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.

}, Author = {Robens, C.}, Journal = {}, Pages = {}, Title = {{Testing the Quantumness of Atom Trajectories}}, Volume = {}, Year = {2017} }