Equation of State of the Two-Dimensional Hubbard Model.

The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0≲U/t≲20 and temperatures, down to k_{B}T/t=0.63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.

Attractive and repulsive Fermi polarons in two dimensions.

The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well known case is an impurity coupled to a bosonic bath (such as lattice vibrations); the impurity and its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-transition-temperature superconductors, as well as in colossal magnetoresistance in manganites. For impurities in a fermionic bath, studies have considered heavy or immobile impurities which exhibit Anderson's orthogonality catastrophe and the Kondo effect. More recently, mobile impurities have moved into the focus of research, and they have been found to form new quasiparticles known as Fermi polarons. The Fermi polaron problem constitutes the extreme, but conceptually simple, limit of two important quantum many-body problems: the crossover between a molecular Bose-Einstein condensate and a superfluid with BCS (Bardeen-Cooper-Schrieffer) pairing with spin-imbalance for attractive interactions, and Stoner's itinerant ferromagnetism for repulsive interactions. It has been proposed that such quantum phases (and other elusive exotic states) might become realizable in Fermi gases confined to two dimensions. Their stability and observability are intimately related to the theoretically debated properties of the Fermi polaron in a two-dimensional Fermi gas. Here we create and investigate Fermi polarons in a two-dimensional, spin-imbalanced Fermi gas, measuring their spectral function using momentum-resolved photoemission spectroscopy. For attractive interactions, we find evidence for a disputed pairing transition between polarons and tightly bound dimers, which provides insight into the elementary pairing mechanism of imbalanced, strongly coupled two-dimensional Fermi gases. Additionally, for repulsive interactions, we study novel quasiparticles--repulsive polarons--the lifetime of which determines the possibility of stabilizing repulsively interacting Fermi systems.

Scale invariance and viscosity of a two-dimensional Fermi gas.

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.

Glassy behavior in a binary atomic mixture.

We experimentally study one-dimensional, lattice-modulated Bose gases in the presence of an uncorrelated disorder potential formed by localized impurity atoms, and compare to the case of correlated quasidisorder formed by an incommensurate lattice. While the effects of the two disorder realizations are comparable deeply in the strongly interacting regime, both showing signatures of Bose-glass formation, we find a dramatic difference near the superfluid-to-insulator transition. In this transition region, we observe that random, uncorrelated disorder leads to a shift of the critical lattice depth for the breakdown of transport as opposed to the case of correlated quasidisorder, where no such shift is seen. Our findings, which are consistent with recent predictions for interacting bosons in one dimension, illustrate the important role of correlations in disordered atomic systems.

Collinear four-wave mixing of two-component matter waves.

We demonstrate atomic four-wave mixing of two-component matter waves in a collinear geometry. Starting from a single-species Bose-Einstein condensate, seed and pump modes are prepared through microwave state transfer and state-selective Kapitza-Dirac diffraction. Four-wave mixing then populates the initially empty output modes. Simulations based on a coupled-mode expansion of the Gross-Pitaevskii equation are in very good agreement with the experimental data. We show that four-wave mixing can play an important role in studies of bosonic mixtures in optical lattices. Moreover, our system should be of interest in the context of quantum atom optics.

Superfluidity of interacting bosonic mixtures in optical lattices.

We report the observation of many-body interaction effects for a homonuclear bosonic mixture in a three-dimensional optical lattice with variable state dependence along one axis. Near the superfluid-to-Mott insulator transition for one component, we find that the presence of a second component can reduce the apparent superfluid coherence, most significantly when the second component either experiences a strongly localizing lattice potential or none at all. We examine this effect by varying the relative populations and lattice depths, and discuss the observed behavior in view of recent proposals for atomic-disorder and polaron-induced localization.

Analysis of Kapitza-Dirac diffraction patterns beyond the Raman-Nath regime.

We study Kapitza-Dirac diffraction of a Bose-Einstein condensate from a standing light wave for a square pulse with variable pulse length but constant pulse area. We find that for sufficiently weak pulses, the usual analytical short-pulse prediction for the Raman-Nath regime continues to hold for longer times, albeit with a reduction of the apparent modulation depth of the standing wave. We quantitatively relate this effect to the Fourier width of the pulse, and draw analogies to the Rabi dynamics of a coupled two-state system. Our findings, combined with numerical modeling for stronger pulses, are of practical interest for the calibration of optical lattices in ultracold atomic systems.