The Bichromatic Force for Laser Cooling Without Spontaneous Emission

The bichromatic force ($F_b$) can produce laser cooling without relying on spontaneous emission (SpE).\footnote{H. Metcalf, Phys. Rev. A {\bf77}, 061401 (2008).} It is implemented with two laser frequencies $\omega_\ell =\omega_a\pm\delta$ where $\omega_a$ is the atomic transition frequency and $\delta$ is a detuning, $\delta\gg\gamma =1/\tau$ where $\tau$ is the excited atomic state lifetime. This produces multiple absorption-stimulated emission cycles to cause many momentum exchanges on a timescale faster than $\tau$. The resulting magnitude of $F_b=2\hbar k\delta /\pi$ is much larger than the radiative optical force ($\hbar k\gamma/2$) and spans a much larger velocity range ($\Delta v_b=\delta /2k$). Previous measurements have demonstrated $F_b$ over time scales that included many SpE events.\footnote{M. Partlow et al., Phys. Rev. Lett. {\bf93}, 213004 (2004).} We have made measurements with a $F_b$ cooling time ($M\Delta v_b/F_b$) that is on the order of $\tau$, thus having zero or at most one SpE during the experimental interaction time. Our intensity dependent studies show the atomic velocities changing over a range of many atomic recoils and accumulating at the edge of the $F_b$ velocity profile, and we have developed numerical simulations that corroborate these results.