Production and stabilization of a spin mixture of ultracold dipolar Bose gases

Abstract

Mixtures of ultracold gases with long-range interactions are expected to open new avenues in the study of quantum matter. Natural candidates for this research are spin mixtures of atomic species with large magnetic moments. However, the lifetime of such assemblies can be strongly affected by the dipolar relaxation that occurs in spin-flip collisions. Here we present experimental results for a mixture composed of the two lowest Zeeman states of $^{162}$Dy atoms, that act as dark states with respect to a light-induced quadratic Zeeman effect. We show that, due to an interference phenomenon, the rate for such inelastic processes is dramatically reduced with respect to the Wigner threshold law. Additionally, we determine the scattering lengths characterizing the s-wave interaction between these states, providing all necessary data to predict the miscibility range of the mixture, depending on its dimensionality.

Figures (10)

• Figure 1: Schematic representation of the experimental protocol. Top panels: two horizontal laser beams (Raman 1 and Raman 2) induce a Raman transition between nearest Zeeman sublevels. The vertical laser beam induces a spin-dependent light shift, allowing us to selectively couple the two lowest-energy Zeeman sublevels. Orange line represents the energy of $\left\vert-6\right\rangle$ in the absence of the light-induced quadratic Zeeman effect. Bottom panel: absorption images of Bose-Einstein condensates in different internal states, captured after time-of-flight (TOF) expansion in the presence of a magnetic field gradient. The right-most absorption image corresponds to a BEC preparation in $\left\vert-7\right\rangle$ with purity $> 95\%$. Dashed lines serve as guides to the eye for the spatial position of atoms in states $\left\vert-8\right\rangle$, $\left\vert-7\right\rangle$, and $\left\vert-6\right\rangle$.
• Figure 2: Dipolar relaxation. Time evolution of the atom number in state $\left\vert-7\right\rangle$ for (a) minority component in $\left\vert-7\right\rangle$ ($<5\%$) immersed in the majority component $\left\vert-8\right\rangle$ (blue pentagon $B = 1.1\gauss$, blue crossed circle $B = 2.0\gauss$, and blue square $B=4.5\gauss$) and for (c) pure sample in $\left\vert-7\right\rangle$ (red crossed circle $B = 2.5\gauss$, red pentagon $B = 3\gauss$ and red square $B=4.77\gauss$). (b) Two-body loss rate as a function of $B$ for the case of a minority component in $\left\vert-7\right\rangle$. The lines correspond to theoretical predictions (see main text) for scattering length: $a_{ 78} = -20\, a_0$ (blue dotted line), $a_{ 78} = 20\, a_0$ (blue dash dot line), $a_{ 78} = 60\, a_0$ (blue line) and $a_{ 78} = 100\, a_0$ (dashed blue line). (d) Two-body loss rate as a function of $B$ for the case of a pure sample in $\left\vert-7\right\rangle$. The lines correspond to theoretical predictions for scattering length: $a_{77} = -40\, a_0$ (red dotted line), $a_{77} = 40\, a_0$ (red dash dot line), $a_{77} = 120\, a_0$ (red line) and $a_{77} = 200\, a_0$ (red dashed line). The brown lines correspond to the Wigner law $\propto \sqrt{B}$.
• Figure 3: Determination of the scattering length from time-of-flight expansion of a pure BEC in $\left\vert-7\right\rangle$ at a magnetic field $B = 1.43\gauss$. Area of the BEC, defined as the product of the Thomas-Fermi radii extracted from inverted parabola fits to absorption images, plotted as a function of atom number $N$ in the (a) $x$--$y$ and (b) $\tilde{x}$--$z$ planes, with $\tilde{x}$ at a $70^\circ$ angle from ${x}$ and perpendicular to $z$. The lines correspond to numerical simulations for the BEC expansion, assuming scattering lengths of $a_{77} = 110 \, a_0$ (solid line), $a_{77} = 98 \, a_0$ (dashed line), and $a_{77} = 122 \, a_0$ (dot-dash line). The trapping frequencies are $\left\lbrace\omega_x,\,\omega_y,\,\omega_z\right\rbrace = 2\pi \times \left\lbrace100,\, 260,\, 200\right\rbrace \text{ Hz}$.
• Figure 4: Spin-dependent loss features following a 40ms hold time at the target magnetic field. (a) Population variation with magnetic field for a pure BEC in $\left\vert-8\right\rangle$. (b) Population variation for a pure BEC in $\left\vert-7\right\rangle$. (c) Population variation for the case of a 50-50 spin mixture in $\left\vert-8\right\rangle$ (blue) and $\left\vert-7\right\rangle$ (red). The vertical lines represent the different spin-dependent Feshbach resonances. The vertical black arrows point to the interspecies loss features.
• Figure S1: Characterization of the green transition. Left panel: transmission response ($t$) through a ULE cavity with a finesse of 300 000. Sidebands at 4MHz are added to characterize the laser linewidth. Right panel: size of an atomic sample after a 6ms time-of-flight expansion following exposure to a near-resonant laser beam for 40µs.