Two-Dimensional Fermi Liquid with Attractive Interactions

We realize and study an attractively interacting two-dimensional Fermi liquid. Using momentum-resolved photoemission spectroscopy, we measure the self-energy, determine the contact parameter of the short-range interaction potential, and find their dependence on the interaction strength. We successfully compare the measurements to a theoretical analysis, properly taking into account the finite temperature, harmonic trap, and the averaging over several two-dimensional gases with different peak densities.

Figure 1

Momentum-resolved photoemission signal in experiment and theory. (a) Measured signal at $1/\ln (k_F{a}_{2D})=0.35$. A free particle corresponds to a straight horizontal line. (b) Energy distribution curves at different momenta $\hslash k$. The solid lines represent a fit to the data. We see a shift of the maximum toward lower energies, which indicates the effective mass of the quasiparticles. The dashed line indicates $E_0$, the position of the peak at $k=0$. (c) and (d) Calculated intensity and energy distribution curves for the same parameters as in the experiment.

Figure 2

Dependence of the effective mass parameter on the interaction parameter $1/\ln (k_F{a}_{2D})$. The thick blue line shows the numerical calculation of the trap average and averaging over a density distribution with an rms width of 46 layers for the experimental conditions. The red dashed curve is the trap average for the central layer only. The thin green curve includes only the Hartree term in the self-energy.

Figure 3

Temperature dependence of the effective mass parameter. For our lowest temperature $T/T_F=0.27$, this corresponds to an interaction strength of $1/\ln (k_F{a}_{2D})=0.35$; samples at higher temperatures contain more atoms and have a slightly larger Fermi energy, which decreases the coupling strength to $1/\ln (k_F{a}_{2D})=0.32$ at $T/T_F=1.09$. The lines show the numerical simulation for the experimental parameters. The thick blue line is the trap average over 46 layers corresponding to the experimental conditions. The red dashed curve is the trap average for the central layer only. The thin green line includes only the Hartree term in the self-energy. The difference between Hartree only and the full self-energy changes with the number of trapped atoms, showing the intricate relation between the Hartree energy and the effective mass parameter.

Figure 4

Dimensionless contact $C^{\prime }=C/k_{\mathrm{F}}^2$ in the Fermi liquid regime. We compare with our theoretical results for the trap average in the weakly interacting regime (solid blue line). Moreover, we show the quantum Monte Carlo calculation at zero temperature [30] (dashed gray line) and the second-order Fermi liquid prediction (dotted line). Inset: To determine the contact, we divide the measured rf transition rate $I_{\sigma }(\nu )$ by $\mathcal{I}(\nu )$ (see text) and fit a constant at large $\nu$. This data set is for $1/\ln (k_F{a}_{2D})=0.49$.