Figure 1

Plots of the hybrid magnetic-optical trap. Atoms are trapped at the focus of a laser beam propagating in the $z$ (axial) direction. The laser wavelength is $1.08\mu \mathrm{m}$ and the beam is focused with a Gaussian beam waist ($1/e^2$ radius) of $30\mu \mathrm{m}$. A residual magnetic curvature contributes to the axial confinement with a harmonic frequency of 3.8 Hz. (a)–(c) Optical trap depth $U=1.68\mu \mathrm{K}$, corresponding to $t=700\mathrm{ms}$ for the 1 s evaporation trajectory. $U_g$ is the effective trap depth accounting for gravity. The relative contribution of the magnetic curvature and gravity are small. (d)–(f) Potential at the final optical trap depth $U_f=0.74\mu \mathrm{K}$ at $t=1\mathrm{s}$, where the relatively strong magnetic curvature has the effect of opening up a lip at $z=0$. At this trap depth, the combined axial frequency, due to the optical and magnetic forces, is 4.7 Hz. Values of $k_B{T}_F$ from Fig. 3a are indicated by the horizontal blue lines.Reuse & Permissions

Figure 2

Axial densities taken at various times $t$ along the evaporation trajectory. The global polarizations $P$ are (a) 600 ms, $P=0.14$, (b) 700 ms, $P=0.21$, (c) 740 ms, $P=0.28$, (d) 1 s, $P=0.18$. The variation in $P$ is a result of shot-to-shot variations, as each image requires the trap to be reloaded and evaporated to the specified $t$. The upper (black) curves correspond to the majority state ($|\uparrow ⟩$), the middle (blue) curves to the minority state ($|\downarrow ⟩$), and the axial spin densities ($|\uparrow ⟩-|\downarrow ⟩$) are given by the lower (red) curves.Reuse & Permissions

Figure 3

Parameters extracted from the axial densities for both the (aggressive) 1 s and (gentle) 3.4 s trajectories. $T$ is determined from the mean energy $E$ of unpolarized ($P=0$) distributions which are separately evaporated using the same trajectory. $E$ for each distribution is obtained from its mean-squared radius via the virial theorem [27]. The $E$ vs $T$ calibration is given in Ref. 28 and is based on the experimental data of Ref. 29. $\eta =(U_g-{ϵ}_p)/k_{B}T$, where ${ϵ}_p=\frac{1}{2}m{\omega }_z^2{R}^2$, ${\omega }_z$ is the axial trap frequency, and $R$ is the axial radius where the density of the majority state ($\uparrow$) goes to zero. The deformation parameter is defined as $\alpha =n_v/n_p$, as depicted in Fig. 2c. The error bars are mainly statistical uncertainty from the average of $\sim 6$ shots of various values of $P$ at each value of $t$. The vertical dashed line in (d) indicates the onset of deformation.Reuse & Permissions

Figure 4

Axial densities for the 3.4 s trajectory at $t=3.4\mathrm{s}$, with $P=0.24$. Curve designations are the same as in Fig. 2. The dashed vertical lines indicate the location of phase boundaries. The flattopped axial spin density is consistent with the LDA, even though the aspect ratio of the trap potential is $\sim 96$.Reuse & Permissions

Figure 5

Recompression of the trap following the 1 s evaporation. Here, the 1 s evaporation finishes at $t=0$ and is followed by a slow recompression of the trap over the next 0.6 s. Even though the final value of $U_g$ is similar to that shown for the 3.4 s trajectory in Fig. 3, the recompressed values of $T_F$ are lower due to smaller overall numbers ($\sim 3\times {10}^4$ vs $\sim {10}^5$).Reuse & Permissions

Figure 6

Column density images for an axial displacement of the center of magnetic curvature located at $z_m=0$ and indicated by the dotted vertical line, from the focus of the optical trap beam located at $z=-1\mathrm{mm}$. At this trap depth ($U=0.65\mu \mathrm{K}$), the center of the combined potential, indicated by the dashed vertical line, is located at $z_0=-210\mu \mathrm{m}$. The trap beam waist is $26\mu \mathrm{m}$ and the residual magnetic curvature is 6.4 Hz for these data. The image size is $1653\mu \mathrm{m}\times 100\mu \mathrm{m}$ and $P=0.63$. The uncertainty in $z_0$ and $z_m$ is $20\mu \mathrm{m}$ due to uncertainties in the optical trap parameters.Reuse & Permissions