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Physical Review A

Polarization effects in quantum coherences probed by two-color, resonant four-wave mixing in the time domain

Elizabeth F. McCormack, Edina Sarajlic

Published Jan 16, 2001• 16 citations
Publisher

Abstract

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 $X{}^{2}{\ensuremath{\Pi}}_{1/2},$ $v=0$ ground state and the $A{}^{2}{\ensuremath{\Sigma}}^{+},$ $v=0$ 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.

DOI
10.1103/physreva.63.023406

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Polarization properties of pure four-wave mixing (FWM) and dressed-FWM processes in a two-level system and a cascade three-level atomic system are theoretically and experimentally investigated. The relative intensities and polarization characteristics of the FWM signals in different laser polarization configurations and different level systems are experimentally investigated and compared. Also, the results are theoretically explained by different transition paths combinations. In the dressed-FWM processes, we study the dependence of dressing effect on the incident field's polarization. The FWM signal generated by a linearly polarized pumping field is suppressed more by the dressing field than the one generated by a circularly polarized pumping field. However, an opposite effect was observed when the probe field's polarization is changed. The multidressing mechanisms are used to explain these effects. In addition, the interference and polarization dependence of the coexisting FWM signals in the same atomic system are discussed.

Journal of the Optical Society of America B•Aug 13, 2009•12 citations
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 X2\ensuremathΠ1/2,X{}^{2}{\ensuremath{\Pi}}_{1/2},X2\ensuremathΠ1/2​, v=0v=0v=0 ground state and the A2\ensuremathΣ+,A{}^{2}{\ensuremath{\Sigma}}^{+},A2\ensuremathΣ+, 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.
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.
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.
In degenerate four-wave-mixing (DFWM) experiments the polarization of the incident laser pulses can have a strong influence on the measured signal. For GaAs quantum wells a number of DFWM experiments were performed by using either parallel or perpendicular polarization of the incident laser pulses. Experimentally, it turned out that some characteristic features of the signal differ appreciably for the two configurations. In particular, different dephasing times, phase shifts of the quantum beats, different time-resolved behavior (echoes versus free-induction decay), and intensity dependence of the measured signal have been reported.1–3
In recent years, transient four-wave mixing (FWM) techniques have been used to investigate the dephasing times of non-equilibrium carriers in semiconductor heterostructures by monitoring the decay of the macroscopic polarization. Initially, this decay was measured by temporally-integrating the scattered FWM signal as a function of time delay between two (or more) pump pulses. More recently, the macroscopic polarization decay has been measured by time-resolving the FWM signal by cross correlating it with an ultrashort laser pulse via frequency up-conversion in a nonlinear crystal. When excitons with slightly different energies are excited, oscillations (or beats) have been observed both in the time-integrated FWM signal and in the time-resolved FWM signal. Such beats have been observed, for example, between light- and heavy-hole excitons and between excitons in wells of different widths. Both the spectral behavior1 of the time-integrated FWM signal and the temporal behavior2 of the time-resolved signal have been shown to allow the distinction between the polarization interference associated with two independent oscillators and the quantum beats associated with two coupled oscillators which share a common level. In addition, it has been demonstrated3 that the quantum beats produced by incident pulses with parallel polarizations are exactly out of phase (by π) with the beats produced by orthogonally polarized pulses. In each case1-3, the period and phase of the beats and the polarization of FWM signal were explained by using a six-level model, which excluded many-body effects, to describe the J=1/2 conduction and J=3/2 valence states. Within the last few months, however, it has been shown that a complete description of the polarization selection rules for the FWM signal requires excitation-induced dephasing4 or disorder-induced coupling of the σ + and σ – excitonic transitions5.
In this study, we extended the observation of the effect of the coherence of a laser field to four-wave mixing interactions in atomic media. These measurements will help us understand quantitatively recent techniques employing broad-band nanosecond laser pulses for measurements of sub-picosecond dipole relaxation lifetimes in a variety of media. The coherence of the laser field in this work is controlled using random phase/frequency modulation techniques, creating a field in the laboratory known as the phase diffusion field. The four-wave mixing signal is generated by an ensemble of two-level atoms (Na) interacting with degenerate broad-band, correlated, pump and probe fields. This two-level system is produced by optically pumping the sodium atoms into a single hyperfine component of the ground state. Data sets were taken without and with noise applied to the optical field. For the latter, we measured the dependence of the power of the four-wave mixing signal on the delay times between the pump and probe beams. These data sets were compared with the computer simulation results.
Polarization properties of pure four-wave mixing (FWM) and dressed-FWM processes in a two-level system and a cascade three-level atomic system are theoretically and experimentally investigated. The relative intensities and polarization characteristics of the FWM signals in different laser polarization configurations and different level systems are experimentally investigated and compared. Also, the results are theoretically explained by different transition paths combinations. In the dressed-FWM processes, we study the dependence of dressing effect on the incident field's polarization. The FWM signal generated by a linearly polarized pumping field is suppressed more by the dressing field than the one generated by a circularly polarized pumping field. However, an opposite effect was observed when the probe field's polarization is changed. The multidressing mechanisms are used to explain these effects. In addition, the interference and polarization dependence of the coexisting FWM signals in the same atomic system are discussed.