Dipl.Phys. Carsten Robens  

Sampling from a quantum distribution can be exponentially hard for classical computers and yet could be performed efficiently by a noisy intermediatescale quantum device. A prime example of a distribution that is hard to sample is given by the output states of a linear interferometer traversed by N identical boson particles. Here, we propose a scheme to implement such a boson sampling machine with ultracold atoms in a polarizationsynthesized optical lattice. We experimentally demonstrate the basic building block of such a machine by revealing the HongOuMandel interference of two bosonic atoms in a fourmode interferometer. To estimate the sampling rate for large N, we develop a theoretical model based on a master equation. Our results show that a quantum advantage compared to today's best supercomputers can be reached with N≳40.
Transforming an initial quantum state into a target state through the fastest possible route—a quantum brachistochrone—is a fundamental challenge for many technologies based on quantum mechanics. Here, we demonstrate fast coherent transport of an atomic wave packet over a distance of 15 times its size—a paradigmatic case of quantum processes where the target state cannot be reached through a local transformation. Our measurements of the transport fidelity reveal the existence of a minimum duration—a quantum speed limit—for the coherent splitting and recombination of matter waves. We obtain physical insight into this limit by relying on a geometric interpretation of quantum state dynamics. These results shed light upon a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.
We present a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists in superimposing two laser light fields with the same wavelength, but with opposite circular polarizations, where the phase and amplitude of each light field are individually controlled. We find that the polarizationsynthesized beam reaches a degree of polarization of 99.99%, which is mainly limited by static spatial variations of the polarization state over the beam profile. We also find that the depolarization caused by temporal fluctuations of the polarization state is about two orders of magnitude smaller. In a recent work, Robens et al. [Phys. Rev. Lett. 118, 065302 (2017)] demonstrated an application of the polarization synthesizer to create two independently controllable optical lattices, which trap atoms depending on their internal spin state. We here use ultracold atoms in polarizationsynthesized optical lattices to give an independent, in situ demonstration of the performance of the polarization synthesizer.
This thesis reports on a novel concept of statedependent 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, welldefined trajectories. Furthermore, I demonstrate the generation of arbitrary lowentropy states of neutral atoms following a bottomup approach by rearranging a dilute thermal ensemble into a predefined, ordered distribution in a onedimensional optical lattice. Additionally, I probe twoparticle quantum interference effects of two atom trajectories by realizing a microwave HongOuMandel 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: threedimensional ground state cooling of single atoms, which are trapped in the combined potential of a polarizationsynthesized optical lattice and a bluedetuned hollow dipole potential; A highNA (0.92) objective lens achieving a diffraction limited resolution of 460 nm; and an improved superresolution 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 opticallattice technique that relies on a highprecision, highbandwidth synthesis of light polarization. Polarizationsynthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two longlived 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 nonclassicality 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 LeggettGarg inequality. The experiment is carried out using socalled ideal negative measurements – an essential requisite for any genuine LeggettGarg test – which acquire information about the atom’s position while avoiding any direct interaction with it. This interactionfree measurement is based on our polarizationsynthesized 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 LeggettGarg 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 twoatom densities and demonstrate a HongOuMandel interference with massive particles. Our precise control over individual indistinguishable particles embodies a direct analogue of the original HongOuMandel experiment. By carrying out a Monte Carlo analysis of our experimental data, I demonstrate a signature of the twoparticle interference of twoatom 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 onemillionoperation quantum cellular automaton.
We create lowentropy states of neutral atoms by utilizing a conceptually new opticallattice technique that relies on a highprecision, highbandwidth synthesis of light polarization. Polarizationsynthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two longlived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, we provide a proof of concept using four atoms that selected regions of the periodic potential can be filled with one particle per site. We expect that our results can be scaled up to thousands of atoms by employing an atomsorting algorithm with logarithmic complexity, which is enabled by polarizationsynthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottomup approach to creating ultralowentropy states of a manybody system.
We have designed, built, and characterized a high resolution objective lens that is compatible with an ultrahigh vacuum environment. The lens system ex ploits the principle of the Weierstrasssphere solid immersion lens to reach a numerical aperture (NA) of 0.92. Tailored to the requirements of optical lattice experiments, the objective lens features a relatively long working distance of 150 μm. Our twolens design is remarkably insensitive to mechanical tolerances in spite of the large NA. Additionally, we demonstrate the application of a tapered optical fiber tip, as used in scanning nearfield optical microscopy, to measure the point spread function of a high NA optical system. From the point spread function, we infer the wavefront aberration for the entire field of view of about 75 μm. Pushing the NA of an optical system to its ultimate limit enables novel applications in quantum technolo gies such as quantum control of atoms in optical mi crotraps with an unprecedented spatial resolution and photon collection efficiency.
We report on image processing techniques and experimental procedures to determine the latticesite positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in superresolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate superresolution of the atoms' position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with subpixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object—in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interactionfree measurement scheme can be put in direct relation with falsification tests of the macrorealistic worldview. Here we have implemented the "bomb test" with a single atom trapped in a spindependent optical lattice to show explicitly a violation of the LeggettGarg inequality—a quantitative criterion fulfilled by macrorealistic physical theories. To perform interactionfree measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used pushout technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the LeggettGarg inequality.
We report on a stringent test of the nonclassicality 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 violation of the LeggettGarg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, welldefined trajectories. We use socalled ideal negative measurements—an essential requisite for any genuine LeggettGarg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interactionfree measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the LeggettGarg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.
We report on an ultralow birefringence dodecagonal glass cell for ultrahigh vacuum applications. The epoxybonded trapezoidal windows of the cell are made of SF57 glass, which exhibits a very low stressinduced birefringence. We characterize the birefringence Δn of each window with the cell under vacuum conditions, obtaining values around 10^{8}. After baking the cell at 150 ºC, we reach a pressure below 10^{10} mbar. In addition, each window is antireflection coated on both sides, which is highly desirable for quantum optics experiments and precision measurements.
Die Erfindung betrifft ein Verfahren, eine Vorrichtung und die Verwendung einer Vorrichtung zur Anwendung oder Messung polarisierter elektromagnetischer Strahlung im Vakuum, wobei die Doppelbrechung Δn < 10^{6} beträgt.
We report on the state of the art of quantum walk experiments with neutral atoms in statedependent optical lattices. We demonstrate a novel statedependent transport technique enabling the control of two spinselective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of singleparticle quantum interference based on the violation of the LeggettGarg inequality and, more recently, to probe twoparticle quantum interference effects with neutral atoms cooled into the motional ground state. These experiments lay the groundwork for the study of discretetime quantum walks of strongly interacting, indistinguishable particles to demonstrate quantum cellular automata of neutral atoms.
We present an insitu method to measure the birefringence of a single vacuum window by means of microwave spectroscopy on an ensemble of cold atoms. Stressinduced birefringence can cause an ellipticity in the polarization of an initially linearlypolarized laser beam. The amount of ellipticity can be reconstructed by measuring the differential vector light shift of an atomic hyperfine transition. Measuring the ellipticity as a function of the linear polarization angle allows us to infer the amount of birefringence Δn at the level of 10^{8} and identify the orientation of the optical axes. The key benefit of this method is the ability to separately characterize each vacuum window, allowing the birefringence to be precisely compensated in existing vacuum apparatuses.