Sub-Doppler cooling in reduced-period optical lattice geometries

It is shown that sub-Doppler cooling occurs in an atom-field geometry that can lead to reduced-period optical lattices. Four optical fields are combined to produce a “standing wave” Raman field that drives transitions between two ground state sublevels. In contrast to conventional Sisyphus cooling, sub-Doppler cooling to zero velocity occurs when all fields are polarized in the same direction. Solutions are obtained using both semiclassical and quantum Monte Carlo methods in the case of exact two-photon resonance. The connection of the results with conventional Sisyphus cooling is established using a dressed state basis.

Figure 1

(Color online) Atom-field geometry that can be used to create a two-photon, standing wave Raman field on the 1-2 transition.

Figure 2

(Color online) Momentum distribution, $S\left(\overline{p}\right)$, as a function of $I={\chi }^2∕\left(\Delta {\omega }_r\right)$ for $\sigma =\Delta ∕\Gamma =10$.

Figure 3

(Color online) Dimensionless steady-state kinetic energy obtained using QMCWF simulations (symbols with error bars) and semiclassical calculations (lines) as a function of dimensionless intensity $I={\chi }^2∕\Delta {\omega }_r$ for $\sigma =2,16$.

Figure 4

Graphs of the momentum distribution, $S\left(\overline{p}\right)$, multiplied by ${\overline{p}}^2$ for $\sigma =8$ and several values of $I:I=3.11$, solid line; $I=8.4$, dashed line; $I=50$, dotted line; lines, semiclassical theory; lines with circles, QMCWF.

Figure 5

(Color online) Dimensionless cooling rate vs ${\Gamma }^{\prime }∕\Gamma$ for several values of $\sigma$. The dashed line shows a quadratic fit to the data for $\sigma =16$.

Figure 6

(Color online) Modulation depth of the density distribution of the atoms in the lattice wells vs $I$ for several values of $\sigma$.

Figure 7

(Color online) Graphs of the dressed-state optical potentials (a) and the modified dressed state potentials (b). Solid line, ${\lambda }_{+}$; dashed line, ${\lambda }_{-}$.