In this thesis, I present single-site detection of neutral atoms stored in a three-dimensional optical lattice using a numerical aperture objective lens (NAdesign = 0.92). The combination of high-resolution imaging with state-dependent trapping along two-direction of the lattice opens up the path towards quantum simulations via quantum walks. Suppressing the interactions of a quantum system with the environment is essential for all quantum simulation experiments. It demands a precise control of both the external magnetic (stray) fields and the polarization properties of laser beams inside the vacuum chamber. I designed a metal shielding to reduce magnetic field fluctuations and designed, assembled and characterized a novel ultra-high vacuum glass cell. The glass cell consists of special glass material and exhibits an ultra-low birefringence Δn of a few times 10^-8 to highly suppress polarization disturbances originating from stress birefringence in vacuum windows. Furthermore, anti-reflection coatings avoid reflections on all window surfaces. The cell hosts the assembled vacuum-compatible objective, that exhibits a diffraction limited resolution of up to 453 nm and allows to optically resolve the spacing of the optical lattice. Fluorescence images of single trapped atoms are used to characterize the imaging system. The filling, orientation and geometry of the optical lattice is precisely reconstructed using positions of atoms that can be determined from fluorescence images. Furthermore, I present a scheme to realize state-dependent transport and discuss its robustness against experimental imperfections in a technical implementation. This transport scheme enable the realization of discrete-time quantum walks with neutral atoms in two dimensions. These quantum walks pave the way towards the simulation of artificial magnetic fields and topologically protected edge states.
In this thesis, I present single-site detection of neutral atoms stored in a three-dimensional optical lattice using a numerical aperture objective lens (NAdesign = 0.92). The combination of high-resolution imaging with state-dependent trapping along two-direction of the lattice opens up the path towards quantum simulations via quantum walks. Suppressing the interactions of a quantum system with the environment is essential for all quantum simulation experiments. It demands a precise control of both the external magnetic (stray) fields and the polarization properties of laser beams inside the vacuum chamber. I designed a metal shielding to reduce magnetic field fluctuations and designed, assembled and characterized a novel ultra-high vacuum glass cell. The glass cell consists of special glass material and exhibits an ultra-low birefringence Δn of a few times 10^-8 to highly suppress polarization disturbances originating from stress birefringence in vacuum windows. Furthermore, anti-reflection coatings avoid reflections on all window surfaces. The cell hosts the assembled vacuum-compatible objective, that exhibits a diffraction limited resolution of up to 453 nm and allows to optically resolve the spacing of the optical lattice. Fluorescence images of single trapped atoms are used to characterize the imaging system. The filling, orientation and geometry of the optical lattice is precisely reconstructed using positions of atoms that can be determined from fluorescence images. Furthermore, I present a scheme to realize state-dependent transport and discuss its robustness against experimental imperfections in a technical implementation. This transport scheme enable the realization of discrete-time quantum walks with neutral atoms in two dimensions. These quantum walks pave the way towards the simulation of artificial magnetic fields and topologically protected edge states.
The present work investigates the state-selective transport of single neutral cesium atoms in a one-dimensional optical lattice. It demonstrates experimental applications of this transport, including a single atom interferometer, a quantum walk and controlled two-atom collisions. The atoms are stored one by one in an optical lattice formed by a standing wave dipole trap. Their positions are determined with sub-micrometer precision, while atom pair separations are reliably inferred down to neighboring lattice sites using real-time numerical processing. Using microwave pulses in the presence of a magnetic field gradient, the internal qubit states, encoded in the hyperfine levels of the atoms, can be separately initialized and manipulated. This allows us to perform arbitrary single-qubit operations and prepare arbitrary patterns of atoms in the lattice with single-site precision. Chapter 1 presents the experimental setup for trapping a small number of cesium atoms in a one-dimensional optical lattice. Chapter 2 is devoted to fluorescence imaging of atoms, discussing the imaging setup, numeric methods and their performance in detail. Chapter 3 focuses on engineering of internal states of trapped atoms in the lattice using optical methods and microwave radiation. It provides a detailed investigation of coherence properties of our experimental system. Finally manipulation of individual atoms with almost single-site resolution and preparation of regular strings of atoms with predefined distances are presented. In Chapter 4, basic concepts, the experimental realization and the performance of the state-selective transport of neutral atoms over several lattice sites are presented and discussed in detail. Coherence properties of this transport are investigated in Chapter 5, using various two-arms single atom interferometer sequences in which atomic matter waves are split, delocalized, merged and recombined on the initial lattice site, while the interference contrast and the accumulated phase difference are measured. By delocalizing a single atom over several lattice sites, possible spatial inhomogeneities of fields along the lattice axis in the trapping region are probed. In Chapter 6, experimental realization of a discrete time quantum walk on a line with single optically trapped atoms is presented as an advanced application of multiple path quantum interference in the context of quantum information processing. Using this simple example of a quantum walk, fundamental properties of and differences between the quantum and classical regimes are investigated and discussed in detail. Finally, by combining preparation of atom strings, position-dependent manipulation of qubit states and state-selective transport, in Chapter 7, two atoms are deterministically brought together into contact, forming a starting point for investigating two-atom interactions on the most fundamental level. Future prospects and suggestions are finally presented in Chapter 8.
This thesis reports on a novel concept of state-dependent transport, which achieves an unprecedented control over the position of individual atoms in optical lattices. Utilizing this control I demonstrate an experimental violation of the Leggett Garg inequality, which rigorously excludes (i.e. falsifies) any explanation of quantum transport based on classical, well-defined trajectories. Furthermore, I demonstrate the generation of arbitrary low-entropy states of neutral atoms following a bottom-up approach by rearranging a dilute thermal ensemble into a predefined, ordered distribution in a one-dimensional optical lattice. Additionally, I probe two-particle quantum interference effects of two atom trajectories by realizing a microwave Hong-Ou-Mandel interferometer with massive particles, which are cooled into the vibrational ground state. The first part of this thesis reports on several new experimental tools and techniques: three-dimensional ground state cooling of single atoms, which are trapped in the combined potential of a polarization-synthesized optical lattice and a blue-detuned hollow dipole potential; A high-NA (0.92) objective lens achieving a diffraction limited resolution of 460 nm; and an improved super-resolution algorithm, which resolves the position of individual atoms in small clusters at high filling factors, even when each lattice site is occupied. The next part is devoted to the conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two long-lived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, I provide a proof of concept that selected regions of the periodic potential can be filled with one particle per site. In the following part I report on a stringent test of the non-classicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6σ (standard deviation) violation of the Leggett-Garg inequality. The experiment is carried out using so-called ideal negative measurements – an essential requisite for any genuine Leggett-Garg test – which acquire information about the atom’s position while avoiding any direct interaction with it. This interaction-free measurement is based on our polarization-synthesized optical lattice, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond its fundamental aspect, I demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. The witness allows us to discriminate the quantumness of different types of walks spanning from merely classical to quantum dynamics and further to witness the decoherence of a quantum state. In the last experimental part I will discuss recent results on collisional losses due to inelastic collisions occurring at high two-atom densities and demonstrate a Hong-Ou-Mandel interference with massive particles. Our precise control over individual indistinguishable particles embodies a direct analogue of the original Hong-Ou-Mandel experiment. By carrying out a Monte Carlo analysis of our experimental data, I demonstrate a signature of the two-particle interference of two-atom trajectories with a statistical significance of 4σ. In the final part I will introduce several new experiments which can be realized with the tools and techniques developed in this thesis, spanning from the detection of topologically protected edge states to the prospect of building a one-million-operation quantum cellular automaton.
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.
The imaging of neutral atoms confined in an optical lattice has been demonstrated by a number of groups, resolving single fluorescing atoms in samples of hundreds of atoms. To obtain a high signal the atoms remain confined in the wells of a deep optical lattice whilst fluorescence excitation light is applied for high resolution imaging. In most cases, the excitation light frequency is chosen so that there is a concomitant laser cooling effect. In existing implementations of an imaging lattice the preceding manipulation stage has used optical trapping and manipulation. In this thesis I describe work towards applying this imaging lattice technique on a magnetic trapping apparatus, in particular for carrying out quantum simulation experiments. An introduction to the specific challenge of performing a quantum simulation of the fractional quantum Hall effect is given, with the link to and nature of the imaging lattice technique explained. The existing quantum-gas machine that has been developed to produce Bose-Einstein condensates of 87Rb in this work is then described, including the new optical lattice subsystem and the associated diode laser system. An auxiliary project to develop a servo-control system for frequencies that are several GHz away from an atomic reference is presented. We implement an optical lattice using laser light with a frequency detuning of -20 GHz below the D1-resonance line. The construction and geometry of the individual dipole trapping beams in combination with our existing apparatus is discussed as well as the alignment methods used. We confirm the presence of three independent 1D lattices through diffraction, and observe the decay of a BEC loaded into a lattice using absorption imaging. We observe good long-term alignment and operational stability of the optical lattice. This system will enable us to ultimately detect single fluorescing atoms in the optical lattice, following the application of excitation light co-propogating with lattice beams, via an imaging system with a moderate numerical aperture of 0:27.
This thesis focuses on the simulation of the physics of a charged particle under an external magnetic field by using discrete-time quantum walks of a spin-1/2 particle in a two-dimensional lattice. By Floquet-engineering the quantum-walk protocol, an Aharonov–Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an abelian gauge field—the analog of a magnetic flux threading a two-dimensional electron gas. I show that in the strong-field regime, i.e. when the flux per plaquette of the lattice is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands. I demonstrate that the system behaves like a Chern insulator by computing the Chern numbers of the energy bands and studying the excitation of the midgap topologically protected edge modes. These modes are extended all along the boundaries of the magnetic domains and remain robust against perturbations that respect the gap closing conditions. Furthermore, I discuss a possible experimental implementation of this scheme using neutral atoms trapped in two dimensional spin-dependent optical lattices. The proposed scheme has a number of unique features, e.g. it allows one to generate arbitrary magnetic-field landscapes, including those with sharp boundaries along which topologically protected edge states can be localized and probed. Additionally, I introduce the scattering matrix approach in discrete-time quantum walks to probe the Hofstadter spectrum and compute its topological invariants. By opening up a discrete-time quantum walk system and connecting it to metallic leads, I demonstrate that the reflection/transmission probabilities of a particle from the scattering region give information on the energy spectrum and topological invariants of the system. Although the work presented here focuses on the physics of a single particle in a clean system, it sets the stage for studies of many-body topological states in the presence of interactions and disorder.
Exercising microscopic control over quantum systems is a central theme in modern physics. Neutral-atom quantum simulators leverage this control to explore quantum many-body phenomena by realizing paradigmatic Hamiltonians, such as the Hubbard model, in isolated systems. Advances in single-atom-resolved manipulation and detection have allowed measurements of microscopic correlations in strongly interacting quantum systems. Quantum gas microscopes have successfully approached this from the top down, starting from bulk quantum gases, while optical tweezers offer a complementary bottom-up route based on controlled few-particle systems. Combining these approaches opens a pathway towards assembling many-body systems atom by atom, enabling deterministic control over the initial quantum state. This thesis presents the development of a compact quantum gas microscope for programmable ensembles of fermionic lithium-6. The apparatus integrates laser cooling, magnetic field control, quantum-gas preparation, optical tweezers, projected potentials, and high-resolution imaging around a high-numerical-aperture microscope objective. Evaporative cooling in a crossed optical dipole trap produces degenerate two-component Fermi gases and molecular Bose--Einstein condensates, providing the quantum-degenerate reservoir for subsequent experiments. We demonstrate uniform loading of degenerate fermionic ensembles into programmable two-dimensional tweezer arrays, overcoming reservoir-size limitations by translating the tweezer array across the reservoir. Leveraging fermionic statistics and the resolved motional spectrum, we prepare a singlet pair in the three-dimensional motional ground state of each tweezer trap. Across an 8x8 array, this yields an average single-particle preparation fidelity of 98.47%. We develop a novel approach combining the deterministic preparation with spin- and site-resolved control via global magnetic field gradients and locally projected repulsive potentials to produce arbitrary product state configurations in parallel across all sites. In this way, we achieve programmable assembly of spin--charge product states of up to 128 atoms, with fast experimental cycle times of 3 seconds. Furthermore, we realize a new scheme for simultaneous spin-, site-, and density-resolved imaging of individual lithium-6 atoms. Encoding the spin information in the fluorescence polarization, we resolve the two spin components within a single 20 microsecond exposure, achieving detection fidelities exceeding 98.5%. These capabilities establish a fast route to preparing low-entropy fermionic product states with microscopic control over their initial spin, charge, and motional configuration. Coupling such states through optical lattices or tunnel-coupled tweezers provides a route for initializing far-from-equilibrium many-body systems, with applications to strongly correlated physics, quantum transport and thermalization, and fermionic quantum information processing.