Toward Laser Cooling without Spontaneous Emission

The bichromatic force (BF) can be used for laser cooling in the absence of closed cycling transitions because it can cool without spontaneous emission\footnote{H. Metcalf, \textit{Phys. Rev. A} \textbf{77}, 061401 (2008).} (SE). Previous BF experiments have used transitions with long characteristic cooling times \mbox{$\tau_c = \Delta p/F \sim \pi /4 \omega_r$} thereby allowing many SE events. We are building an experiment using the $2^3S_1 \rightarrow 3^3P_2$ transition at $\lambda$ = 389 nm in He because its large recoil frequency $\omega_r = 2 \pi \times 330$ kHz makes $\tau_c$ comparable to the $3^3P_2$ lifetime $\sim$100 ns so that there would be minimal SE events during $\tau_c$. We will describe our experiment as well as studies of the density matrix solutions for the force integrated over short interaction times accounting for atomic velocity changes. These solutions are used for Monte Carlo simulations of experimental conditions incorporating He beam trajectories and velocity distributions.