Observation of Pair Condensation in the Quasi-2D BEC-BCS Crossover

The condensation of fermion pairs lies at the heart of superfluidity. However, for strongly correlated systems with reduced dimensionality the mechanisms of pairing and condensation are still not fully understood. In our experiment we use ultracold atoms as a generic model system to study the phase transition from a normal to a condensed phase in a strongly interacting quasi-two-dimensional Fermi gas. Using a novel method, we obtain the in situ pair momentum distribution of the strongly interacting system and observe the emergence of a low-momentum condensate at low temperatures. By tuning temperature and interaction strength, we map out the phase diagram of the quasi-2D BEC-BCS crossover.

Figure 1

Experimental setup. A quasi-2D gas (the red disk) is created by loading a two-component ultracold Fermi gas of ${}^6\mathrm{Li}$ atoms into a single layer of a standing-wave trap created by two interfering laser beams ($\lambda =1064\mathrm{nm}$, the green arrows) that cross under a small angle (14°). Using absorption imaging along the vertical direction (the red arrow) we obtain the column density of the sample.

Figure 2

Density distributions at the lowest accessible temperature for different interaction strengths. (a) In situ density distribution obtained from absorption imaging along the $z$ axis. (b) Pair momentum distribution obtained from the $\tau /4$ method with a pair projection ramp to ${\ell }_z/a_{3D}=7.11$ (692 G). The strong enhancement at low momenta in the momentum distribution for $\ln (k_F{a}_{2D})<3.24$ is a clear signature of pair condensation. Each picture is the average of about 30 individual measurements. The temperature of the samples ranges from 64 nK at $\ln (k_F{a}_{2D})=-7.13$ to 78 nK at $\ln (k_F{a}_{2D})=3.24$.

Figure 3

Quantitative analysis of the momentum distribution at ${\ell }_z/a_{3D}=1.55$. (a) Radial momentum distribution $\tilde{n}(k)$ at the coldest accessible temperature. We logarithmically plot $\tilde{n}(k)$ as a function of $k^2$. The thermal wing thus appears as a straight line from which we extract the temperature of the sample with a Boltzmann fit (line). The figure is the average of about 30 individual measurements. (b) Nonthermal fraction $N_q/N$ as a function of $T/T_F$. $N_q$ is indicated by the gray area in (a). (c) Normalized peak momentum density ${\tilde{n}}_0/n_0$ as a function of $T/T_F$. The intersection of linear fits to the high and low temperature regime yields the critical temperature $T_c/T_F$. Each data point in (b) and (c) is the average of about 30 individual measurements; the error bars indicate the standard error of the mean. Solid lines indicate the fitted data range.

Figure 4

Phase diagram of the strongly interacting 2D Fermi gas. The experimentally determined critical temperature $T_c/T_F$ is shown as black data points and the error bars indicate the statistical errors. Systematic uncertainties are discussed in detail in Ref. [27]. The color scale indicates the nonthermal fraction $N_q/N$ and is linearly interpolated between the measured data points (the white crosses). Each data point is the average of about 30 measurements. The dashed white line is the theoretical prediction for the BKT transition temperature given in Ref. [52].