Strongly Interacting Two-Dimensional Bose Gases

We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength $0.05<g<3$ is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when $g$ approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.

Figure 1

Equations of state for 2D Bose gases and 2D lattice gases with $0.05\le g\le 2.8$. The filled circles represent measurements of 2D gases with (from left to right) $g=0.05$ (black), 0.15 (red), 0.24 (blue), 0.41 (green), and 0.66 (purple). The open circles represent measurements of 2D lattice gases with (from left to right) $g=0.45$ (black), 0.85 (red), 1.2 (blue), 1.9 (green), and 2.8 (purple). The upper blue shaded area is the superfluid regime, and the red boundary corresponds to the BKT transition regime. The black dashed line $\tilde{\mu }=0$ indicates where we evaluate the density and pressure for a vacuum-to-superfuid quantum critical gas. The inset compares the equations of state of a 2D gas and a 2D lattice gas with an almost identical $g\approx 0.4$.

Figure 2

Coupling constant $G_{\mathrm{SF}}$ of strongly interacting 2D superfluids. We determine $G_{\mathrm{SF}}$ by fitting the slope of the equations of state in the superfluid region for 2D gases (filled circles) and 2D lattice gases (open circles). Extensions of theoretical predictions into the strong interaction regime based on the third-order perturbation expansion [12] (upper green line) [see Eq. (1)], the mean-field theory (middle red line), and the Ginzburg-Landau theory [22] (bottom black line) are shown for comparison. The error bars are dominated by the uncertainty of the density calibration.

Figure 3

Critical coupling constant  (a), scaled critical chemical potential (b), and scaled critical density (c) determined in the BKT transition regime. By overlapping all scaled equations of state in the transition regime, shown in the inset in (a), critical parameters are determined from Eq. (2). The results from 2D gases (filled circles) and 2D lattice gases (open circles) are compared to the predictions from the mean-field theory (red line), the perturbation theory [12] (green line), the classical-field theory [18] (blue line), and the Ginzburg-Landau theory [22] (black line).

Figure 4

Pressure (a) and density (b) of a quantum critical gas at $\tilde{\mu }=0$. The measurements based on 2D gas (filled circles) and 2D lattice gas (open circles) at temperatures between $T=11–15\mathrm{nK}$ are compared with NPRG theory [24] (black solid line), mean-field theory for a 2D gas [42] (blue dotted line), and for a 2D lattice gas [43] (red dashed line) at 13 nK.