We use 40K atoms trapped in a cubic optical lattice to simulate the Fermi-Hubbard model. The work in this thesis focuses on investigating dynamics in the Fermi-Hubbard model and developing techniques for engineering Hamiltonians beyond the minimal Hubbard model. We discussed three experiments. In the first, we investigated the transport properties of a Fermi lattice gas by directly measuring the transport lifetime at various interaction strengths and temperatures. The resistivity is inferred from the measured transport lifetime. We observe anomalous transport behavior, which is analogous to bad-metal behavior in strongly correlated electronic materials. The second experiment presents the first realization of correlated, density-dependent tunneling in a Fermi-Hubbard optical lattice model by applied Raman laser fields. This correlated tunneling involves spin-flips and the generation of doublons, which have been observed experimentally. We also confirmed that the amplitude of correlated tunneling is suppressed when neighboring lattice sites are unoccupied. The last experiment explores the possibility to introduce long-range interactions for fermions trapped in optical lattices via Rydberg-dressed states. We developed a novel velocity-selective spectroscopy method to measure the transition between the 5P_1/2 and Rydberg states via electromagnetically induced transparency. This measurement is a first step toward inducing Rydberg-dressed interactions in optical lattices.
We use 40K atoms trapped in a cubic optical lattice to simulate the Fermi-Hubbard model. The work in this thesis focuses on investigating dynamics in the Fermi-Hubbard model and developing techniques for engineering Hamiltonians beyond the minimal Hubbard model. We discussed three experiments. In the first, we investigated the transport properties of a Fermi lattice gas by directly measuring the transport lifetime at various interaction strengths and temperatures. The resistivity is inferred from the measured transport lifetime. We observe anomalous transport behavior, which is analogous to bad-metal behavior in strongly correlated electronic materials. The second experiment presents the first realization of correlated, density-dependent tunneling in a Fermi-Hubbard optical lattice model by applied Raman laser fields. This correlated tunneling involves spin-flips and the generation of doublons, which have been observed experimentally. We also confirmed that the amplitude of correlated tunneling is suppressed when neighboring lattice sites are unoccupied. The last experiment explores the possibility to introduce long-range interactions for fermions trapped in optical lattices via Rydberg-dressed states. We developed a novel velocity-selective spectroscopy method to measure the transition between the 5P_1/2 and Rydberg states via electromagnetically induced transparency. This measurement is a first step toward inducing Rydberg-dressed interactions in optical lattices.
Ultracold fermionic atoms in a disordered optical lattice can realize the disordered Fermi-Hubbard model, allowing investigations of the nature of strongly-correlated fermions in a minimal setting. This thesis describes two such studies. In the first, we observe the momentum relaxation of strongly-correlated fermions in the absence of disorder. We find a violation of the weak-scattering prediction for the scaling with temperature, which is analogous to the linear-in-temperature scaling of resistivity in substances called ``bad metals.'' In the second, we probe a disordered and strongly-correlated system using quenches of the interaction strength that take it far from equilibrium. We find that the relaxation of double occupancies following the quenches has distinct dynamical regimes controlled by the interplay of interactions and disorder. We present a minimal picture of the relaxation process that illustrates the origin of these regimes, which are related to the Mott--metal--Anderson transitions of the ground state at half-filling.
These lecture notes review recent progress in studying the Fermi-Hubbard model using ultracold gases in optical lattices. We focus on results from quantum gas microscope experiments that have allowed site-resolved measurements of charge and spin correlations in half-filled and doped Hubbard systems, as well as direct imaging of various types of polaronic quasiparticles. We also review experiments exploring dynamical properties of the Hubbard model through transport and spectroscopy. Moving beyond the plain-vanilla square-lattice Hubbard model, we present more recent work exploring Hubbard systems with novel lattice geometries and long-range interactions that stabilize new phases. Finally, we discuss the realization of entropy distribution protocols to cool these systems to ultralow temperatures where comparison to unbiased numerics is no longer possible.
"This thesis presents research on a variety of dynamical phenomena in strongly correlated systems. We use 87Rb atoms trapped in a disordered optical lattice to realize the 3D Bose Hubbard model, with independently, dynamically tunable lattice depth and disorder strength. The equilibrium behavior of the Bose Hubbard and disordered Bose Hubbard models are understood, but there are many outstanding questions about dynamics. One area of interest is in dynamical behavior near quantum phase boundaries, such as the generation of quench-induced excitations in the presence of disorder. Another area concerns heat flow, relaxation, and thermalization. The primary focus of this thesis is driving a gas across a disorder-induced quantum phase transition from the Bose glass to the superfluid phase via quenching the disorder. We measured excitations generated during the quench and related them to crossing the equilibrium phase transition determined by quantum Monte Carlo simulations of the trapped system. The behavior we observe is reminiscent of the quantum Kibble Zurek mechanism, where the relaxation timescale diverges and local fluctuations are ""frozen"" into the system near the phase boundary. Understanding how disorder impacts the Kibble Zurek paradigm about behavior near a phase boundary provides insight into the dynamics of strongly interacting, disordered systems. The three other works discussed in this thesis concern relaxation and energy transfer in clean optical lattices. Understanding these dynamical properties of lattice gases is key to developing tools such as cooling in a lattice. In the first result, a gas comprised of two spin states was loaded into a spin-dependent optical lattice, such that one spin state experienced the lattice, and the other did not. We found that when the lattice gas was heated, energy transfer to the non-lattice gas did not occur at higher lattice depths due to the mismatch in the dispersion relations. In the second result, lattice atoms were excited to a higher band and found to decay to the ground state via two mechanisms. One decay channel involved generating excitations in the non-lattice atoms, while the other channel involved collisions between lattice atoms, where one atom decayed to the ground state and the other was excited to a higher band. The final result measured relaxation timescales by removing atoms with low quasimomentum and measuring rethermalization. The observed timescales are faster than the tunneling time and interaction time of the lattice. Proof-of-principle cooling was also demonstrated by removing atoms with higher quasimomentum and allowing the remaining atoms rethermalize to a cooler temperature."
This thesis describes experiments focused on investigating out-of-equilibrium phenomena in the Bose-Hubbard Model and exploring novel cooling techniques for ultracold gases in optical lattices. In the first experiment, we study quenches across the Mott-insulator-to-superfluid quantum phase transition in the 3D Bose-Hubbard Model. The quench is accomplished by continuously tuning the ratio of the Hubbard energies. We observe that the degree of excitation is proportional to the fraction of atoms that cross the phase boundary, and that the amount of excitations and energy produced during the quench have a power-law dependence on the quench rate. These phenomena suggest an excitation process analogous to the mechanism for defect generation in non-equilibrium classical phase transitions. This experiment constitutes the first observation of the Kibble-Zurek mechanism in a quantum quench. We have reported our findings in Ref. [1]. In a second experiment, published in Ref. [2], we investigate dissipation as a method for cooling a strongly interacting gas. We introduce dissipation via a bosonic reservoir to a strongly interacting bosonic gas in the Mott-insulator regime of a 3D spin-dependent optical lattice. The lattice atoms are excited to a higher energy band using laser-induced Bragg transitions. A weakly interacting superfluid comprised of atoms in a state that does not experience the lattice potential acts as a dissipative bath that interacts with the lattice atoms through collisions. We measure the resulting bath-induced decay using the atomic quasimomentum distribution, and we compare the decay rate with predictions from a weakly interacting model with no free parameters. A competing intrinsic decay mechanism arising from collisions between lattice atoms is also investigated. The presence of intrinsic decay can not be accommodated within a non-interacting framework and signals that strong interactions may play a central role in the lattice-atom dynamics. The intrinsic decay process we observe may negatively impact the success of cooling via dissipation because a fraction of intrinsic decay events can deposit a large amount of energy into the lattice gas. In a third experiment, we develop and carry out the first demonstration of cooling an atomic quasimomentum distribution. Our scheme, applied in a proof-of-principle experiment to 3D Bose-Hubbard gas in the superfluid regime, involves quasimomentum-selective Raman transitions. This experiment is motivated by the search of new cooling techniques for lattice-trapped gases. Efficient cooling exceeding heating rates is achieved by iteratively removing high quasimomentum atoms from the lattice. Quasimomentum equilibration, which is necessary for cooling, is investigated by directly measuring rethermalization rates after bringing the quasimomentum distribution of the gas out of equilibrium. The measured relaxation rate is consistent at high lattice depths with a short-range, two-particle scattering model without free parameters, despite an apparent violation of the Mott-Ioffe-Regel bound. Our results may have implications for models of unusual transport phenomena in materials with strong interactions, such as heavy fermion materials and transition metal oxides. The cooling method we have developed is applicable to any species, including fermionic atoms. Our results are available in Ref. [3]
We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing.The system is approximately described by a t -V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction.We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime.To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas.We find that strong nearest-neighbor interactions slow down the relaxation.Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.
We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.