We report enhanced three-dimensional degenerated Raman sideband cooling (3D DRSC) of caesium (Cs) atoms in a standard single-cell vapour-loading magneto-optical trap. Our improved scheme involves using a separate repumping laser and optimized lattice detuning. We load $1.5 times 10^7$ atoms into the Raman lattice with a detuning of -15.5 GHz (to the ground F = 3 state). Enhanced 3D DRSC is used to cool them from 60 $mu$K to 1.7 $mu$K within 12 ms and the number of obtained atoms is about $1.2 times 10^7$. A theoretical model is proposed to simulate the measured number of trapped atoms. The result shows good agreement with the experimental data. The technique paves the way for loading a large number of ultracold Cs atoms into a crossed dipole trap and efficient evaporative cooling in a single-cell system.
} In this article, we put forward a Neumann eigenvalue problem for the bi-harmonic operator $Delta^2$ on a bounded smooth domain $Om$ in the Euclidean $n$-space ${bf R}^n$ ($nge2$) and then prove that the corresponding first non-zero eigenvalue $Upsilon_1(Om)$ admits the isoperimetric inequality of Szego-Weinberger type: $Upsilon_1(Om)le Upsilon_1(B_{Om})$, where $B_{Om}$ is a ball in ${bf R}^n$ with the same volume of $Om$. The isoperimetric inequality of Szego-Weinberger type for the first nonzero Neumann eigenvalue of the even-multi-Laplacian operators $Delta^{2m}$ ($mge1$) on $Om$ is also exploited.
