Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region.

We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature with predictions for both fermions and bosons from quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.

Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap.

We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system.

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.

Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas.

We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime are of Berezinskii-Kosterlitz-Thouless type and lie within the same universality class. On the bosonic side of the crossover, our data are well described by the quantum Monte Carlo calculations for a Bose gas. In contrast, in the strongly interacting regime, we observe a superfluid phase which is significantly influenced by the fermionic nature of the constituent particles.

Pairing in few-fermion systems with attractive interactions.

We study quasi-one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by observing the tunneling of particles out of the trap. For even particle numbers, we observe a tunneling behavior that deviates from uncorrelated single-particle tunneling indicating the existence of pair correlations in the system. From the tunneling time scales, we infer the differences in interaction energies of systems with different number of particles, which show a strong odd-even effect, similar to the one observed for neutron separation experiments in nuclei.

Precise characterization of 6Li Feshbach resonances using trap-sideband-resolved RF spectroscopy of weakly bound molecules.

We perform radio-frequency dissociation spectroscopy of weakly bound 6Li2 Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the 6Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad 6Li Feshbach resonances with an accuracy better than 7×10(-4) of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter ξ measured by Ku et al. [Science 335, 563 (2012)], which is ξ=0.370(5)(8).

Coherent molecule formation in anharmonic potentials near confinement-induced resonances.

We perform a theoretical and experimental study of a system of two ultracold atoms with tunable interaction in an elongated trapping potential. We show that the coupling of center-of-mass and relative motion due to an anharmonicity of the trapping potential leads to a coherent coupling of a state of an unbound atom pair and a molecule with a center of mass excitation. By performing the experiment with exactly two particles we exclude three-body losses and can therefore directly observe coherent molecule formation. We find quantitative agreement between our theory of inelastic confinement-induced resonances and the experimental results. This shows that the effects of center-of-mass to relative-motion coupling can have a significant impact on the physics of quantum systems near center-of-mass to relative-motion coupling resonances.

Fermionization of two distinguishable fermions.

We study a system of two distinguishable fermions in a 1D harmonic potential. This system has the exceptional property that there is an analytic solution for arbitrary values of the interparticle interaction. We tune the interaction strength and compare the measured properties of the system to the theoretical prediction. For diverging interaction strength, the energy and square modulus of the wave function for two distinguishable particles are the same as for a system of two noninteracting identical fermions. This is referred to as fermionization. We have observed this phenomenon by directly comparing two distinguishable fermions with diverging interaction strength with two identical fermions in the same potential. We observe good agreement between experiment and theory. By adding more particles our system can be used as a quantum simulator for more complex systems where no theoretical solution is available.

Atom-dimer scattering in a three-component Fermi gas.

Ultracold gases of three distinguishable particles with large scattering lengths are expected to show rich few-body physics related to the Efimov effect. We have created three different mixtures of ultracold 6Li atoms and weakly bound 6Li2 dimers consisting of atoms in three different hyperfine states and studied their inelastic decay via atom-dimer collisions. We have found resonant enhancement of the decay due to the crossing of Efimov-like trimer states with the atom-dimer continuum in one mixture as well as minima of the decay in another mixture, which we interpret as a suppression of exchange reactions of the type |12+|3→|23+|1. Such a suppression is caused by interference between different decay paths and demonstrates the possibility of using Efimov physics to control the rate constants for molecular exchange reactions in the ultracold regime.

From few to many: observing the formation of a Fermi sea one atom at a time.

Knowing when a physical system has reached sufficient size for its macroscopic properties to be well described by many-body theory is difficult. We investigated the crossover from few- to many-body physics by studying quasi-one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions. We measured the interaction energy of such a system as a function of the number of majority atoms for different strengths of the interparticle interaction. As we increased the number of majority atoms one by one, we observed fast convergence of the normalized interaction energy toward a many-body limit calculated for a single impurity immersed in a Fermi sea of majority particles.

Deterministic preparation of a tunable few-fermion system.

Systems consisting of few interacting fermions are the building blocks of matter, with atoms and nuclei being the most prominent examples. We have created a few-body quantum system with complete control over its quantum state using ultracold fermionic atoms in an optical dipole trap. Ground-state systems consisting of 1 to 10 particles are prepared with fidelities of ∼90%. We can tune the interparticle interactions to arbitrary values using a Feshbach resonance and have observed the interaction-induced energy shift for a pair of repulsively interacting atoms. This work is expected to enable quantum simulation of strongly correlated few-body systems.