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.
In this work I present the experimental realization of a versatile platform for the interplay between light and matter at the single-quanta level. In particular, I demonstrate the high cooperativity of small ensembles of rubidium atoms strongly coupled to a state-of-the-art, open fiber-based microcavity, emphasizing the capabilities of the system as an efficient source and storage device for single photons.
The first part of this thesis focusses on the construction and characterization of the microresonator, which is composed of two dielectric mirrors machined on the end-facets of optical glass fibers. Through the implementation of an in-house facility, a large number of fiber-based mirrors are manufactured and precisely characterized. The intrinsic properties of this particular type of resonator are then analyzed and discussed. I present a theoretical model that explains, for the first time, the asymmetry in their reflective line shape and that has important implications for the optimal alignment of fiber-based cavities.
In the following chapter, I introduce the main experimental apparatus, which contains a miniaturized fiber cavity — with small mode volume and a linewidth of ϰ=2π×25 MHz — that is actively stabilized and integrated in a compact assembly. The monolithic structure features several high–numerical aperture (NA) lenses that provide the necessary tools for the trapping, manipulation and high-resolution imaging of atoms inside the resonator. Neutral rubidium atoms are delivered by an optical conveyor belt from the cooling region into the cavity mode, where their deterministic coupling to the resonator is ensured by the tight confinement of a 3D optical lattice. The high linewidth of our open cavity also prevents the manifestation of cavity-heating mechanisms, enabling a constant monitoring of the atom’s presence by probing the cavity field without increased trap losses. This atom detection method allows us to perform real-time optical feedback in the transport scheme and to observe the characteristic vacuum Rabi splitting for individual atoms in a non-destructive manner.
The rest of this work focusses on the interplay between atomic and photonic excitations inside the resonator. Due to the small mode volume of the microcavity, coupling strengths up to g=2π×100 MHz are observed for single atoms, corresponding to light–matter interaction in the strong coupling regime. The system’s cooperativity is collectively enhanced more than five times when placing a small atomic ensemble inside the resonator. Such a fast interaction rate — along with the relatively high transmission of the input cavity mirror — provides a rapid, non-destructive readout of the internal hyperfine state of a coupled atom when probing the cavity field. The state-detection method yields fidelities of 99.8% in 5 ms with less than 1% population transfer and negligible atom losses.
The last part of the thesis is dedicated to the study of the influence of the cavity on the emission properties of an atom. I show how, despite the small solid angle covered by the cavity mode, the resonator alters the radiation pattern of an externally pumped single atom and increases its emission rate by a factor of 20 due to the process known as cavity back-action. More than 85% of the emitted photons are collected by the single cavity-mode — as a result of the strong Purcell enhancement — and subsequently channeled out by one of the fiber mirrors. A characterization of the photon statistics of the cavity output shows a clear antibunching dip, confirming that the emission corresponds to a single quantum emitter and that our system can be used as a readily fiber-coupled, efficient single-photon source. The geometry of our fiber-based resonator provides wide optical access that — in combination with the high-NA lenses — allows us to study the free-space emission rate of an atom coupled to the cavity. The various coupling strengths associated to different positions of the atom in the cavity mode lead to a clear visualization of the cavity back-action for all cooperativity regimes.
The high cooperativity, intrinsic fiber coupling and scalability properties of our system make it suitable for the realization of an efficient, high-bandwidth quantum memory and its implementation in quantum networks. Additionally, the ability to couple an ensemble of indistinguishable atoms to the same cavity mode provides a versatile platform for the study of multipartite entangled states.
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 6 σ (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 4 σ.
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.
Neutral atoms trapped in optical lattices are promising candidates for quantum information processing and quantum simulation. Over the last decades, elegant tools for the manipulation of the internal and external states of optically trapped atoms have been developed. The crucial capability of scalable internal state readout in these systems, however, still relies on destructive methods. In spite of the important role of near-resonant illumination for the manipulation and detection of atoms in the lattice, there also exists a significant lack of studies on the heating and cooling dynamics of optically trapped atoms interacting with near-resonant light. An in-depth understanding of the heating and cooling processes is essential to finding the conditions of illumination that enable the non-destructive internal state readout of multiple atoms.
This work presents an experimental system to cool, trap, manipulate, and detect the internal and external states of a small ensemble of ^{87}Rb neutral atoms trapped in a one-dimensional optical lattice. A high photon detection efficiency in our experimental system allows for fast fluorescence imaging with acquisition times of 20 ms and fast position determination of atoms in the optical lattice with an accuracy of ∼40 nm.
Using this experimental system, we investigate the heating dynamics of a neutral atom trapped in a standing wave dipole trap illuminated by a single near-resonant laser beam. A theoretical description to describe our measurements is provided in two experimentally relevant regimes. First, we consider the case of a weak near-resonant beam and later the case of off-resonant illumination. From this analysis, we find settings for the illumination light which allows an atom to scatter many photons before it is expelled from the trap.
Building on these results we demonstrate simultaneous, non-destructive determination of the internal state of spatially resolved atoms trapped in a one-dimensional optical lattice with a fidelity of 98.6 ± 0.2% and a survival probability of 99.0 ± 0.2%. During the readout process, less than 2% of the atoms change their initial ground state.
In order to determine the state of atoms that are not spatially resolved, a novel image analysis technique is presented. The technique uses Bayesian methods, which include the statistics of the detected photons as well as the response from the EMCCD camera. The Bayesian method is implemented on experimental data for atoms trapped in a one-dimensional optical lattice and its accuracy is tested by numerical simulations. In addition, an extension of this algorithm for atoms trapped in two-dimensional lattices is provided.
Finally, the non-destructive state detection method is utilized as a tool for the state determination following the coherent control of the internal and external states of atoms in the optical trap. Here Raman sideband cooling is implemented and utilized in an atomic compression sequence for the creation of a small and dense atomic ensemble. These techniques will play an important role in experiments studying the collective light interaction of the atomic ensemble in a recently added optical fiber cavity.
In this thesis, I present single-site detection of neutral atoms stored in a three-dimensional optical lattice using a numerical aperture objective lens (NA_{design} = 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.