Collisions of atoms in superpositions of dissimilar states have special significance in that, classically, each state follows a different trajectory. Hence the scattering of such a system as a unit has no classical analog and is of fundamental interest. We report studies of velocity-changing collision kernels in 174Yb for two types of superposition states: optical radiators, consisting of a ground S state and an excited P state, and P-state multipole moments, involving magnetic substate superpositions.
A measurement is reported of the velocity dependence of the total cross section for Yb optical radiator-Xe perturber collisions in which the active atom is in a superposition of dissimilar (
S and
P) states. The total cross section is found to vary with relative velocity in a simple manner, consistent with van der Waals scattering as the dominant interaction for this nonclassical system.
Photon-echo measurements in atomic Na perturbed by He provide the first demonstration of the contribution of velocity-changing-like effects to the transverse relaxation of atoms in superposition of two states even when the states follow different post-collision trajectories. The apparent anomaly that broadening cross sections derived from either absorption line widths or photon-echo relaxation measurements are smaller than the total cross section for scattering of atoms in either pure state is explained.
We present experiments which study velocity-changing collisions for
174Yb 3P1 atomic multipoles. New laser polarization-rotation-transient techniques are used to select anisotropic moments for which the velocity-changing collision kernel is diagonal. The results are compared to those obtained for the collisional evolution of the state populations, and demonstrate that wave mechanical effects play an important role in anisotropic-moment scattering.
Collisional processes occurring within an atomic vapor can be conveniently described in terms of collision kernels. The population kernel ${W}_{\mathrm{ii}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}})$ gives the probability density per unit time that an "active" atom in state
i undergoes a collision with a perturber that changes the active atom's velocity from ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}$ to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$. For active atoms in a linear superposition of states
i and
j, there is an analogous coherence kernel ${W}_{\mathrm{ij}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}}^{\ensuremath{'}}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}) (i\ensuremath{\ne}j)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\ensuremath{\rho}}_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states
i and
j differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states
i and
j. Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.
The collisional scattering of magnetically polarized atoms is of fundamental interest since the scattering process couples translational and internal degrees of freedom.1 Photon-echo techniques have recently been used to study this coupling by preparing active atoms in a superposition of magnetic sublevels and then quantitatively correlating collisional velocity changes with collisional depolarization.2–5 These experiments provide previously unmeasured information about the collision process. For example, they elucidate the differential relaxation experienced by different types of magnetic order (k-multipoles) and clarify the structure of polarization preserving collision kernels.