Quantum degenerate mixtures of Cs and Yb

We report the production of quantum degenerate Bose-Bose mixtures of Cs and Yb with both attractive ($\mathrm{Cs}+{}^{174}\mathrm{Yb}$) and repulsive ($\mathrm{Cs}+{}^{170}\mathrm{Yb}$) interspecies interactions. Dual-species evaporation is performed in a bichromatic optical dipole trap that combines light at 1070 nm and 532 nm to enable control of the relative trap depths for Cs and Yb. Maintaining a trap which is shallower for Yb throughout the evaporation leads to highly efficient sympathetic cooling of Cs for both isotopic combinations at magnetic fields close to the Efimov minimum in the Cs three-body recombination rate at around 22 G. For $\mathrm{Cs}+{}^{174}\mathrm{Yb}$, we produce quantum mixtures with typical atom numbers of $N_{\mathrm{Yb}}\sim 5\times {10}^4$ and $N_{\mathrm{Cs}}\sim 5\times {10}^3$. We find that the attractive interspecies interaction (characterized by the scattering length $a_{\mathrm{CsYb}}=-75a_0$) is stabilized by the repulsive intraspecies interactions. For $\mathrm{Cs}+{}^{170}\mathrm{Yb}$, we produce quantum mixtures with typical atom numbers of $N_{\mathrm{Yb}}\sim 4\times {10}^4$ and $N_{\mathrm{Cs}}\sim 1\times {10}^4$. Here, the repulsive interspecies interaction ($a_{\mathrm{CsYb}}=96a_0$) can overwhelm the intraspecies interactions, such that the mixture sits in a region of partial miscibility.

Figure 1

Balanced trapping potentials for Cs and Yb. (a) Atomic polarizability versus wavelength for Cs (red) and Yb (green). For reference, vertical lines are placed at 532 nm (dashed) and 1070 nm (dotted), the wavelengths of the bichromatic optical dipole trap (BODT) beams. The polarizability of Cs (Yb) is $-211a_0^3$ ($264a_0^3$) at 532 nm and $1142a_0^3$ ($160a_0^3$) at 1070 nm. (b) and (c) Cross sections of a representative balanced trapping potential formed from the sum of the 532 nm (dashed) and 1070 nm (dotted) potentials for Cs and Yb, respectively. Both beams have $1/e^2$ waists of $w_0=50\mu \mathrm{m}$ and the powers are $P_{532}=1\mathrm{W}$ and $P_{1070}=0.5\mathrm{W}$.

Figure 2

Optical beam layout for the bichromatic optical dipole trap (BODT) overlaid on top of a vertical view of all beam paths traveling through the science chamber. The BODT consists of a $532\mathrm{nm}$ beam copropagating with a $1070\mathrm{nm}$ beam (DB1), which are arranged at a ${40}^{\circ }$ angle to the second $1070\mathrm{nm}$ beam (DB2). We define the coordinate system ($x,y,z$) with $x$ along the copropagating beams, $y$ perpendicular to $x$ in the horizontal plane, and $z$ the vertical direction. The Cs (Yb) imaging axes are rotated ${35}^{\circ }$ (${25}^{\circ }$) from the $y$ axis.

Figure 3

Timing sequence for Cs and Yb preparation in the bichromatic optical dipole trap (BODT). Yb is loaded in a magneto-optical trap (MOT) which is then compressed (CMOT) and loaded into the BODT. The Yb MOT operates on the ${}^{1}S_0$ to ${}^{3}P_1$ transition at 556 nm; linewidth ${\mathrm{\Gamma }}_{\mathrm{Yb}}/2\pi =182.2\mathrm{kHz}$ and saturation intensity ${\mathrm{I}}_{\mathrm{Sat}}^{\mathrm{Yb}}=0.139\mathrm{mW}{\mathrm{cm}}^{-2}$. Yb undergoes an initial 3.1 s of forced evaporation. Cs is then loaded in a MOT and compressed (CMOT), followed by optical molasses, and degenerate Raman sideband cooling (DRSC). The Cs MOT operates on the ${}^{2}S_{1/2}$ to ${}^{2}P_{3/2}$ transition at 852 nm; ${\mathrm{\Gamma }}_{\mathrm{Cs}}/2\pi =5.23\mathrm{MHz}$ and ${\mathrm{I}}_{\mathrm{Sat}}^{\mathrm{Cs}}=1.105\mathrm{mW}{\mathrm{cm}}^{-2}$. The MOT cooling beams are detuned from the $F=4$ to $F^{\prime }=5$ transition as shown, and the MOT repump beams are detuned from the $F=3$ to $F^{\prime }=4$ transition by a constant $-5.4$ MHz. The DRSC lattice beams are resonant with the $F=4$ to $F^{\prime }=4$ transition. After DRSC, Cs is loaded into a hybrid optical and magnetic reservoir trap, and from there atoms are loaded into the BODT. The BODT consists of two 1070 nm dimple beams (DB1 and DB2), and one $532\mathrm{nm}$ beam. DB1's horizontal waist is controlled by dithering the frequency of the AOM used to servo DB1's power, with a range of 35 to $68\mu \mathrm{m}$. DB1's vertical waist is 29(2)$\mu \mathrm{m}$. The beam waists of DB2 and the $532\mathrm{nm}$ beam are 70(4)$\mu \mathrm{m}$ and 50(3)$\mu \mathrm{m}$, respectively. To reduce heating of Cs during the reservoir load, we use slightly lower powers of DB1 (0.2 W) and DB2 (0.37 W) during the Cs MOT and reservoir load compared to the final powers for the Cs BODT load.

Figure 4

Optimal atom cloud overlap indicated by increased thermalization as a function of the 532 nm beam displacement measured with a quadrant photodiode (QPD). (a) and (b) The Cs (red circles) and Yb (green squares) temperatures versus beam displacement for (a) horizontal displacement $\mathrm{\Delta }y$, and (b) vertical displacement $\mathrm{\Delta }z$. We define zero to be the beam position corresponding to the minimum temperature for the Cs atoms. Solid lines are Lorentzian fits to the temperature data. (c) and (d) The Cs (red circles) and Yb (green squares) atom numbers versus beam displacement. Gray shading corresponds to the regions where the atoms are in good thermal contact $T_{\mathrm{Cs}}\sim T_{\mathrm{Yb}}$.

Figure 5

Evaporation of Cs and ${}^{174}\mathrm{Yb}$ to dual degeneracy in the bichromatic optical dipole trap (BODT). (a) Temperature versus time during the initial evaporation of the Yb sample (i), preparation of the Cs sample (ii), and subsequent dual-species evaporation sequence (iii). Open (filled) green squares denote ${}^{174}\mathrm{Yb}$ before (after) loading Cs into the BODT. Red circles denote Cs. Inset shows phase-space density (PSD) as a function of atom number. In the absence of Cs, the Yb efficiency is ${\gamma }_{\mathrm{Yb}}=3.0\left(6\right)$ (fit to open green squares shown by the dashed green line). The solid red line, with $\gamma =6$, and solid green line connecting the Yb data points are guides to the eye for the dual evaporation of Cs and Yb. Arrows denote initial dual-evaporation measurement at $t=0$ s, which occurs pre-thermalization. (b) and (c) Cross sections through the center of the optical depth (OD) images (inset) for the ${}^{174}\mathrm{Yb}$ and Cs BECs, respectively. Solid lines are a bimodal fit to the 1D OD cuts. Dashed lines show the Gaussian fit to the thermal contribution. Condensate atom numbers extracted from the fits are $N_{\mathrm{Yb}}=6\times {10}^4$ and $N_{\mathrm{Cs}}=1.6\times {10}^4$ with an Yb (Cs) condensate fraction of 0.5 (0.4).

Figure 6

Timing sequence for dual-species evaporation in the bichromatic optical dipole trap (BODT). Forced evaporation of Yb is used to sympathetically cool Cs, resulting in dual degeneracy. (a) Beam powers for dimple beam 1 (DB1, dotted red line), dimple beam 2 (DB2, solid red line), and the $532\mathrm{nm}$ beam (dashed green line). (b) Geometric mean trap frequencies for Cs (solid red line) and Yb (dashed green line). (c) Trap depths for Cs (solid red line) and Yb (dashed green line). Trap depths include tilting of the trap due to gravity.

Figure 7

Lifetime of dual-degenerate Cs-${}^{174}\mathrm{Yb}$ mixture in the bichromatic optical dipole trap (BODT). Plot shows Cs (red circles) and Yb (green squares) atom numbers versus hold time after the final dual-species evaporation ramp. Fit to Cs data points (solid red line) is a double exponential with offset with ${\tau }_{\mathrm{Cs},1}=0.5\left(1\right)$ s and ${\tau }_{\mathrm{Cs},2}=5\left(4\right)$ s. After 1 s of hold time Cs is no longer a BEC. Fit to Yb data points (dashed green line) is a single exponential with ${\tau }_{\mathrm{Yb}}=5\left(1\right)$ s. Early data points $t<1.2$ s are excluded from the fit to the Yb data.

Figure 8

Evaporation of Cs and ${}^{170}\mathrm{Yb}$ to dual degeneracy in the bichromatic optical dipole trap (BODT). Temperature versus time during the initial evaporation of the Yb sample (i), preparation of the Cs sample (ii), and subsequent dual-species evaporation sequence (iii). Open (filled) green squares denote ${}^{170}\mathrm{Yb}$ before (after) loading Cs into the BODT. Red circles denote Cs. Inset shows phase-space density (PSD) as a function of atom number. Fits to PSD data give a Cs evaporation efficiency of ${\gamma }_{\mathrm{Cs}}=7.7\left(6\right)$, Yb efficiency of ${\gamma }_{\mathrm{Yb}}=1.6\left(2\right)$ with Cs present, and an Yb efficiency of ${\gamma }_{\mathrm{Yb}}=1.6\left(5\right)$ with Cs absent.

Figure 9

Number-dependent immiscibility in a dual-degenerate mixture of Cs and ${}^{170}\mathrm{Yb}$. (a) Optical depth (OD) profiles showing ${}^{170}\mathrm{Yb}$ (top row) and Cs (middle row). OD profiles are extracted from absorption images taken after 20 ms time-of-flight expansion. The bottom row shows horizontal cross sections through the center of the OD profiles (averaged over a range of 6 pixels centered on $\mathrm{\Delta }z=0$) for Cs (solid red lines) and Yb (dashed green lines). We have independently centered each image, using a Gaussian fit to the atom cloud. From left to right the atom number ratios are $N_{\mathrm{Yb}}/N_{\mathrm{Cs}}=0.7$, $N_{\mathrm{Yb}}/N_{\mathrm{Cs}}=1.9$, and $N_{\mathrm{Yb}}/N_{\mathrm{Cs}}=4.7$, with $N_{\mathrm{Cs}}=5.5\times {10}^3$ for all three images. Scattering lengths are $a_{\mathrm{Yb}}=64a_0$, $a_{\mathrm{Cs}}=440a_0$, and $a_{\mathrm{CsYb}}=96a_0$. Note that the condensates shown in the two rightmost columns are partially immiscible which is observable in the distortions of the Cs OD profile. The slight asymmetry observed in the rightmost Cs profile is due to a small misalignment in horizontal trap centers. (b) Ground state profiles for Cs (red: double lobed) and Yb (green: cigar shaped) calculated using imaginary-time propagation of the coupled Gross-Pitaevskii equations. The choice of atom number $N_{\mathrm{Yb}}=2.6\times {10}^4$, $N_{\mathrm{Cs}}=5.5\times {10}^3$ corresponds to the rightmost experimental images, and further confirms the partial immiscibility observed for Cs-${}^{170}\mathrm{Yb}$ mixtures with larger Yb atom numbers.

Figure 10

Optical setup to track the relative beam positions of the copropagating 532 nm and 1070 nm beams that make up the bichromatic optical dipole trap (BODT). The beam positions in the plane of the atoms are imaged onto a quadrant photodiode (QPD) using a pair of achromatic lenses with focal lengths $f=300$ mm and $f=500$ mm. Inset: calibration of the QPD sensitivity for the 532 nm beam. The measured vertical QPD voltage versus the vertical center of mass (CoM) Yb atom position is plotted in green circles. Here the vertical CoM position of a cloud of Yb atoms confined solely by the 532 nm beam gives an independent measure of the 532 nm beam position. Gray shaded areas denote QPD voltages excluded from the linear fit (green line), which gives a sensitivity of $2.9\left(1\right)\mathrm{mV}/\mu \mathrm{m}$.