A theoretical study of the nonlinear polarization in a molecular medium is presented. It enables us to stress the importance and to evaluate the contribution of the population and orientational gratings in four-wave mixing depending on the pump- and probe-beam polarizations. The medium is described as an ensemble of two-level systems and is subject to rotational diffusion. The model is valid far or near resonance, as well. It is only assumed that time variation of the field envelopes and rotational diffusion constant are much smaller than the transverse decay rate ${\ensuremath{\Gamma}}_{2}$. The nonlinear polarization is expressed as a function of the field polarizations. The results are applied to a four-wave-mixing experiment to discuss the influence of the rotational diffusion. Finally, by including propagation effects, we use this formalism to calculate a phase-conjugated signal. This enables us to stress the influence of rotational diffusion to achieve time reversal of the envelope of a light pulse.
A comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments is presented. Signals in both the probe and conjugate directions are discussed. The effects of recombination, nonradiative scattering, and spatial and orientational diffusion are included. The analysis is applied to both a molecular and a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. From the solid-state point of view, we show that state-filling, and in particular, anisotropic state-filling, can be identified from the configurational and time dependence of the detected signal, and thereby establish a theoretical explanation for our recent observations in germanium.
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.
We present comprehensive determinations of the diffusion coefficients for rubidium atoms in six commonly used buffer gases using a newly developed coherent transient technique. The experiments are carried out by establishing a spatially periodic rubidium population grating using two laser beams intersecting at an angle of a few milliradians. The grating decays exponentially in time due to diffusive motion induced by momentum-changing elastic collisions with buffer gas atoms. The decay can be monitored over a large dynamic range using a heterodyne detection system that records the coherently scattered light from the grating. We are able to distinguish the contribution of diffusion from other collisional processes by measuring the characteristic dependence of the decay rate on the angle between excitation beams. These experiments are carried out in a non-magnetic atomic vapour cell manifold that allows magnetic fields and magnetic field gradients to be cancelled so that rubidium atoms can be manipulated in targeted internal ground states in the presence of different inert gases that can be maintained at pressures ranging from a few hundred pascals to one atmosphere. Our measurements agree with theoretical calculations of diffusion coefficients after reconciling key systematic effects, and this agreement appears to resolve both the widespread scatter in the values of diffusion coefficients using other techniques obtained over several decades and their disagreement with theory. Our measurements lay the groundwork for the development of a quantum pressure sensor that will rely on the intrinsic properties of atoms to calibrate commercial pressure gauges and impact emerging quantum technologies such as magnetometry, spin polarized imaging, and quantum memory that rely on accurate knowledge of diffusion coefficients. We also describe preliminary, comparative studies of a traditional population magnetometer and a unique coherence magnetometer developed by our group, which led to the development of the technique for measuring diffusion. All our experiments were carried out using a low-cost, home-built diode laser system. We present a detailed characterization of this system, which has supported wide-ranging experiments in precision metrology such as optical tweezers-based determination of micro-particle masses, measurements of atomic lifetimes, and atom interferometric measurements of velocity and gravitational acceleration.
This chapter is devoted to the description of the main methods employed in the investigation of optical transient processes in gas media and the apparatus used in these studies. Recently, a new direction of laser spectroscopy has appeared. This direction is based on several methods of extracting the information concerning a resonant medium, including: a ) analysis of decay curves for the intensities of optical coherent responses within certain time intervals; b) analysis of temperature lowering, i.e., the dependencies of the intensities of coherent responses on the temperature of a gas medium under study; c) investigation of the modulated structures of optical coherent responses related to the hyperfine coupling of unpaired electrons with nuclei of molecules or atoms in the gas (modulation coherent spectroscopy), including the regime of double resonances; d) polarization coherent spectroscopy associated with the identification of the type of the energy transition being studied and the determination of characteristics of this transition from the polarization properties of optical coherent responses; e) the method of optical “coherent averaging,” which is closely related to a multipulse excitation of gas particles and the regime of double resonances; and ƒ) the method of angular spectroscopy, which is based on the spatial features of the generation of optical coherent responses and superradiance.