Ground-State Pressure of Quasi-2D Fermi and Bose Gases

Using an ultracold gas of atoms, we have realized a quasi-two-dimensional Fermi system with widely tunable $s$-wave interactions nearly in a ground state. Pressure and density are measured. The experiment covers physically different regimes: weakly and strongly attractive Fermi gases and a Bose gas of tightly bound pairs of fermions. In the Fermi regime of weak interactions, the pressure is systematically above a Fermi-liquid-theory prediction, maybe due to mesoscopic effects. In the opposite Bose regime, the pressure agrees with a bosonic mean-field scaling in a range beyond simplest expectations. In the strongly interacting regime, measurements disagree with a purely 2D model. Reported data may serve for sensitive testing of theoretical methods applicable across different quantum physics disciplines.

Figure 1

(a) Linear density profile $n_1(x)$, no noise filtering applied. Dots are the data for $a_2\sqrt{n_2}=0.89$ ($B=850\mathrm{G}$, $N=500\pm 10$, $l_z=-0.29a$). Solid and dashed curves are the fits by Thomas-Fermi and Gaussian distribution, respectively. The Gaussian fit is off, which proves deep degeneracy. (b) Surface density $n_2(\tilde{\rho })$ derived from noise-filtered $n_1(x)$. Dots are the data. The curve is the fit of the parabola $n_2(\tilde{\rho })=n_2-{\tilde{\rho }}^2{n}_2^{\prime \prime }/2$ to the data, which yields the central density $n_2\equiv n_2(\tilde{\rho }=0)$.

Figure 2

Normalized local pressure vs interaction parameter. Data are coded in color by the atom number $N$: smallest $N=220–350$ [$E_F=(0.40–0.51)\hslash {\omega }_z$] are shown by empty red circles, intermediate $N=410–560$ [$E_F=(0.54–0.64)\hslash {\omega }_z$] by green circles with a thicker border, and largest $N=640–910$ [$E_F=(0.69–0.82)\hslash {\omega }_z$] by blue solid dots. Solid red curve: Smooth approximation of the pure 2D Monte Carlo simulation [12]. Dashed curve: Model [30] of a homogeneous 2D Fermi liquid at $T=0$. Dotted line: Mean-field model based on the BCS state [31]. The vertical dash-dotted line separates data into two regions: $a_2<l_z$ on the left and $a_2>l_z$ on the right. The data in table form are in Ref. [17].

Figure 3

Demonstration of linear scaling $P_2/P_{2\text{ideal}}\propto a/l_z$ in the Bose regime. Markers: The data $(P_2/P_{2\text{ideal}})/(a/l_z)$ vs the interaction parameter. Color coding and the vertical dash-dotted line are the same as in Fig. 2. Dashed horizontal line: Model for pointlike molecular bosons with 3D interactions, $P_2=P_{2\text{ideal}}(0.6a/l_z\sqrt{8\pi })$. The solid line connects points calculated via $P_2=P_{2\text{Bose}}/2$.

Figure 4

Ratio of the measured normalized pressure to the respective values of a smooth fitting function [17] vs the normalized chemical potential. Color coding is the same as in Fig. 2.