Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice

We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold ${}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}$ Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance’s zero crossing. We form molecules out of atom pairs and characterize the mixing process in terms of sample overlap and mixing speed. The dense and ultracold sample of more than 5000 RbCs molecules is an ideal starting point for experiments in the context of quantum many-body physics with long-range dipolar interactions.

Figure 1

Simplified experimental optical trap setup and overlap strategy. (a) Bose-Einstein condensates of Rb (blue) and Cs (orange) are initially produced in separate crossed dipole traps. They are merged along the direction of one of the trapping beams ($x$ direction) at the center of a six-beam optical lattice (standing waves as indicated, center part omitted for clarity). (b) Starting from the two BECs, the lattice first induces a one-atom Mott insulator (MI) for the Cs sample. The Rb sample, yet superfluid (SF), is brought into overlap with the Cs sample by precisely moving the underlying dipole trap beam. The lattice is raised further to create a double-species MI with high Rb-Cs atom pair fraction.

Figure 2

Sample spatial overlap. Number of Feshbach molecules $N_{\mathrm{RbCs}}$ and normalized number $N_{\mathrm{RbCs}}/N_{\mathrm{Cs}}^{\mathrm{BEC}}$ as a function of (a) Rb sample vertical position $z_{\mathrm{Rb}}$ and (b) Rb sample horizontal position $x_{\mathrm{Rb}}$ as indicated by the cartoons. Each data point is the average of 3 runs, and the error bars indicate the standard error. The solid lines in (a) and (b) are simple fits to the data to extract the sample radii $(r_z^{\mathrm{Cs}},r_z^{\mathrm{Rb}},r_x^{\mathrm{Cs}},r_x^{\mathrm{Rb}})=\mathbf{(}9.6(4),11.3(2),8.0(5),10.1(3)\mathbf{)}\mu \mathrm{m}$, assuming the convolution of spherical samples with homogenous densities and taking into account the trailing tail by allowing for a one-sided offset [24].

Figure 3

(a) Characterization of mixing process and subsequent evolution. Circles: Number of Feshbach molecules $N_{\mathrm{RbCs}}$, respectively, normalized number $N_{\mathrm{RbCs}}/N_{\mathrm{Cs}}^{\mathrm{BEC}}$ as a function of $a_{\mathrm{RbCs}}$. Triangles: $N_{\mathrm{RbCs}}$, respectively, $N_{\mathrm{RbCs}}/N_{\mathrm{Cs}}^{\mathrm{BEC}}$ after a fixed hold time $\tau =270\mathrm{ms}$ upon ramping $a_{\mathrm{RbCs}}$ within 10 ms to the value as indicated. The vertical dotted line at $a_{\mathrm{RbCs}}=-82$ $a_0$ indicates the resonance condition $U_{\mathrm{RbCs}}=-U_{\mathrm{RbRb}}$ as discussed in the text. (b) Mixing efficiency as quantified by $N_{\mathrm{RbCs}}$, respectively, $N_{\mathrm{RbCs}}/N_{\mathrm{Cs}}^{\mathrm{BEC}}$ as a function of final lattice depth $V_{\mathrm{fin}}^{\mathrm{Rb}}$ as seen by the Rb atoms. Error bars in (a) and (b) reflect the standard error for 3 to 11 runs of the experiment.

Figure 4

Mixing speed limit. (a) Mixing efficiency as quantified by $N_{\mathrm{RbCs}}$, respectively, $N_{\mathrm{RbCs}}/N_{\mathrm{Cs}}^{\mathrm{BEC}}$ as a function of lattice depth $V_{\mathrm{mix}}^{\mathrm{Rb}}$, respectively, $V_{\mathrm{mix}}^{\mathrm{Cs}}$ during mixing for various transport speeds as indicated. The solid lines are error-function fits to determine the critical lattice depth. (b) Lifetime $t_{\mathrm{MI}}$ of the Cs one-atom Mott insulator (circles) as a function of lattice depth $V_{\mathrm{lat}}^{\mathrm{Cs}}$ at $a_{\mathrm{CsCs}}\approx 2500$ $a_0$. The diamond indicates the duration of the mixing process at the mixing lattice depth $V_{\mathrm{mix}}^{\mathrm{Cs}}=20$ $E_{\mathrm{rec}}^{\mathrm{Cs}}$. (c) Critical transport speed $v_{\mathrm{crit}}$ (circles) as determined from data shown in (a) as a function of lattice depth $V_{\mathrm{mix}}^{\mathrm{Rb}}$ during mixing. The diamond indicates the conditions used in most experiments reported here. The dashed-dotted line is the theory prediction from Ref. [34]. The dashed line through the data is the same prediction but shifted horizontally by $3.5E_{\mathrm{rec}}^{\mathrm{Rb}}$. The error bars reflect the standard error.