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.
It has been shown recently that molecular gas samples excited with coherent light can display a variety of transient phenomena, similar to those found in nuclear magnetic resonance. This article elucidates how these coherence effects can be used to isolate or unfold molecular collision mechanisms that normally remain hidden within the optical line shape. Elastic collisions, for example, are easily detected here in two-pulse photon echo experiments for a
13CH3F vibration-rotation transition. The echo-decay function which provides a signature for the velocity-changing collision diffusion mechanism, is not just a simple exponential in time but exhibits an $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ contribution for short times and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\Gamma}t)$ decay for long times. This behavior, which is unknown heretofore, contrasts with spin echoes in molecular liquids where Brownian motion leads only to the cubic decay law. An $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ behavior can be understood in terms of a solution of the Fokker-Planck equation which describes the effect of Brownian motion on echo decay. Such a treatment is valid for small phase excursions; in the case of a gas, this implies the Doppler phase factor $k\ensuremath{\Delta}u\ensuremath{\tau}\ensuremath{\ll}1$, where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ is the propagation vector of light, $\ensuremath{\Delta}u$ is a characteristic velocity jump for a binary collision, and $\ensuremath{\tau}$ is the echo-pulse delay time. When $k\ensuremath{\Delta}u\ensuremath{\tau}\ensuremath{\gg}1$ as in the long-time regime, the Fokker-Planck solution fails. We, therefore, present a new solution to the Boltzmann transport equation using a weak collision model and find agreement with the entire echo time dependence observed. The echo measurements indicate very small changes in longitudinal velocity per
13CH3F-
13CH3F collision, i.e., $\ensuremath{\Delta}u=85$ cm/sec, thereby justifying the weak-collision model. The total elastic collision cross section is 430
A˚2. It follows that elastic collisions lead to velocity thermalization in a time of \ensuremath{\sim}5 sec when the
13CH3F pressure is 1 mTorr. A comparison is also made of the
13CH3F dephasing time ${\ensuremath{\tau}}_{2}$ in a coherent Raman beat decay, which is independent of velocity-changing collisions, with the longitudinal decay time
T1. Here,
T1 represents the molecule-optical interaction time, due largely to jumps in molecular rotation (
J) and orientation (
M) state, and is obtained from a delayed nutation measurement. The fact that the pressure dependent part of ${\ensuremath{\tau}}_{2}={T}_{1}$ shows that
T1 is also independent of velocity diffusion. Futhermore, when a hole is burned in the Doppler distribution, population recovery must be due to inelastic rather than elastic collisions. Optical Carr-Purcell echoes, multiple pulse echoes, provide a direct measure of the
13CH3F transverse dephasing time
T2 without the effect of elastic collisions while being sensitive to "phase interrupting collisions." Again, we find that
T2=T1 so that phase interruptions are negligible. Had such a process dominated the two-pulse echo, an $\mathrm{exp}(\ensuremath{-}\frac{t}{{T}_{2}})$ damping would have been noticed with no $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ contribution. Thus, the present study covers several new aspects of molecular collisions. It represents the first detailed examination of velocity-changing collisions by coherence methods and without the complication of Doppler broadening.
This paper outlines new ways for separating the different channels of optical dephasing of molecules in beams. It is shown that both the population loss and the optical phase relaxation rates can be obtained under collisionless conditions (molecular beams). These dephasing rates, which measure directly the homogeneous width of the prepared resonance, can be obtained with an energy resolution of better than one part in 108. Under these conditions the solution of the density matrix equations of motion is given for effusive and nozzle beams which represent a statistically open ensemble. The results, which we applied to our recent measurements of optical T1 and T2, are discussed in different limits of power broadening, beam geometry, detector characteristics, temperature of the oven (or material container), and the transit time the molecules of different velocities spend in the laser beam. Furthermore, we indicate that the treatment of coherent transients in beams utilizing conventional Bloch equations is not valid since there is a loss of optically excited molecules. Finally, we discuss possible differences between small and large molecules when they undergo radiationless (or reactive) processes following the selective laser excitation (∼10 kHz–10 MHz).
Early in the study of nuclear magnetic resonance, it was recognized that coherent transient signals could possess shapes highly correlated with the radio frequency pulses used to generate them.1 Similar results were observed in the case of optical coherent transients.2 The information necessary to recreate the excitation pulse shapes has traditionally been seen to reside in the polarization of the sample or in the population difference between two energy states. Information so stored is constrained to relax at rates determined by the transverse T2 or the longitudinal T1, relaxation times of the excited nuclear or optical transition. Owing to the shortness of T1 and T2, coherent transient pulse shape storage has been viewed previously as having limited utility.
In this paper we describe a new technique for the generation of multiple pulse phase coherent sequences in optical spectroscopy. The technique is an extension of the acousto‐optic modulation and fluorescence detection methods developed for optical transitions by Zewail and Orlowski (Zewail et al., Chem. Phys. Lett.48, 256 (1977); Orlowski et al., Chem. Phys. Lett.54, 197 (1978)). Application of these multiple pulse trains (of different phases) to optical transitions of two‐level and multilevel systems is demonstrated experimentally. It is shown that they can be used to (i) suppress spontaneous emission background, (ii) enhance coherent transients such as photon echoes, (iii) measure additional relaxation parameters in systems with complex rotational‐vibrational levels, and (iv) enhance the effective laser bandwidths through composite pulse trains, as demonstrated on I2 gas. Finally, the potential of this development is extended to the possibility of observing selective multiquantum excitation in molecules.
Two different time-resolved spectroscopic techniques are discussed theoretically and demonstrated experimentally in dilute gases. The first technique involves extending the advantages of Stark-effect based time-resolved spectroscopy to non-polar molecules. This involves the development of a stable, TEM₀₀ mode, cw, CO₂ laser capable of switching rapidly and controllably between two frequencies. Design problems and output characteristics are discussed. The frequency switchable laser is applied to the CO₂ 10.6 μm P(16) coincidence with the non-polar molecule SF₆. The population relaxation time, T₁, is measured using two-pulse delayed nutation. The decay of induced dipoles is studied using the phenomenon of photon echoes. It is found that the echoes decay in a manner characteristic of dephasing dominated by velocity-changing collisions. A fit of the data to a model for such decays gives values of γ(ab) ≡ 1/T₂ (the non-velocity-changing contribution to the dipole decay rate), Γ(VC) (the total probability of a velocity-changing collision per unit time), and Δu which is related to the mean velocity change of SF₆ upon a velocity changing collision. A comparison with the published results of the similar Stark experiments on C¹³ H₃F are made. The second technique involves the development of an alternative to the pulsed excitation typically used in time-resolved T₁ studies. This involves inversion of a portion of the velocity distribution by adiabatic rapid passage (ARP) techniques. The center of this portion is then probed in the manner of previous delayed nutation experiments. The system preparation is shown theoretically to be different and simpler than the pulse case. In addition, ARP preparation gives a larger signal than two-pulse delayed nutation experiments. ARP experiments on N¹⁴H₃ and N¹⁵H₃ are described and compared to two-pulse delayed notation experiments. The single exponential decay best fits to the data from the two methods are found to be in agreement. We would expect the N¹⁵H₃ results to be very similar to the N¹⁴H₃ results, though reduced rotational resonance effects in its upper state should give it an overall slower decay. It is indeed found that the decay appears to be a simple exponential as did the N¹⁴H₃ data over the time range studied. The pressure dependent single exponential decay rate for N¹⁵H₃ is however roughly 45% larger than the rate for N¹⁴H₃ in the pressure range from 0.5 to 9 mTorr.