Quantum simulation using ultracold fermions in optical lattices provides valuable insights for strongly correlated many-body phenomena in regimes challenging for classical simulations. In this dissertation, we report the design and construction of an apparatus capable of producing quantum degenerate Bose and Fermi gases. The atoms are then loaded into hexagonal optical superlattices created using two commensurate wavelengths. The apparatus lays the foundation for studying interacting fermions in geometrically frustrated lattices.We also report our experimental results on the characterization of the quantum geometry of Bloch band structures. Using rubidium Bose-Einstein condensates in the honeycomb lattice, we were able to measure the quantum distance around band touching points using parallel transport. Additionally, by simulating optical excitations using noninteracting fermions in a periodically modulated lattice, we observe quasimomentum-dependent optical selection rules, which stem from interband quantum geometry of the honeycomb lattice.
Quantum simulation using ultracold fermions in optical lattices provides valuable insights for strongly correlated many-body phenomena in regimes challenging for classical simulations. In this dissertation, we report the design and construction of an apparatus capable of producing quantum degenerate Bose and Fermi gases. The atoms are then loaded into hexagonal optical superlattices created using two commensurate wavelengths. The apparatus lays the foundation for studying interacting fermions in geometrically frustrated lattices.We also report our experimental results on the characterization of the quantum geometry of Bloch band structures. Using rubidium Bose-Einstein condensates in the honeycomb lattice, we were able to measure the quantum distance around band touching points using parallel transport. Additionally, by simulating optical excitations using noninteracting fermions in a periodically modulated lattice, we observe quasimomentum-dependent optical selection rules, which stem from interband quantum geometry of the honeycomb lattice.
Ultracold atomic gases trapped at the interference of coherent beams of light constitute an artificial material. This optical lattice material may be used for controlled quantum simulations of condensed matter theories. The bulk of this dissertation concerns the construction and calibration of an optical superlattice that can form the triangular, honeycomb and kagome crystal structures. The properties and geometry of this artificial material may be dynamically changed, allowing for the experiments discussed in this thesis that would be impossible with real materials. The use of ultracold atoms in optical lattices for quantitative tests is challenging because of the novelty of many of the techniques in the field, and because of the myriad experimental differences between these artificial materials and true materials. This thesis reports the development of a method to characterize optical lattice potentials using matter-wave diffraction. We observe an enhancement of inversion asymmetry in matter-wave diffraction from a honeycomb lattice, which we explain using a time-independent perturbative treatment of the single-particle band structure of the lattice. Our experiment also provides new insight into a commonly used detection technique. This thesis culminates in the development and experimental realization of a quantitative test of a condensed-matter theory. The test is insensitive to the experimental differences between artificial materials and real materials. We focus on a prediction from a mean-field treatment of the Bose-Hubbard model that concerns the difference in behavior of itinerant particles on lattices that are identical but for their geometry. Using the tunable geometry of our quantum simulator, we measure the properties of ultracold atomic gases trapped in the triangular and kagome lattices under otherwise identical conditions and find that they are consistent with the mean-field scaling prediction.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
Ultracold atoms in optical lattices represent a valuable resource for atom interferometry and for the quantum simulation of condensed matter systems, taking advantage of the possibility to tune interactions, adding disorder and changing quantum statistics. I will present a review of the work recently conducted at LENS in this fascinating field, discussing experiments with ultracold bosons, fermions and atomic mixtures in both periodic and disordered optical potentials, as well as the applications of a novel noninteracting 39K Bose-Einstein condensate.
Ultracold atoms in optical lattices have recently emerged as promising candidates for investigating the geometric and topological aspects of band structures. In this thesis, we exploit the high degree of control available in these systems to directly probe the band geometry of an optical honeycomb lattice. In the first series of experiments, we realize an atomic interferometer in quasimomentum space to measure the singular Berry flux associated with a Dirac point. This technique enables us to determine the distribution of Berry curvature in the Brillouin zone with high quasimomentum resolution. Next, we realize strong-force dynamics that are described by matrix-valued Wilson lines, which are generalizations of the Berry phase to degenerate systems. In this strong-force regime, we show that the evolution in the band populations directly reveals the band geometry. This method enables the reconstruction of both the cell-periodic Bloch states at every quasimomentum and the eigenvalues of Wilson-Zak loops. Our techniques can be used to determine the topological invariants, such as the Chern and Z2 numbers, that characterize the band structure. Lastly, having established our ability to detect the band geometry, we present preliminary experiments on engineering band structures.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.
In the past fifteen years ultracold atoms confined to optical lattices, which are artificial crystals of light, have proven to be powerful tools in the study of strongly correlated many-body systems widely known from a condensed matter context. The detailed knowledge, high tunability and control of microscopic parameters has enabled the creation and control of highly non-trivial quantum systems for which a direct comparison of model calculations to experimental measurements is now possible. In order to gain precise information on the properties of ultracold gases in optical lattices, many powerful methods have been developed. In particular spectroscopic methods have enabled to probe different characteristic excitations. However, many fascinating properties of strongly interacting quantum many-body systems are not yet fully characterized. Therefore, this thesis explores further possibilities of lattice modulation spectroscopy which is a time-periodic modulation of the optical lattice amplitude. We theoretically investigate the response of different (mostly one-dimensional) cold atom systems to a lattice modulation by means of the time-dependent density matrix renormalization group method and different analytical approximations. In addition to the normal lattice modulation, we consider a superlattice modulation scheme where the lattice amplitude is modulated in a dimerized fashion, coupling to a certain class of excitations in the system. The lattice modulation spectroscopy is a versatile probe which we use to study different situations relevant for experimental applications. We show that a detection of signatures of the exotic bond order wave phase is feasible in a system of interacting fermions on a one-dimensional optical lattice with staggered energy offset. Moreover, we demonstrate that a temperature measurement of fermions confined to an optical lattice is possible as well as a determination of the interaction strength of bosonic atoms confined to a one-dimensional optical lattice. In addition, various excitations in all these systems are investigated in detail.