Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.
Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. \n\nUsing a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. \n\nWe study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons.\n\nMany-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Rényi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition.\n\nOur experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.
Ultracold quantum gases in optical lattices provide a rich experimental toolbox for simulating the physics of condensed matter systems. With atoms in the lattice playing the role of electrons or Cooper pairs in real materials, it is possible to experimentally realize condensed matter Hamiltonians in a controlled way. To realize the full potential of such quantum simulations, we leverage a quantum gas microscope which can spatially resolve the atoms in the optical lattice at the single site level and project arbitrary potential landscapes onto the atoms by combining the high resolution optics with static holographic masks or a spatial light modulator. The versatility of this system allows for a wide range of studies. In this thesis, we focus on three experiments that highlight the utility of a tunable platform and demonstrate the richness of physics that comes with interactions.\nIn the first, we observe on-site interparticle interactions introduce a non-linearity into the many-body energy spectrum of a harmonic oscillator. The excitation of a single atom into a higher band induces an energy shift in the excitation energy for the second atom, blockading the orbital excitation. We demonstrate a technique for deterministic number filtering based upon orbital excitation blockade. When applied to a high temperature Mott insulator, this number filtering realizes a form of algorithmic cooling, which can be used for initializing a large quantum register or creating low entropy initial states for many-body simulation.\nIn the second, we study the applicability of statistical physics in an isolated system governed by quantum mechanics. While the descriptive power of these two fields has been confirmed through repeated and varied empirical studies, their underlying axioms of entropy maximization and unitary evolution appear mutually exclusive. With our quantum gas microscope, we have the ability to probe local observables such as the on-site number statistics as well as measure the quantum mechanical purity through interference operations. With these capabilities, we are able to observe the local thermalization of a manifestly quantum mechanically pure many-body system.\nIn the last chapter, we report on the first cold atoms studies of an interacting system under an artificial gauge field. We consider the propagation of a pair of atoms in a 2timesN ladder governed by the Harper-Hofstadter model. The eigenstates of this system include both scattering states, which can exhibit chiral propagation, and bound states. A superexchange energy shift in our initial state leads to imbalanced population in the two chiral scattering sectors, leading to chiral propagation dynamics. This effect is the result of both the presence of interactions and the artificial gauge fields. These two components are essential ingredients for fractional quantum Hall physics. Moreover, the dynamic tunable gauge field we develop and the control afforded by a quantum gas microscope make this platform well-suited for future studies in this regime.
A system of ultracold atoms in an optical lattice provides a powerful platform for quantum simulation. In our laboratory, we use a quantum gas microscope to tune lattice parameters not only in a global scale but also at the level of individual sites. This allows us to control and detect the quantum state of interacting many-body systems as well as to engineer a broad class of Hamiltonians with high fidelity. Leveraging this versatility, we can realize several types of strongly correlated bosonic systems, which present intriguing behaviors and implement novel phases of matter. Analyzing snapshots of the atomic distribution with single-site resolution, we measure correlations and entanglement within these systems to reveal their main features, including non-equilibrium dynamics and quantum phase transitions. In this thesis, I present the works performed by our team for four different types of systems. First of all, I briefly introduce the behavior of a 1D disordered system in the critical regime between the thermal and the many-body-localized phases. In particular, we discuss what happens when a disordered and a non-disordered region are coupled via a single site. We find evidence for accelerated transport of thermal inclusion into the localized region, which shows the existence of a quantum avalanche, i.e. thermalization via accelerated transport throughout the localized system. In the second part, we realize a fractional quantum Hall state using an artificial gauge field, by implementing an adiabatic preparation protocol. We identify a topological phase transition in our system and characterize several key physical features expected for a Laughlin state by measuring density correlations and Hall conductivity. The next topic of this thesis relates to quantum magnetism. Mapping nearest hopping in a tilted optical lattice to spin flips, we realize a finite one-dimensional chain of 1/2-spins with closed boundary conditions. We perform an in-depth investigation on behaviors shown across the quantum phase transition between paramagnetic and antiferromagnetic ground states, including the evolution of the magnetization and Néel order parameter. Also, we find evidence for quantum superposition at the many-body level as a result of geometric frustration. In the last chapter, I report the experimental realization of a novel dipolar Bose-Hubbard Hamiltonian, based on a strongly tilted lattice system. When the tilt becomes the dominant energy scale, the Hamiltonian is fragmented, and the system behaves in a way that conserves dipole moment. Starting from a 1D chain of unity filled sites, we generate individual dipolar and anti-dipolar excitations at desired pinpoints. We observe quantum walks of these dipolar quasi-particles as well as their scattering dynamics, which allows us to study this new type of Hamiltonian using a bottom-up approach.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.
In this thesis, I describe the development of and scientific results from a new platform for creating ultracold atoms via single-atom control. We employ Raman-sideband cooling to isolated bosonic 87Rb atoms confined within sub-micron optical tweezers, yielding single particle three- dimensional ground-state fractions of 90%. We create multiple, independent, mobile optical tweezers, which simultaneously allows multi-particle studies with single-atom microscopy and highly tunable length-scales. We employ this toolset in both of the main experiments discussed in this thesis. In one experiment, we observe Hong-Ou-Mandel interference of two bosonic atoms, each of which is independently prepared in spatially separated optical tweezers. The interference we observe is a direct consequence of the purity of the single particle quantum states produced, and the indistinguishability of the atoms. In a second experiment, we introduce a spin-degree of freedom and exploit spin-exchange dynamics, driven by the quantum-statistics of the particles, to create a spin-entangled pair of spatially separated atoms.
This thesis details the complete upgrade and renovation of an existing experimental platform into a high-resolution quantum gas microscope for ultracold 87Rb atoms. Quantum gas microscopes enable site-resolved imaging, providing unprecedented access to quantum statistical effects and many-body phenomena. While such instruments are often employed to study physics in optical lattices, we have innovatively adapted our apparatus to investigate bulk system behavior. A major part of this project involved upgrading the scientific apparatus and retrofitting the previous system. We introduced new optical components, including a high-NA objective, and improved the vacuum system for better optical access. Extensive lab renovations, from upgrading the optical table to reorganizing the laser and imaging setups, were carried out to enhance mechanical and thermal stability. Rigorous optical benchmarking confirmed that the objective achieves diffractionlimited imaging, which is critical for resolving single atoms. This capability allowed us to detect density fluctuations at the scale of the thermal de Broglie wavelength in a quasi-two-dimensional gas of 87Rb atoms. In an experiment resembling Hanbury Brown and Twiss interferometry, we measured a 30% enhancement in the second-order correlation function in situ, demonstrating strong bosonic bunching. This outcome underscores the microscope’s precision and the importance of high-resolution imaging in capturing subtle quantum statistical effects. The successful realization of this apparatus demonstrates the utility of quantum gas microscopes in probing bulk systems. With this new platform in place, future studies can explore critical phenomena, many-body correlations, matter-wave emission, and quantum simulations with cold atoms.