All-optical cooling of ${}^{39}\mathrm{K}$ to Bose-Einstein condensation

We report the all-optical production of Bose-Einstein condensates (BEC) of ${}^{39}\mathrm{K}$ atoms. We directly load $3\times {10}^7$ atoms in a large volume optical dipole trap from gray molasses on the D1 transition. We then apply a small magnetic quadrupole field to polarize the sample before transferring the atoms in a tightly confining optical trap. Evaporative cooling is finally performed close to a Feshbach resonance to enhance the scattering length. Our setup allows one to cross the BEC threshold with $3\times {10}^5$ atoms every 7 s. As an illustration of the interest of the tunability of the interactions we study the expansion of Bose-Einstein condensates in the one-dimensional to three-dimensional crossover.

Figure 1

Sample polarization procedure in a quadrupole field. Each Zeeman sublevel (represented with different colors) experiences a different longitudinal potential. It is a confining potential only for the $m_F=-1$ (plain black line). The two others are repulsive and given by the second order Zeeman shift for the $m_F=0$ (dashed blue line), and by the first order Zeeman shift for the $m_F=+1$ (dash-dotted orange line).

Figure 2

Power reduction during the evaporation process of the large beam (orange circles) and of the tightly confining one (blue triangles). During the first part of the evaporation the atoms mainly see the second (confining) trap. Indeed $k_{B}T\gtrsim U_1$ where $U_1$ is the depth of the large beam. The potential is changed by reducing the power of the confining beam and the atoms enter the crossed region when $k_{B}T\lesssim U_1$. The large beam then determines the longitudinal frequency. The crossover between the two trapping regimes is shown by a dashed line. The powers of both beams are reduced together during the remaining part of the evaporation.

Figure 3

Phase space density $D$ (orange circles) and two-body collision rate $\Gamma$ (blue triangles) during the evaporation process as functions of the atom number. The corresponding average efficiency is $\varrho \sim 3$. The dashed line represents the stage at which the atoms enter the crossed region of the traps as explained in Fig. 2.

Figure 4

Radial Thomas Fermi radius after 34.5 ms of expansion as a function of $N_{c}a$, where $N_c$ is the number of condensed atoms. The theoretical curve (continuous blue line) corresponds to the size given by an approximate theory in the 1D to 3D crossover. The blue dashed line corresponds to the Thomas-Fermi model in 3D which does not match our data.