Elliptic flow in a strongly interacting normal Bose gas

We study the anisotropic, elliptic expansion of a thermal atomic Bose gas released from an anisotropic trapping potential, for a wide range of interaction strengths across a Feshbach resonance. We show that this hydrodynamic phenomenon is for all interaction strengths fully described by a microscopic kinetic model with no free parameters. The success of this description crucially relies on taking into account the reduced thermalizing power of elastic collisions in a strongly interacting gas, for which we derive an analytical theory. We also perform time-resolved measurements that directly reveal the dynamics of the energy transfer between the different expansion axes.

Figure 1

Elliptic flow in a normal atomic Bose gas. Hydrodynamic behavior is seen in the inversion of a cloud's spatial aspect ratio during time-of-flight (TOF) expansion, after release from an anisotropic harmonic trap. The sketch on top illustrates an anisotropic density profile of a trapped gas, whose parameters are given in the left panel of Fig. 2. The bottom panels show absorption images of the cloud after 10 ms of expansion, for two different interaction strengths. A quasi-ideal gas (left) expands essentially isotropically, while a strongly interacting one (right) shows a pronounced aspect-ratio inversion. Note that the trapped-gas cartoon is not to scale; for these experiments the aspect ratio of the trapped cloud was $\eta =24$.

Figure 2

Spatial aspect ratio of the cloud after expansion, $w_z/w_r$, for various interaction strengths across a Feshbach resonance, and different trap geometries. For each data set (panel) the inset cartoons (not to scale) indicate the trap geometry characterized by $\eta ={\omega }_z/{\omega }_r$, the ratio of axial and radial trapping frequencies in our cylindrically symmetric harmonic trap. The legends also show the trapped-cloud atom number $N$, temperature $T$, and peak phase-space density $\mathcal{D}$. In each panel we show three different theoretical curves, corresponding to progressively more refined models. In red we show the theory for a weakly interacting gas, in blue a theory that accounts for the unitarity-imposed limitations on the elastic scattering rate, and finally in green our theory that also takes into account the reduced ability of collisions to transfer momentum in a strongly interacting Bose gas (see the text for details). The shading of the theoretical curves reflects the variations and uncertainties in $N$ and $T$, and also the atom-number uncertainty due to small ($<8\%$) three-body losses during the expansion.

Figure 3

Dynamics of the interaxis energy transfer in the early stages of the expansion. The top panel illustrates our experimental protocol for obtaining time-resolved measurements of the momentum distribution. In the bottom panel we show the effective temperature $T^{\mathrm{eff}}$ associated with motion along the axial (blue) and radial (red) directions during expansion of a resonantly interacting gas ($\lambda /a=0$) released from a strongly oblate trap ($\eta =24$); all the trapped-cloud parameters are essentially the same as in the left panel of Fig. 2. In purple we show the average temperature, $(2T_r^{\mathrm{eff}}+T_z^{\mathrm{eff}})/3$, which remains essentially constant. The green bands show numerical simulations for our experimental parameters, with the band thickness reflecting the atom-number and temperature uncertainties. The dashed lines show the predictions for an ideal experiment with infinite TOF.