Anisotropic Expansion of a Thermal Dipolar Bose Gas

We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the postexpansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases. Furthermore, we present a simple method to determine scattering lengths in dipolar gases, including near a Feshbach resonance, through observation of thermal gas expansion.

Figure 1

Measured gas AR after 16 ms of TOF for ${}^{162}\mathrm{Dy}$ in (a) and ${}^{164}\mathrm{Dy}$ in (b). In both (a) and (b), red is for magnetic field along $\widehat{z}$ and blue is for $\widehat{y}$. Points are data with $1\sigma$ total error: statistical plus 1% systematic [26]. Solid red and blue curves are calculated using the full theory with the best-fit scattering lengths. Dashed curves are calculated for only the MF effect with the best-fit scattering lengths found using the full theory. Horizontal solid gray line marks unity AR and vertical gray line marks $T_c$.

Figure 2

(a) Illustration of Bose-corrected TOF thermometry to a dipolar thermal Bose gas, showing that the theory fails to yield the same temperature along the $\widehat{x}$, $\widehat{y}$, and $\widehat{z}$ directions. Field along $\widehat{z}$. Theory curves are $T_x$ (blue, dashed), $T_y$ (gray, solid), and $T_z$ (red, dotted). (b) Observed difference between $T_x$ and $T_z$, the two dimensions in the imaging plane. The discrepancy is large if only the Bose-corrected TOF thermometry is applied directly (gray points), but can be reduced to close to zero (gray line) using the additional corrections provided in Eqs. (1) and (2) (red points). Theoretical curves in (a) and data in (b) are presented for the experimental parameters used in the ${}^{162}\mathrm{Dy}$ measurement of Fig. 1 with the magnetic field along $\widehat{z}$: $N=1.4(1)\times 10^5$ and $[{\omega }_x,{\omega }_y,{\omega }_z]=2\pi \times [107(1),49(5),266(1)]\mathrm{Hz}$.

Figure 3

(a) High resolution atom-loss spectrum for ${}^{162}\mathrm{Dy}$ showing a resonance at 5.1 G and three nearby narrower resonances. Line is to guide the eye. (b) Measured gas AR as a function of magnetic field. Horizontal line marks unity AR. (c) Scattering lengths corresponding to the data in (b). We are unable to extract a scattering length for four points near the 5.2 G small resonance with AR below unity; see text for details. All error bars represent $1\sigma$ uncertainty.