Production of quantum-degenerate strontium gases

We report on an improved scheme to generate Bose-Einstein condensates (BECs) and degenerate Fermi gases of strontium. This scheme allows us to create quantum gases with higher atom number, a shorter time of the experimental cycle, or deeper quantum degeneracy than before. We create a BEC of ${}^{84}$Sr exceeding ${10}^7$ atoms, which is a 30-fold improvement over previously reported experiments. We increase the atom number of ${}^{86}$Sr BECs to $2.5\times {10}^4$ (a fivefold improvement) and refine the generation of attractively interacting ${}^{88}$Sr BECs. We present a scheme to generate ${}^{84}$Sr BECs with a cycle time of 2 s. We create deeply degenerate ${}^{87}$Sr Fermi gases with $T/T_F$ as low as 0.10(1), where the number of populated nuclear spin states can be set to any value between one and ten. Furthermore, we report on a total of five different double-degenerate Bose-Bose and Bose-Fermi mixtures. These studies prepare an excellent starting point for applications of strontium quantum gases anticipated in the near future.

Figure 1

Schematic illustration of the energy levels and transitions used for cooling and trapping Sr atoms. The blue MOT is operated on the strong ${}^1{S}_0$-${}^1{P}_1$ transition. The loading of the magnetic trap proceeds via the weak leak of the excited state (branching ratio 1:50 000) into the ${}^1{D}_2$ state, which itself decays with a 1:3 probability into the metastable ${}^3{P}_2$ state. Here the atoms can be magnetically trapped and accumulated for a long time, forming a reservoir. The transition ${}^3{P}_2$-${}^3{D}_2$ allows us to depopulate the metastable state by transferring the atoms into the ${}^3{P}_1$ state. The latter represents the excited state of the ${}^1{S}_0$-${}^3{P}_1$ intercombination line, used for narrow-line cooling in the red MOT.

Figure 2

Schematic view of the setup as seen from above (a) and from the side (b). Shown are the quadrupole field coils (light gray areas with dark gray outline), the MOT beams (rectangular blue areas), the elliptical horizontal and the circular vertical dipole trap beams (bow-tie-shaped red areas), and the direction of imaging, the ($\widehat{\mathbf{x}}\text{−}\widehat{\mathbf{y}}$) direction (open arrow). The horizontal dipole trap is elongated in the $x$ direction and quantum degenerate gases are created in the pancake-shaped crossing region of the two dipole trap beams. For clarity, only the focus of the horizontal (vertical) dipole trap beam is shown in the side (top) view.

Figure 3

Narrow-line MOTs of (a) the bosonic ${}^{88}$Sr and (b) the fermionic ${}^{87}$Sr isotopes, shown by in situ absorption images taken along the horizontal direction. In case (a), the MOT beams have a detuning of $-$50 kHz and a peak intensity of $I_{\mathrm{sat}}$. Gravity and laser-cooling forces balance each other on the surface of an ellipsoid, which has a vertical radius of $200\mu$m, giving rise to a pancake-shaped MOT. In the fermionic case (b), we operate at a detuning of about $-$20 kHz and an intensity equal to $I_{\mathrm{sat}}$ for both MOT frequency components. The atoms occupy the volume of an ellipsoid. In both cases, the magnetic field gradient is $\partial B/\partial z=1.15$ G/cm, the atom number $1.3\left(1\right)\times {10}^6$, and the temperature $\sim$700 nK. The white ellipses are a guide for the eye.

Figure 4

Generation of ${}^{84}$Sr BECs exceeding ${10}^7$ atoms. Panel (a) shows a series of absorption images (left) and density profiles (right) for different times along the evaporative cooling ramp. The density profiles are obtained from the absorption images by integration along the vertical direction. The black circles are data points, which are fitted with a bimodal distribution (solid red line), capturing the thermal fraction (dashed blue line) and the BEC. Panel (b) shows the evolution of the atom number in the thermal (black squares) and condensate fractions (red circles) during evaporation. The temperature of the thermal fraction is shown in (c).

Figure 5

Generation of ${}^{84}$Sr BECs with a short cycle time of the experimental sequence. Panel (a) shows a sketch of the experimental sequence. Absorption images taken after 22 ms free expansion and integrated density profiles show the appearance of an an almost pure BEC of ${10}^5$ atoms at the end of evaporation (b). Dashed blue lines indicate Gaussians, dotted green lines double-Gaussians, and solid red lines bi- and trimodal distributions; see the text for details. Panel (c) shows the development of the total atom number and of the temperature corresponding to the narrower of the two Gaussian distributions during evaporation.

Figure 6

Essentially pure BECs of (a) ${}^{86}$Sr and (b) ${}^{88}$Sr. The free expansion time is 25 ms for both images, and the geometric and color scales are identical. The BEC of ${}^{86}$Sr contains 25 000 atoms and expands to much larger size compared to the almost noninteracting BEC of ${}^{88}$Sr, which contains 5000 atoms.

Figure 7

Creation of double-degenerate Bose-Bose mixtures. The development of atom number (a) and temperature (b) during evaporation are shown for the mixture of ${}^{86}$Sr (black squares) and ${}^{88}$Sr (red circles). Despite a significant temperature difference at the start of evaporation, the sample thermalizes within 1 s. Below, we show absorption images of the mixtures ${}^{86}\mathrm{Sr}+{}^{88}\mathrm{Sr}$ (c) and ${}^{84}\mathrm{Sr}+{}^{86}\mathrm{Sr}$ (d), taken after 26 ms of free expansion. The BEC of ${}^{84}$Sr is nearly pure and contains $2\times {10}^6$ atoms. The other three BECs are accompanied by a significant amount of thermal gas. The insets show the optical density integrated along the vertical direction, with bimodal fits to the data. Imaging of ${}^{84}$Sr is performed with a detuning of $30$MHz, the other isotopes are imaged on resonance. The color scale of the ${}^{84}$Sr image differs from the color scale used for the other three images, but the integrated optical densities in the insets are to scale.

Figure 8

Detection of spin-state distribution using the optical Stern-Gerlach technique [45, 65]. Samples of ${}^{87}$Sr in a ten-state mixture or optically pumped into two or one spin states are shown.

Figure 9

Deeply degenerate Fermi gases of ${}^{87}$Sr in a balanced mixture of ten nuclear spin states. Panel (a) shows the azimuthally averaged density distribution of a degenerate Fermi gas at $T/T_F=0.08\left(1\right)$ after 25.4 ms of free expansion (black circles). The measurement is well described by a Fermi-Dirac distribution (red line) but not by a Gaussian (dashed blue line). The corresponding absorption image is shown in the inset. Panel (b) shows the evolution of the atom number per spin state and of the temperature during evaporation, derived from two-dimensional fits of Fermi-Dirac distributions to time-of-flight absorption images. Panel (c) shows the value of $T/T_F$ in dependence of atom number per spin state, derived from the fugacity (open circles) or calculated from the temperature, the atom number, and the trap oscillation frequencies (solid circles). Some data points have been taken multiple times (red circles with error bars) to determine the statistical uncertainty.

Figure 10

Double-degenerate Bose-Fermi mixtures. The two combinations shown here are ${}^{84}\mathrm{Sr}+{}^{87}\mathrm{Sr}$ (a) and ${}^{88}\mathrm{Sr}+{}^{87}\mathrm{Sr}$ (b), where all ten nuclear spin states of ${}^{87}$Sr are populated. The absorption images of the bosonic (left column) and fermionic isotopes (middle column) are taken after 25.4 ms of free expansion. The color and length scales are identical for all four images. Azimuthally integrated optical density distributions of the fermionic cloud are shown in the right column, together with Fermi-Dirac (solid red line) and Gaussian fits (dashed blue line).