces in strong polychromatic fields, magnetically assisted Sisyphus effect, or multiphoton resonances in \ensuremath{\Lambda} atoms, the existence in molecules of additional processes such as nonradiative transitions and rotational or vibrational dephasings requires the extension of previous models. For this reason, we give here a general description of the internal dynamics for a molecule undergoing two strong grating beams, acting either on two different transitions sharing a common level or on the same transition, and one weak probe beam to reproduce the ground-state grating and stimulated emission pumping configurations of TC-RFWM spectroscopy. By combining high spectral resolution and strong grating beams, we show that the TC-RFWM spectrum is very sensitive to the transition constants, dephasing constants, as well as to the transverse velocity of the molecules in the jet. The last case corresponding to a bichromatic field acting on a single transition is used to explain the origin of the line-shape asymmetry observed experimentally on jet-cooled molecules.