All-optical production of a large Bose-Einstein condensate in a double compressible crossed dipole trap

We report on an all-optical production of a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate (BEC) of ${10}^6$ atoms. We construct a double compressible crossed dipole trap (DCDT) formed by a high-power multimode fiber laser (MCDT) and a single-mode fiber amplifier (SCDT), which are both operated at $1.06\mu \mathrm{m}$. A very cold dense gas is first cooled by polarization gradient cooling in a three-dimensional optical lattice. More than $2\times {10}^7$ atoms are loaded into the enlarged DCDT. Both CDTs are then simultaneously compressed to significantly different sizes followed by evaporation, which is performed by lowering only the MCDT power. The tighter SCDT produces an extremely high collision rate and maintains the trap stiffness, which leads to rapid and efficient evaporation. After 0.4 s, a gas of $5\times {10}^6$ atoms with a phase-space density of 0.2 is confined within the SCDT alone. Further evaporation in 2.8 s yields a nearly pure BEC of $1.2\times {10}^6$ atoms in the $|F{m}_F\rangle =|11\rangle$ state. This number is the largest generated among all-optical methods. Our approach significantly improves the atom number of a condensate and circumvents the severe atom loss previously reported for multimode fiber lasers.

Figure 1

Schematic configuration of the DCDT. AOM1 and AOM2 control each trap depth and AOM3 creates two separate beams of the SCDT with 80 MHz offset. Three lenses LS1, LS2, and LM1 and their corresponding pairs on a motorized stage form 1:3.3 telescopes, respectively. Here HWP denotes a half waveplate. The side view imaging system is composed of a pair of $f=150\mathrm{mm}$ achromatic lenses with a 50 mm diameter. The top view imaging system is not shown.

Figure 2

Transverse beam radii ($1/e^2$ radii) of the MCDT (red squares) and SCDT (orange circles) at the crossing point as functions of the stage positions. For convenience, the location to minimize the SCDT is defined as zero. The vertical radii have similar dependences, but due to astigmatism, each curve is slightly shifted. The uncertainty of the radius is $\pm 5\%$.

Figure 3

Loss and heating in the compressed MCDT: (a) atom number, (b) temperature evolution, and (c) decay rate. In (a) and (b) the beam radii are $250\mu \mathrm{m}$ (circles), $190\mu \mathrm{m}$ (diamonds), $160\mu \mathrm{m}$ (squares), $130\mu \mathrm{m}$ (up triangles), and $100\mu \mathrm{m}$ (down triangles). The peak intensity is for one beam. The decay curves are fits of the number data to a sum of two exponentials. Interpolated dashed lines in (b) are simply guides for the eye. In (c) the decay rate is the longer time constant of the fitted curves in (a). At $\sim 20\mathrm{kW}/{\mathrm{cm}}^2$ (vertical dashed line), the rate suddenly changes by a factor of 2. The decay rates in the DCDT are also shown by solid circles as functions of the MCDT peak intensity. The definition of the decay rate is the same as that of the MCDT, except for the right end data, which is given by a single exponential fit.

Figure 4

Effective trap depths for $\gamma =\pm 1$ states (blue solid line) and the $\gamma =+2$ state (green dashed line) as functions of the radius. The measured temperatures are those at the 300-ms hold time and shown by red circles (with a line as a guide). The inset shows the potential curves of the MCDT along the $z$ direction for $w_r=160\mu \mathrm{m}$ (the stage position equals 0). Here the $\gamma =+1$ state is shown by the thin blue line, the $\gamma =+2$ state by the thin dashed green line, and the $\gamma =0$ state by the thick black line. The position-independent energy offsets are subtracted.

Figure 5

In situ fluorescence image (top view) at the initial loading. The image is taken after 300 ms holding in the DCDT by using a high-intensity fluorescence probe [26]. Trapping beams are represented by dashed lines.

Figure 6

Radial trapping potentials of a DCDT (black solid line), MCDT (red dashed line), and SCDT (orange dotted line). Both CDTs are assumed to be axially symmetric (a) at initial loading and (b) after compression.

Figure 7

(a) Progress of phase-space density: phase-space density (closed circles) and atom number (closed squares). The left end data are at the initial loading. (b) Time evolution of truncation parameters ${\beta }_d=U_d/k_{B}T$ and ${\beta }_s=U_s/k_{B}T$. Here $U_d=U_s$ after turning off the MCDT. (c) Calculated collision rates ${\mathrm{\Gamma }}_{\mathrm{col}}$ in the DCDT (closed circles) and ${\mathrm{\Gamma }}_{\mathrm{col}}$ in the MCDT at the initial loading and after the compression to $160\mu \mathrm{m}$ are also shown (open squares). The collision rates are calculated as ${\mathrm{\Gamma }}_{\mathrm{col}}=n{v}_{th}8\pi a^2$, where $n$ is the peak density, $v_{th}=\sqrt{3k_{B}T/m}$ is the thermal velocity, and $a=5.3$ nm is the scattering length of ${}^{87}\mathrm{Rb}$.

Figure 8

Optical density profiles and absorption images at the last three stages of evaporation: (a) after the fourth evaporation, just before the BEC transition ($N=2.5\times {10}^6$ and $T=940$ nK); (b) after the fifth evaporation, bimodal density profile with $35\%$ condensation ($N=1.8\times {10}^6$ and $T=390$ nK); and (c) after the final evaporation, almost pure condensation ($N=1.2\times {10}^6$). Images are taken after a 40-ms time of flight. A ${}^{87}\mathrm{Rb}$ BEC is created in the $|F{m}_F\rangle =|11\rangle$ state.