Direct Laser Cooling to Bose-Einstein Condensation in a Dipole Trap

We present a method for producing three-dimensional Bose-Einstein condensates using only laser cooling. The phase transition to condensation is crossed with $2.5\times {10}^4$ ${}^{87}\mathrm{Rb}$ atoms at a temperature of $T_c=0.6\mu \mathrm{K}$ after 1.4 s of cooling. Atoms are trapped in a crossed optical dipole trap and cooled using Raman cooling with far-off-resonant optical pumping light to reduce atom loss and heating. The achieved temperatures are well below the effective recoil temperature. We find that during the final cooling stage at atomic densities above ${10}^{14}{\mathrm{cm}}^{-3}$, careful tuning of trap depth and optical-pumping rate is necessary to evade heating and loss mechanisms. The method may enable the fast production of quantum degenerate gases in a variety of systems including fermions.

Figure 1

(a) Geometry of the experimental setup with 795 nm optical pumping and Raman coupling beams, and 1064 nm trapping beams. (b) Molecular potentials. Light-assisted collisions are suppressed if the detuning from atomic resonance $\mathrm{\Delta }$ is chosen to be far from photoassociation resonances (solid red horizontal lines). (c) Partial atomic level scheme. The Raman transition is resonant for atoms with a two-photon Doppler shift ${\delta }_R$. (d) Velocity distribution of the atoms along the two-photon momentum $\hslash (\mathrm{\Delta }\mathbf{k})$. A Raman transition reduces the velocity of atoms in the velocity class ${\delta }_R/|\mathrm{\Delta }\mathbf{k}|$ by $\hslash (\mathrm{\Delta }\mathbf{k})/m$.

Figure 2

(a) Schematic of the trapping potential during the cooling sequence, along with the values of the trapping frequencies for each cooling stage. (b) Atomic temperature $T$ as a function of cooling time $t$. Discrete jumps are caused by changes of the trapping potential between the cooling stages. Inset: Temperature on a linear scale. (c) Atom number (open symbols) and condensate fraction $N_0/N$ (solid circles) during the cooling sequence. (d) Classical phase-space density ${\mathrm{PSD}}_c$ (see main text) as a function of cooling time $t$. The gray shaded area denotes the quantum degenerate region. Panels (b)–(d) are all plotted along the same time axis.

Figure 3

(a) Classical phase-space density ${\mathrm{PSD}}_c$ as a function of remaining atom number $N$. The cooling is very efficient until ${\mathrm{PSD}}_c\sim 1$ is reached. The black symbols denote the performance of the same sequence with the initial atom number reduced by a factor 5. The final atom number is only reduced by a factor 2, indicating a density limit in the cooling. The solid (dashed) black line indicates the $\mathrm{S}1\text{−}\mathrm{S}2$ ($\mathrm{S}1\text{−}\mathrm{X}3$) path with an efficiency $\gamma =7.2$ ($\gamma =11$) for each case. (b) Line optical density (dots) of the cloud in time of flight along the $y^{\prime }$ direction (slightly rotated from the $y$ direction in the $x\text{−}y$ plane, see Supplemental Material [27]). The data are taken after 1.6 s of cooling and fitted with a $g_{5/2}$ Bose distribution with a Thomas-Fermi distribution superimposed (orange line). The shaded area indicates the condensed fraction. (c) False-color image of the optical density (OD) of the same cloud (before integration along the vertical direction), showing the anisotropic expansion of the condensed fraction in the center.

Figure 4

(a) Photoassociation loss spectrum. Survival probability of trapped atoms as a function of the detuning $\mathrm{\Delta }$ of the optical pumping beam, when scattering $\sim 100$ photons. In substantial portions of the spectrum, the atomic loss is large, due to photoassociation resonances, whereas the peaks correspond to gaps in the photoassociation spectrum away from resonances. The green arrow indicates the detuning used for the data in Figs. 2 and 3. (b) Performance of the full cooling sequence as a function of optical pumping detuning $\mathrm{\Delta }$ near a locally optimal detuning. A condensate fraction $N_0/N$ is visible only when the losses are limited. To keep the Raman resonance detuning ${\delta }_R$ constant between data points, the magnetic field is adjusted to compensate the change in light shift associated with varying $\mathrm{\Delta }$. (c) Temperature and condensate fraction as a function of the scattering rate ${\mathrm{\Gamma }}_{\mathrm{sc}}$ in the final cooling stage. Here, the intensity of the $\pi$-polarized beam is adjusted to keep the Raman coupling strength constant between data points, and ${\delta }_R$ is adjusted to optimize the cooling performance for each data point.