Session G5: Fermions in Optical Lattices

Observation of antiferromagnetic correlations in the Fermi-Hubbard model

The physics of high temperature superconductors is not well understood, although it is known that the undoped parent compounds of many of them are antiferromagnetic (AF) insulators. The Fermi-Hubbard model at half filling (one atom per lattice site) is known to exhibit a phase transition to an antiferromagnetic insulator at a low temperature. We realize the Fermi-Hubbard model by loading ultracold $^{6}$Li atoms into a three-dimensional red-detuned optical lattice. We have compensated the confining potential of the lattice with blue-detuned laser beams in order to evaporatively cool the atoms. We have cooled sufficiently to observe AF correlations using spin-sensitive Bragg scattering of near-resonant light. Comparison with Quantum Monte Carlo (QMC) calculations indicates that the temperature is between 2-3 $T_{N}$, where short-range correlations begin to develop. Bragg scattering combined with QMC provides sensitive thermometry in a previously unexplored regime.   

Finite-temperature properties of strongly correlated fermions in the honeycomb lattice

We study finite-temperature properties of the Hubbard model in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. Specifically, we calculate experimentally relevant quantities, such as the entropy, the specific heat, uniform and staggered spin susceptibilities, nearest-neighbor spin correlations, and the double occupancy at and away from half filling. We show that in homogeneous systems adiabatic cooling is more efficient at finite doping than at half filling, and that this can be used in trapped geometries to create a Mott insulating phase with exponentially long antiferromagnetic correlations at relatively high entropies. Those entropies are found to be higher in the honeycomb lattice than in the square one suggesting that the experimental realization of an antiferromagnetic Mott insulator may be easier in the former geometry.   

Quasi-1D Fermi Gases with Spin Imbalance

We report investigations of the spin density in spin-imbalanced Fermi gases confined to 1D tubes using a 2D optical lattice. Measurements of density profiles along the tubes reveal phase transitions between partially polarized superfluid cores and either ferromagnetic or BCS-like wings.\footnote{Y.A. Liao et~al., Nature 467, 567 (2010)} Variations of these phase boundaries with temperature can reveal quantum critical behavior.\footnote{X.W. Guan and T.-L. Ho, PRA 84, 023616 (2011)} Weak tunneling between the tubes should stabilize long-range ordering in the gas, increasing the chance of observing FFLO physics.\footnote{M. M. Parish et~al., PRL 99, 250403 (2007)}   

A numerical approach to few-atom dynamics in one dimension

We develop a numerical approach based on the Time-Evolution-Block-Decimation (TEBD) method to study the dynamics of one-dimensional system consisting of a few ultracold atoms. As an example, we investigate the ferromagnetic transition of a two-component Fermi gas. Recent study has shown that for such a system, a ferromagnetic transition is expected to occur when the 1D interaction strength diverges. We study how this transition occurs in real time when the interaction strength is varied and a very small magnetic field gradient is present. We also discuss the eigenstates and eigenenergies of a two-particle system in the presence of a magnetic gradient and compare our numerical calculation with a semi-analytic model.   

A one-dimensional liquid of Fermions with tunable spin

Correlations in physical systems with spin degree of freedom are at the heart of several fundamental phenomena, ranging from magnetism to superconductivity. In general, the effects of correlations depend strongly on the dimensionality of the system. A striking example are fermions confined in one dimension, whose small-energy excitations have a collective nature. We report on the realization of multi-component one-dimensional liquids of ultracold $^{\mathrm{173}}$Yb fermions. These two-electron atoms are characterized by a large nuclear spin and highly-symmetric atom-atom interactions, which result in the possibility of performing quantum simulations of systems with intrinsic SU(N) symmetry. In one dimension, repulsive interactions between atoms in different nuclear spin states cause static and dynamic properties of the system to significantly depart from those of an ideal Fermi gas, in accordance with the Luttinger theory for a 1D liquid of spin-1/2 interacting fermions. Much stronger deviations are measured when the fermionic liquid is prepared in more than 2 internal states. This work provides the first experimental study of Luttinger physics with repulsive spinful atoms and the first realization of multi-component Luttinger liquids with tunable SU(N) symmetry.   

Decoherence of fermions in optical lattices due to spontaneous emissions

A major experimental challenge in reaching low-entropy states with ultra cold fermionic atoms in optical lattices arises from various heating and decoherence mechanisms. Here we study systems exhibiting quantum magnetism, investigating how these many-body states are affected by spontaneous emission processes at a rate that can be comparable to the typical dynamical timescales. We show, by deriving a many-body master equation for two spin fermions, that the spin order can be robust against this decoherence mechanism when we work in appropriate parameter regimes. This formalism can also be generalized to group-II species exhibiting SU(N) magnetism. The decoherence processes in these systems is measurable in current experiments. In addition to strongly repulsive regimes, we also look at attractive interactions, where decay rates of correlations can be enhanced by superradiance. We also consider processes involving higher bands, and dynamics of thermalization of the excitations created in the lattice after spontaneous emissions have occurred.   

A Closer Look at Fermions in Optical Lattices

Quantum gases of interacting fermionic atoms in optical lattices promise to shed new light on the low-temperature phases of Hubbard-type models, such as spin-ordered phases or, in particular, on possible $d$-wave superconductivity. However, reaching the very low temperatures required necessitates the implementation of novel cooling schemes. As a first step towards this goal, we employ high-resolution imaging together with radio-frequency spectroscopy in order to spatially resolve the in-trap distributions of singly and doubly-occupied lattice sites after having loaded a quantum degenerate two-component Fermi gas of $^{40}$K atoms into a three-dimensional optical lattice geometry. Here, I will report on our recent progress towards the observation and characterization of a fermionic Mott insulator, together with an outlook on future steps towards lowering the temperature in the lattice.   

Beyond Artifcial Graphene with Ultracold Fermions in a Tunable-Geometry Optical Lattice

Ultracold fermions in optical lattices offer the possibility to simulate the behavior of solids and explore regimes, which are not accessible in current materials. We have created an articifal graphene-like system and study how it can be driven from the usual Dirac-metal state to various insulating states (including the first implementation of a 2D Mott-insulator of fermions) by changing interactions, on-site energies or the tunneling structure. We present recent results on the behavior of static and dynamic observables in insulating regimes.   

Precision spectroscopy of ultracold fermions in a triangular optical lattice

Ultracold fermions in optical lattices provide an ideal testing ground for solid-state theories due to the high experimental control and wide range of tunable parameters. It is of substantial interest to probe the elementary excitation spectrum and to measure both the band structure and the filling of the lowest bands. In this talk, we present measurements of the full two-dimensional band structure of ultracold fermions in a triangular lattice using a versatile, fully momentum-resolved spectroscopy method based on lattice amplitude modulation. Our newly implemented lattice setup allows us to tune the tunneling matrix elements in each lattice direction independently. In combination with the high precision of the spectroscopy technique, this is promising for engineering and investigating novel lattice systems with interacting fermionic spin-mixtures and non-equilibrium phenomena in exotic lattice geometries including strong artificial gauge fields.   

Observation of Collapse and Revival Dynamics in the Fermionic Component of a Lattice Bose-Fermi Mixture

The collapse and revival of quantum fields is one of the most pristine forms of coherent quantum dynamics very far from equilibrium. So far, it has only been observed in the dynamical evolution of bosonic fields, for example in a coherent light field interacting with a single atom in cavity QED or in the matter wave field of a Bose-Einstein condensate. Here we report on the first experimental observation of collapse and revival dynamics in a many-body state of fermionic particles. The experiment is performed using an interacting Bose-Fermi mixture of ${}^{87}$Rb and ${}^{40}$K atoms, loaded to an optical lattice. After simultaneous preparation of a bosonic superfluid and a metallic state of spin-polarized fermions, the lattice depth is rapidly increased and non-equilibrium dynamics are initiated. Mediated by interactions with the bosons, the fermions show long-lived dynamical evolution with more than ten revivals, observed in the fermionic momentum distribution after time-of-flight. Fourier transform of the evolution shows that the on-site interaction energy between bosons and fermions is the only relevant energy scale. Our observations demonstrate that, even in systems with short-range coherence, collapse and revival dynamics can be a sensitive probe for correlations.