Observation of the Presuperfluid Regime in a Two-Dimensional Bose Gas

In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density $\rho$ increases toward degenerate values, we observe a gradual divergence of the compressibility $\kappa$ from the value predicted by a bare-atom model, ${\kappa }_{\mathrm{ba}}$. $\kappa /{\kappa }_{\mathrm{ba}}$ grows to 1.7 before $\rho$ reaches the value for which we observe the sudden emergence of a spike at $p=0$ in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.

Figure 1

(a) A trap-focused, momentum-space image. (b) An in situ, coordinate-space image. The corresponding azimuthal averages are shown in Figs. 2g, 2c.

Figure 2

(a)–(d) Coordinate-space distributions and (e)–(h) corresponding momentum distributions. Two distributions in the same row are taken under near-identical conditions. The thin black curves give the azimuthal averages of $n_{\mathrm{meas}}$ from the raw images. The thick blue curves in the coordinate-space distributions are the ground-state distribution $n_0$ after correcting for $n_{k>0}$. The spike in momentum space that first appears in (g) has no corresponding dramatic change in coordinate space (c). The vertical dotted line in (c) represents the inverse of the momentum resolution limit indicated in (g) and is thus a lower limit on the spatial extent of the coherence of the population of low-$p$ (high-coherence) atoms represented by the area (about 1.4% of total) under the spike in (g).

Figure 3

Scaled compressibility $\kappa$ vs phase-space density ${\rho }_0$. (a) Measured $\kappa$ extracted from images of samples at $T=171\mathrm{nK}$, as in the image in Fig. 2c. Black circles are data averaged over the values calculated from images of three separate clouds. The blue curves are ${\kappa }_{\mathrm{ba}}$ calculated from the bare-atom model. (b) Same but with $\kappa$ extracted from images of samples at $T=128\mathrm{nK}$. The paired vertical dotted lines indicate the location of the jump in coherence discussed in the text.