Transition from Non-Markovian to Markovian Dynamics in a Dense Potassium Vapor

We have observed non-Markovian dynamics in a dense potassium vapor, whose dephasing time is large compared to the collision duration $\tau_c$, allowing clear separation of time scales, using transient four-wave mixing with pulses short compared to all time scales. This is in contrast to molecular systems limited by ultrafast dephasing due to solvent motion [1]. For pulse delays $\tau<\tau_c$, dynamics are dominated by fluctuations of the transition frequency as the atoms form transient dimers (non-Markovian limit). For $\tau\gg\tau_c$, atomic motions make the system homogeneously broadened (Markovian limit). The theoretical TFWM signal is obtained for a 3-level system in the delta-function pulse limit via a perturbation expansion of the density matrix equations of motion, including non-Markovian dynamics through an assumed correlation function [2], $M_{ij}(t) = \Delta_{ij}\exp(-\Lambda_ {ij}t)$, where $i$ and $j$ are energy levels. Theory matches quite well with experimental results at both short (non- Markovian) and long (Markovian) time scales. [1] for a review see G. R. Fleming and M. Cho, ``Chromophore- solvent dynamics,'' Annu. Rev. Phys. Chem. \textbf{47}, 109-134 (1996). [2] S. Mukamel, \textit{Principles of Nonlinear Optical Spectroscopy}, Oxford Univ., NY (1995).