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Journal of the Optical Society of America B

There were no pi pulses in iodine vapor: crafted pulses to compensate for Rabi-frequency inhomogeneities

W. S. Warren, Luciano Mueller, J. L. Bates, Mark A. McCoy, M. Navratil

Published Apr 1, 1986• 31 citations
Publisher

Abstract

In molecular iodine, and most other gas-phase molecules as well, generation of a π/2 or π pulse is theoretically impossible. This result can be understood by analogy with microwave spectroscopy, since the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum F = J + I along the electric-field axis. The only solution is the generation of phase-modulated pulses that inherently compensate for Rabi-frequency inhomogeneity. We present theoretical and experimental evidence that crafted phase- and amplitude-modulated pulse shapes can excite a uniform, localized, and nearly complete inversion in nuclear magnetic resonance and laser spectroscopy.

DOI
10.1364/josab.3.000488

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In molecular iodine, and most other gas-phase molecules as well, generation of a π/2 or π pulse is theoretically impossible. This result can be understood by analogy with microwave spectroscopy, since the rotational contribution to the transition dipole moment is an explicit function of the projection of the total angular momentum F = J + I along the electric-field axis. The only solution is the generation of phase-modulated pulses that inherently compensate for Rabi-frequency inhomogeneity. We present theoretical and experimental evidence that crafted phase- and amplitude-modulated pulse shapes can excite a uniform, localized, and nearly complete inversion in nuclear magnetic resonance and laser spectroscopy.
We discuss experimental applications of specific phase and amplitude modulated laser pulse shapes. Electronic transitions in real molecules generally do not have a well-defined Rabi frequency because of the distribution of the orientation of the transition dipole, and because the density of states for all but the very simplest molecules causes many Doppler broadened transitions (including hyperfine components) to overlap. Crafted pulse shapes generate complete population inversions regardless of Rabi frequency, as well as provide a uniform inversion over the pulse bandwidth.1 These experiments directly observe population transfer between frequency ranges by giving two different frequency π pulses at different times—the use of crafted pulses increases signal to noise by now inverting the entire Rabi distribution. Experimental modifications which select a single velocity range in an arbitrarily complex molecule while retaining the other advantages of pulse shaping are presented, and the velocity dependence of fluorescence and coherence lifetimes in molecular gases is analyzed.2 Applications to monitoring velocity-changing collisional dynamics and generating large vibrational population inversions in l2 are presented, as will experimental methods to extend these sequences to more complex molecules, where velocity selection and frequency resolution are not equivalent.
We address the distinction between resonance Raman scattering and fluorescence as the excitation source is continuously tuned through resonance. The experiments are performed in iodine vapor using a cw laser, whose intensity is electrooptically modulated in the 0.1-50-MHz frequency range. A lock-in amplifier is used to detect both the in-phase and out-of-phase response of the emission. The modulated signal is found to be the sum of two components. One component varies with angular modulation frequency ω, as (1 + ω2τ2)-1/2, where τ is the lifetime of the excited state. The other is found to be flat within the range of modulation frequency used in the experiment. Since the results of the modulation experiment are the Fourier transform of the response to pulsed excitation, the first component corresponds to exponential decay with the fluorescence lifetime and the second corresponds to a prompt response. A density matrix calculation shows that the prompt response would be absent if the absorption were independent of laser frequency. It exists as a result of the finite inhomogeneous linewidth and the laser detuning from the center of the transition. The amplitude of the delayed and prompt components is a function of laser frequency. This gives a full description of the dynamical response to the emission to linear excitation as the laser is tuned continuously through resonance. The response of the sample to nonlinear excitation is also discussed.
Theoretical analysis leads us to the intriguing conclusion that nearly complete electronic population inversion of molecules can be achieved with intense positively chirped broadband laser pulses, as a combined result of vibrational coherence and adiabatic inversion. Strong field quantum calculations demonstrate inversion probabilities of up to 99%. The results are robust with respect to changes in light field parameters as well as to thermal and condensed phase conditions, are supported by experimental evidence, and have many potential applications in chemistry, biochemistry, biology, and physics.
Coherent, optically dressed media composed of two-level molecular systems without inversion symmetry are considered as all-optically tunable sources of coherent radiation in the microwave domain. A theoretical model and a numerical toolbox are developed to confirm the main finding: the generation of low-frequency radiation, and the buildup and propagation dynamics of such low-frequency signals in a medium of polar molecules in a gas phase. The physical mechanism of the signal generation relies on the permanent dipole moment characterizing systems without inversion symmetry. The molecules are polarized with a DC electric field yielding a permanent electric dipole moment in the laboratory frame; the direction and magnitude of the moment depend on the molecular state. As the system is resonantly driven, the dipole moment oscillates at the Rabi frequency and, hence, generates microwave radiation. We demonstrate the tuning capability of the output signal frequency with the drive amplitude and detuning. We find that even though decoherence mechanisms such as spontaneous emission may damp the output field, a scenario based on pulsed illumination yields a coherent, pulsed output of tunable temporal width. Finally, we discuss experimental scenarios exploiting rotational levels of gaseous ensembles of heteronuclear diatomic molecules.