Quantum technologies

2022

• T. Legrand
  Three-Dimensional Imaging of Single Atoms in an Optical Lattice via Helical Point-Spread-Function Engineering, (2022), Master thesisBibTeX
  ABSTRACT »

  In this thesis, I present a novel technique enabling three-dimensional localization of single atoms in an optical lattice up to sub-micrometer precision over an enhanced depth of field from a single experimental image. It consists of changing the microscope’s response to a point source, the so-called point spread function (PSF), such that it has an azimuthally structured shape, performing a rigid rotation along the observation axis, the angle of which provides information about the axial position. This is done by imposing on the collected fluorescence light a phase modulation built up from a superposition of Laguerre-Gauss modes in the pupil plane by a spatial light modulator (SLM). I demonstrate this method using the DQSIM quantum gas microscope with an engineered double-helix-shaped PSF. As I show, this enables axial resolution at the level of the vertical lattice separation of 532 nm even at lower numerical apertures while preserving the lateral resolution, overcoming the limitations of retrieving the axial position through the defocus alone.

  In Chapter 1, I present the experimental setup of the DQSIM experiment in Chapter 2. I particularly address the aspects necessary for the understanding of the subsequent measurements, as well as my contributions to the setup. Chapter 3 is about my contributions to a deep horizontal lattice. In Chapter 4, I present the three-dimensional imaging of single atoms. I describe the technique of preparing atoms in a single plane, the concept of PSF, and the resolution limit. I then discuss existing methods of three-dimensional imaging, in particular the rotating PSFs. Finally, I present the experimental realization and the measurements performed. Chapter 5 draws a conclusion and gives an outlook to this thesis.

2021

• M. R. Lam
  Probing the quantum speed limit of atomic matter waves in optical lattices, (2021), PhD thesisBibTeX
  ABSTRACT »

  The development of quantum technologies requires a deep knowledge of quantum systems and a high level of control of quantum states. In this thesis I report on my contribution to three areas that are important to quantum technologies: (i) Imaging of quantum states (ii) Fast transport of matter wave packets (iii) Estimation of the speed limit of quantum evolution. The platform here used consists of single neutral 133 Cs atoms trapped in a state dependent optical lattice potential. The control over the internal state of the atoms and the potential landscape is used as a tool to study the atomic wave packet dynamics.

  In the first part of the thesis I present the experimental setup as well as various experimental techniques that are required for the measurements presented in the following chapters. Two new implementations have been done in order to realize the desired measurements. One of them is a technique to measure the motional ground state population fraction, with an accuracy that is robust over a wide range of temperatures of the thermal ensemble. The second one is a pair of Raman beams to couple two hyperfine states with Rabi frequencies of around 6.5 MHz. Much faster than the observed wave packet dynamics.

  In chapter 3, I present a new technique to obtain time-resolved single-pixel images of quantum wave packets using Ramsey interferometry. The technique shares a clear analogy to classical optical imaging and can be potentially extended to obtain multi-pixel images that contain the same information as the full wave function. Even though the measurements presented in this thesis are restricted to single-pixel images, important information is extracted from them, including the Hamiltonian moments, the energy spectrum of the Hamiltonian and the population probabilities in the basis of motional eigenstates.

  In the last part of the thesis, the quantum speed limit of two different processes are studied. In chapter 4, the Mandelstam-Tamm and the Margolus-Levitin bounds are verified for atomic wave packets in a static optical lattice potential. The bounds impose a limit to the maximum rate of change of a quantum state. Two different regimes are covered: one where the Mandelstam-Tamm bound is more restrictive and one where the Margolus-Levitin bound is more restrictive. Moreover, it has been observed that the atomic wave packets evolve at a rate very close to the limit imposed by the Mandelstam-Tamm bound. In chapter 5, the speed limit of a different quantum process is studied, namely, fast atom transport without motional excitations over distances much longer than the width of the atomic wave packet. The transport trajectories are obtained with optimal quantum control, making possible to realize transport operations down to the shortest fundamental duration - the quantum speed limit. The Mandelstam-Tamm bound is found to predict an absurdly small estimate of the minimum transport duration, but a meaningful bound consistent with the measured speed limit is obtained based on geometric arguments.

• F. G. H. Winkelmann
  Optical plane selection in a dipole trap, (2021), PhD thesisBibTeX
  ABSTRACT »

  Quantum technology has advanced considerably within the last decades [1, 2]. Quantum simulators are among the primary goals of this ongoing „quantum revolution“ [3]. They promise insight into many-particle phenomena that are too complex to study on classical machines [4].

  In this thesis, I present my contribution to the discrete-time quantum walk simulator (DQSIM) experiment. We trap neutral cesium atom in a two dimensional state-dependent optical lattice [5], with the goal of realizing two-dimensional discrete-time quantum walks [6] and multi-particle entanglement [7].

  The atoms are imaged using a high numerical objective lens [8] that allows us to resolve the spatial distribution inside the lattice. An additional retro-reflected beam provides state-independent confinement along the imaging axis. To measure multi-particle interference, we have to confine the atomic ensemble to a single layer along the imaging axis. I propose a novel way of plane selection with neutral cesium atoms in an optical dipole trap utilizing artificial magnetic fields created by a gradient of polarization. The preparation of thin volumes is demonstrated. With further careful adjustment of the experimental parameters, this technique will enable the selection of single planes.

  We have to apply a magnetic guiding field to enable state-dependent transport of atoms. I designed a current stealing circuit to enable the long coherence times required for quantum simulations. The magnetic guiding field is stabilized to the level of 1 ppm. We measure a coherence time in free fall of T 2 =1.7 (1.4|2.1) ms. Vertical magnetic field gradients appear to be the limiting factor. With plane selection, coherence times of several tens of ms appear possible. This will allow for quantum walks with several hundred steps. The state-dependent potential of the DQSIM experiment can also be used to reconstruct the vibrational state of neutral atoms. I numerically investigate a novel scheme to probe the Wigner function by directly measuring the expectation value of the displaced parity operator. Measuring the parity operator requires us to tune the lattice depth dynamically. Displacing the atoms purely in position space without transferring momentum requires fast modulation of the lattice position. I demonstrate that we can use the processing capabilities of our digital intensity and phase control to achieve this. Stable operation over a large dynamical range is realized by linearizing the system response. Feed-forward control of the lattice position in conjunction with internal model control increases the modulation bandwidth from 230 kHz to 3.3 MHz.

  Precise control over the vibrational degree of freedom is a prerequisite to preparing arbitrary states of motion, such as Fock states. I demonstrate Raman sideband cooling along the vertical direction using the D1 transition of cesium. This complements the microwave mediated sideband cooling that we use to cool horizontally.

  Finally, I discuss possible future experiments such as the release-retrap technique to enhance the filling factor in the center of the trap [9, 10], magnetic quantum walks [11], and direct measurement of the exchange phase of indistinguishable particles [12].

• G. Ramola
  Ramsey Imaging of Optical Dipole Traps and its applications in building a 3D optical lattice, (2021), PhD thesisBibTeX
  ABSTRACT »

  In this work, I present the experimental realization of two-dimensional state-dependent transport of cesium atoms trapped in a three-dimensional optical lattice. Leveraging the ability to state-dependently transport atoms, I demonstrate microwave photon mediated sideband cooling to the motional ground state along two dimensions. Once cooled down to the vibrational ground state, we use these atoms as sensitive probes to detect both magnetic field gradients and optical field inhomogeneities, by means of Ramsey interferometry. This enables us to perform Ramsey imaging of optical dipole traps, an essential technique which helps in the precise alignment of optical beams inside the vacuum cell.

  In the first part of the thesis, I introduce the main experimental apparatus of the Discrete Quantum Simulator (DQSIM) machine, as our experiment is known, with emphasis on the technical improvements over the past few years, such as increasing the atom filling in our optical lattice from double digits to a few thousand. Using these atoms as magnetic probes, I confirm the expected magnetic shielding factor of about 2000 from the mu-metal shielding enclosing the vacuum cell. I finally discuss the control we have over the internal state of the atoms, with a measured Rabi frequency of Ω≈2π × 200 kHz.

  In chapter 3, I introduce the concept of state-dependent transport, which forms the basis of most experiments planned with the DQSIM machine. I go on to discuss the polarization synthesizer, the technical backbone of the state-dependent optical lattices. The polarization synthesizer allows us to create any arbitrary polarization state of light, by independently controlling the phase and amplitude of each circular polarization component of a linearly polarized optical lattice beam. With two such polarization synthesizers implemented in the experiment, I report on the experimental realization of state-dependent transport in two dimensions. This is followed by the demonstration of microwave photon mediated ground state cooling in two dimensions, where we achieve a ground state population of about 95% along each dimension.

  In the following chapter, I introduce the Ramsey spectroscopy technique, a mainstay of high precision experiments. Using Ramsey spectroscopy, I investigate some sources of dephasing in our experiment, from inhomogeneous magnetic fields to differential light shifts. Based on these Ramsey measurements, I show that we can achieve coherence times greater than a millisecond if we restrict the region of interest in our optical lattice. Exploiting the high precision Ramsey interferometry further, in chapter 5, I introduce a versatile technique for the precise in-vacuo reconstruction of optical potentials. This Ramsey imaging technique is used to image the four laser beams that form our three-dimensional lattice, helping us align them with micrometer precision. In the final chapter, I summarize the work done in this thesis and discuss some future experiments that are planned for the DQSIM machine, from plane selection to two-dimensional quantum walks.

2020

• S. Witt
  Machine Learning-Assisted Identification of Atom Positions in Two-Dimensional Optical Lattices, (2020), Bachelor thesisBibTeX
  ABSTRACT »

  This work presents an alternative method for analyzing EMCCD-microscopy images of two-dimensional quantum optical lattices, using neuronal networks to automate the recognition of lattice occupation states. We introduce a multi-step algorithm, whose overall performance as well as step-by-step performance is analyzed, and which is compared to several different architectures. Training the networks requires a large amount of training data with known lattice occupation states. These images are simulated by convolution of the experimentally estimated point spread function of the imaging system with the atomic distribution masks. The algorithm allows for an accuracy of up to 99.76 % on our simulated data.

• K. K. Chandrashekara
  A High-Power Ti:Sa Laser System for Atomic Quantum Walks Experiments, (2020), Master thesisBibTeX
  ABSTRACT »

  This thesis details the experimental efforts towards quantification of laser frequency noise by the use of an optical frequency discriminator and its suppression by means of measuring and reducing optical path length differences to prevent heating and loss of ultracold Caesium atoms trapped in two-dimensional state-dependent optical lattice. The discriminator used is a Fabry-Perót cavity with the side-of-fringe locking technique to be sensitive to frequency fluctuations of the input light field which are detected as changes in the intensity of the cavity signal. The measured noise spectrum revealed the performance of the laser in the frequency domain and was used to refine the same. A reduction in the laser linewidth was achieved in this manner. The same cavity was also transformed in to a transfer cavity to prevent long-term drift in the laser frequency. The frequency noise cannot be completely eliminated from the laser and so the task then became the reduction of the optical path length differences in the experiment by which the noise can manifest at the postion of the atoms. Conditions for achieving minimal path length differences were derived. Three methods were employed to measure the path length differences: A geometric distance measurement, an optical measurement using interferometry and at last using the atoms. The use of the atoms in particular displayed the extent to which the common-mode frequency noise can influence the experiment.

2019

• T. Legrand
  Vergleich der Holografie und der direkten Abbildung mit dem räumlichen Lichtmodulator, (2019), Bachelor thesisBibTeX
  ABSTRACT »

  Diese Bachelorarbeit beschäftigt sich mit dem LCoS räumlichen Lichtmodulator (SLM). Dabei soll die durch Phasenmodulation erfolgende Holografie und der auf Amplitudenmodulation beruhende Aufbau der direkten Abbildung verglichen werden. Insbesondere liegt das Augenmerk auf der Verwendung des SLM zur Erstellung von Intensitätsmustern im zweidimensionalen optischen Gitter des 2D discrete quantum simulator (DQSIM). Es wurden dafür Muster mit beiden Modulationsmodi aufgenommen und analysiert. Die direkte Abbildung liefert im Vergleich zur Holografie Muster mit besserer Ebenheit, Auflösung und Hintergrund-Dunkelheit bei vergleichbarem Kontrast und Signal-Rausch- Verhältnis. Die Holografie kann jedoch je nach Muster eine höhere Lichtausbeute bieten.

• A. Blendl
  Study Of Decoherence Effects In Cold Atom Optical Lattices, (2019), Master thesisBibTeX
  ABSTRACT »

  This thesis is a study of the decoherence mechanisms effecting the apparatus. A feed forward magnetic field stabilisation is presented, aiming at the reduction of magnetic field noise. Furthermore, the dephasing due to magnetic field noise is classified as homogeneous, by carrying out homogeneous dephasing insensitive Ramsey interferometry. During the process of this thesis an analysis technique was developed to investigate the dephasing due to transition frequency fluctuations of the implemented qubit on the example of magnetic field noise. Revealing a full understanding and prediction of the coherence due to the investigated noise source. As an outlook for further investigations a post correction for magnetic field noise effecting the apparatus is presented, indicating a limit for future magnetic field stabilisations.

• J. Uckert
  Fast Raman transitions for Ramsey interferometry, (2019), Master thesisBibTeX
  ABSTRACT »

  During my time at the 1D experiment, we modified the Raman laser setup with an AOM, supplementary optics and control circuitry to allow us to produce fast Raman pulses. We have successfully demonstrated our ability to induce Rabi oscillations in a sample of Caesium atoms with Rabi frequencies up to 1.4 MHz. We have put this to use to develop a new method to measure the radial temperature in our optical lattice setup and perform Ramsey interferometry. The temperature measurement made use of the Gaussian intensity distribution of the Raman laser beams addressing the atoms and of the subsequent differences in induced Rabi frequency over the trapped atoms. We were able to model the behaviour and extract the radial temperature at laser powers of up to 1 mW per Raman beam.
  We performed Ramsey interferometry with the new system, using a Keysight FPGA for the phase modulation of the π/2 pulses. The new hardware was integrated into the existing experimental sequences and it provides the opportunity to further simplify the setup since three of its output channels are still unused. The Mandelstam-Tamm speed limit was probed by measuring the evolution of the wave function from its initial to an orthogonal state. This measurement was done by performing Ramsey interferometry with an additional lattice shift between the two characteristic π/2 pulses. We verified the validity of the quantum speed limit through our measurements, which showed for trap depths of 14.286 μK, 28.689 μK and 57.813 μK that the evolution time was slower than the limit predicted through calculation.
  
  The content of this thesis will be divided into 3 parts. In the first chapter, I will go over the theory behind the optical lattice setup, how the experiment is designed and the necessary steps towards an experiment-ready atom sample. I will also cover the derivation of the quantum speed limit. The second chapter will treat the design, operation and calibration of the Raman laser setup, which was modified to perform fast pulses, phase modulation of these pulses and ultimately Ramsey interferometry. The third chapter treats the experiments performed with the aforementioned laser setup, the results and analysis. At the end, I will give a short summary and an outlook on the next possible steps to take with the working setup and which further experiments might be performed.

• M. Omar
  Atom cloud compression in a 3D optical lattice and laser intensity stabilisation using an in-house developed photodiode amplifier, (2019), Master thesisBibTeX
  ABSTRACT »

  Our group’s 2D Discrete Quantum Simulator (DQSIM) experiment is dedicated to the idea of a discrete time quantum walk. A quantum walk is the quantum mechanical analogue of a classical random walk. Discrete refers here to the timing in which evolution operators are applied to two quantum systems, a walker and a coin. It not only exhibits different statistics than the classical counterpart but may be employed in a multitude of ways. For example the experimental simulation of a perfect conductor in which Bloch oscillations are performed or the simulation of topological systems that are otherwise inaccessible in solid state physical scales.

  The first chapter reviews the DQSIM setup and necessary concepts to assess the place the content of the thesis is going to take within the experimental effort of our group. Then this thesis deals with two additions to the DQSIM experiment. The first part concerns a specifically designed photodiode amplifier circuit to improve the intensity stabilization of the lattice beams. Improving it would ensure that the coherence time of the atoms isn’t limited by intensity noise any more.

  The second part introduces a scheme to realize compression of atomic ensembles trapped in our optical lattice. Furthermore it is a first step in achieving an efficient single plane selection and addressing in our experiment opening the door to many-particle quantum walks. The thesis concludes with a discussion about initial experimental attempts on compression and a summary of the results.

2018

• M. Sajid
  Magnetic Quantum Walks of Neutral Atoms in Optical Lattices, (2018), PhD thesisBibTeX
  ABSTRACT »

  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.

• D. Löwen
  Intensitätsstabilisierung eines Lasers mit hoher Bandbreite, (2018), Bachelor thesisBibTeX
  ABSTRACT »

  Im Rahmen dieser Arbeit soll die Intensität eines Lasers über eine Feedback-Schleife stabilisiert werden, und dabei soll eine Bandbreite von über einem MHz erreicht werden, da Rauschen und Schwankungen bei diesen und höheren Frequenzen von den Atomen nicht mehr "wahrgenommen" werden. Es ist bereits möglich eine Stabilisierung der Intensität des Lasers mit einer Bandbreite bis zu ungefähr 100kHz aufzubauen. Dieser Aufbau soll in dieser Arbeit optimiert werden, um Rauschen bis zu mindestens einem MHz zu unterdrücken. Dabei soll hauptsächlich ein geeigneter Verstärker gebaut und so angepasst werden, dass er eine optimale Rauschunterdrückung gewährleistet.

• W. Zhou-Hanf
  Robust Holographic Generation of Arbitrary Light Patterns: Method and Implementation, (2018), Master thesisBibTeX
  ABSTRACT »

  In the Discrete Quantum Simulator (DQSIM) experiment in Bonn it has been planned to study topologically protected transport of atoms along the edges separating distinct topological phases. To realize sharp edges, structured intensity patterns will be used and are to be holographically projected onto the caesium atoms trapped in a two-dimensional (2D) state-dependent optical lattice. A robust technique to reproduce sharp-edged diffracted patterns has been accomplished and is presented in this thesis. This technique is based on a Gerchberg-Saxton-like algorithm, which has overcome the well-known stagnation problem and is able to suppress speckles induced by random phase vortices, and has been further extended to create sharp, diffraction-limited edges in the reconstructed intensity pattern. Computer-generated holograms (CGHs) corresponding to the desired intensity patterns can be calculated with high computational efficiency (∼ 100 iterations) and the intensity patterns can be reconstructed with high fidelity (relative RMS 3.9%).

• T. Groh
  Fast transport of single atoms in optical lattices using quantum optimal control, (2018), Master thesisBibTeX
  ABSTRACT »

  This thesis describes the theoretical and experimental work for reaching fast, high fidelity transport operations of single cesium atoms in a state-dependent optical lattice. By applying optimal control theory to position and depth of the optical lattice potential and using a computer simulation judging the fidelity, fast transport sequences preserving the internal atomic quantum state and preventing any motional excitation can be identified. To allow transport times down to a few microseconds the feedback control system used for steering depth and position of the optical lattice deterministically is overdriven in a controlled way. Transport induced motional excitations are measured experimentally by means of a special microwave sideband spectroscopy, which is improved to reliably detect any excitation and allows a full tomography of the vibrational states of the anharmonic optical lattice potential. Optimal control sequences allowing single site transport of atoms in the oscillation period of the trapping potential are believed to reach the fundamental quantum speed limit of the system.

• P. Du
  Optical Intensity Control Based on Digital and Analog Systems, (2018), Master thesisBibTeX
  ABSTRACT »

  In our laboratory, we use cesium atoms, which are trapped in the optical lattices. For the practice of quantum walks, atoms must be well isolated from the noisy environment so that long decoherence time can be achieved. It has been analyzed that fluctuations of the lattice depth originated from intensity fluctuations is one mechanism of decoherence. To suppress the intensity noise of optical lattices, we implement an intensity stabilization control loop based on a field-programmable gate array (FPGA) digital platform (Keysight AIO-H3336F). With the advantages of its integratability and flexibility, the application of digital control opens more possibilities for light intensity modulation. In addition to the intensity stabilization, a feedforward control of light intensity becomes feasible with the use of digital signal processing function of FPGA. The realization of intensity feedforward control provides us with a high bandwidth of intensity modulation as well as the conveniences of creating arbitrary intensity ramp implementation. Therefore, it plays an important role in our exploration into the physics related with a time-varying optical trap depth.

2017

• F. Jaekel
  Aktive Intensitätsstabilisierung eines Lasers mithilfe von Elektrooptischen Modulatoren, (2017), Bachelor thesisBibTeX
  ABSTRACT »

  Der Ansatz, der in dieser Arbeit verfolgt wird, verwendet einen elektrooptischen Modulator, welcher eine Bandbreite im Bereich von 100 MHz hat. Das Ziel dieser Arbeit ist es, eine Intensitätsstabilisierung mit einer Bandbreite von mindestens 10 MHz zu erreichen und die daraus resultierende Verbesserung der Störungsunterdrückung zu demonstrieren. Die nötigen theoretischen Grundlagen sowie die Funktionsweise der Intensitätsstabilisierung mithilfe eines elektrooptischen Modulators werden erarbeitet. Weiterhin werden Aufbauten und Messungen, die zum Erreichen einer hohen Bandbreite erforderlich sind, dargestellt und erklärt.

• C. Robens
  Testing the Quantumness of Atom Trajectories, (2017), PhD thesisBibTeX
  ABSTRACT »

  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.

• A. Knieps
  A Spatial Light Modulator for Steering Quantum Walks with Single-Site Precision, (2017), Master thesisBibTeX
  ABSTRACT »

  This master thesis investigates the potential application of a Liquid Crystal on Silicon Spatial Light Modulator for control of the coin flip operation in a two-dimensional quantum walk. First, the phase noise characteristics of two such modulators from different manufacturers are analyzed. Then an optical setup is constructed to perform holography using phase modulation. The evaluation of this setup verifies pattern generation capability and shows further directions for improvement of image quality.

• M. Werninghaus
  Copy of Controlling atom transport in a two-dimensional state-dependent optical lattice, (2017), Master thesisBibTeX
  ABSTRACT »

  This thesis describes the development of an optical phase lock loop on a digital platform, in order to realize state-dependent transport on a two-dimensional optical lattice. The digital platform consists of a field programmable gate array in combination of a vector generator module, which is used to steer the amplitude and phase of the optical lattice deterministically. The digital system enables the implementation of a feedforward control scheme based on internal model control, which overcomes the bandwidth limitations of feedback systems. The control bandwidth is shown to be increased by more than an order of magnitude, directly improving the number of coherent operations that can be executed with the atoms in the optical lattice. The system is implemented into the optical setup of the experimental apparatus, and the first signatures of state-dependent transport of atoms in the two-dimensional optical lattice is observed and presented.

• M. Werninghaus
  Controlling atom transport in a two-dimensional state-dependent optical lattice, (2017), Master thesisBibTeX
  ABSTRACT »

  The content of this thesis is divided into four parts: In chapter one I will describe the experimental techniques and scientific principles used to realize transport in state-dependent optical lattices in two dimensions. The second chapter is dedicated to introducing the digital device platform and a characterization of its basic properties. In the third chapter I will give an overview of control theory with a focus on the fundamentals of feedback control. In addition, I will explain the implementation of the control loops on the digital system in the second part of the chapter. At the end of this chapter, I will present how an internal model control of the lattice can be implemented on the digital platform. The experimental results on state-dependent transport are presented in the last chapter. Furthermore, I will give an outlook of future milestones of the two-dimensional quantum walk experiment.

2016

• W. Zhou-Hanf
  Analyse der Punktspreizfunktion des Abbildungssystems vom DQSIM-Experiment anhand der Fluoreszenzaufnahmen, (2016), Bachelor thesisBibTeX
  ABSTRACT »

  Diese Arbeit beschäftigt sich mit der Untersuchung der Atomfluoreszenzbilder, die im DQSIM - Experiment aufgenommen worden sind. Die Fluoreszenzmikroskopie bzgl. des zweidimensionalen Vielteilchensystems hat eine wichtige Bedeutung für das messungsbasierte Quantenrechnen mit Clusterzuständen. Anhand der Fluoreszenzaufnahmen wird das Abbildungsprinzip erläutert, das Konzept der Punktspreizfunktion (engl. point spread function, kurz PSF) und der Faltung wird eingeführt und deren mathematische Eigenschaften werden vorgestellt. Durch die Analyse der PSF wird die reale numerische Apertur (kurz NA) zusammen mit dem Strehl-Verhältnis (engl. Strehl ratio) untersucht. Die Anwendung der Zernike-Polynome wird ebenso einen Einblick in die Analyse der optischen Aberrationen eines Abbildungssystems anbieten.

• S. Brakhane
  The Quantum Walk Microscope, (2016), PhD thesisBibTeX
  ABSTRACT »

  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.

2015

• T. Groh
  Dekohärenzeffekte in topologischen Phasen von Quantenwalks, (2015), Bachelor thesisBibTeX
  ABSTRACT »

  Die Klassifizierung von Quantenwalks über topologische Phasen ermöglicht die Erklärung der Existenz geschützter Zustände an räumlichen Phasengrenzen. In dieser Arbeit wird die Einwirkung von Dekohärenzeffekten auf die Existenz und Form dieser topologisch geschützten Zuständen in Quantenwalks mit diskreter Zeit auf ein- und zweidimensionalen diskreten Gittern simuliert und untersucht. Für die zeitliche Entwicklung topologisch geschützter, lokalisierter Randzustände wird im eindimensionalen System ein einfaches Modell gefunden. Die Grenzen des verwendeten Dekohärenzmodells werden durch die Konstruktion eines dekohärenzfreien Quantenwalk-Protokolls aufgezeigt. Außerdem wer- den die Möglichkeiten und Einschränkungen einer experimentellen Realisierung von topologischen Effekten in Quantenwalks mit neutralen Atomen in optischen Gittern simuliert und analysiert.

• P. Weitz
  Aufbau und Charakterisierung eines Stokes Polarimeters, (2015), Bachelor thesisBibTeX
  ABSTRACT »

  Den Polarisationszustand elektromagnetischer Strahlung zu kennen, und kontrollieren zu können, ist in der modernen Physik von großer Wichtigkeit. Beispielsweise braucht man zum Laserkühlen von Atomen eine klar definierte Polarisation. Ziel dieser Bachelorarbeit ist es ein Polarimeter aufzubauen, welches die Polarisation eines einfallenden Laserstrahls misst und Auskunft darüber zu geben, wie genau es Polarisationen messen kann. Ferner sollen die wichtigsten systematischen Messfehler untersucht und charakterisiert werden.

  Ein Stokes-Polarimeter wurde erfolgreich aufgebaut und getestet. Es wurde gezeigt, dass die Genauigkeit des Polarimeters von der Polarisation abhängig ist, wobei es zirkulare Polarisation besser als auf 0.5% genau messen kann. Über die Möglichkeit, die zirkulare Polarisation genauer zu messen, lässt sich nichts aussagen, da die Polarisation nicht genauer eingestellt werden konnte. Die Güte der Messung der linearen Polarisation wird am stärksten durch die genaue Kenntnis des Winkels zwischen schneller Achse der QWP und der Polarisationsachse des Analysators bestimmt. Mit der Kenntnis dieses Winkels auf 0.2º genau ist es auch möglich, lineare Polarisation mit 1% Genauigkeit zu messen. Eine Ausnahme stellt hier die horizontale Polarisation dar, bei der eine Abweichung von 5% von den erwarteten Werten beobachtet wurde. Mögliche Ursachen hierfür sind eine geringere Verzögerung der QWP und ein Offset der Intensitätsmessung, der weiter untersucht werden muss. Ferner wurde Wave-Plate-Ripple als eine weitere Fehlerquelle identifiziert und eine qualitative Abschätzung seiner Einflüsse gegeben.

• V. Schilling
  A Magnetic Elevator for Neutral Atoms into a 2D State-dependent Optical Lattice Experiment, (2015), Master thesisBibTeX
  ABSTRACT »

  This master thesis contains two major parts. On the theoretical side simulating the state-dependent transport of neutral caesium atoms in a two-dimensional optical lattice gives an intuitive picture of the state-dependent potential during transport. The more practical part deals with the task to load the atoms into the lattice since they cannot be trapped directly in the plane of the experiment. A magneto-optical trap in a distance of about ∼2 mm below the lattice traps atoms out of the vacuum background and lift them afterwards into the lattice. This is realised using a precise electronic control of the imbalance of current guided through the two coils for building up the required quadrupole field by diverting a certain amount of current around one coil. Analysis of the step-response signal of the used metal band coils yields mandatory characteristics for achieving a fast and stable control. A galvanic isolated signal transfer protects the computer control against damage due to accidental voltage pulses from the high-power system. The diverted current can change with ∼0.9 A ms⁻¹.

2014

• F. Kleißler
  Assembly and Characterization of a High Numerical Aperture Microscope for Single Atoms, (2014), Master thesisBibTeX
  ABSTRACT »

  This master thesis investigates the optical imaging properties of a state of the art in-house developed objective for the observation of single atoms trapped in a two-dimensional spin-dependent optical lattice. After the successful assembly of the objective lenses into a ceramic holder two different approaches for the characterization are presented. First a wave-front analysis for the estimation of the root-mean-square deviation to a planar reference using a Shack-Hartmann sensor and a Shearing interferometer is performed. In the second approach the imaging of a point-like light-source is utilized to determine the point-spread-function of the objective. The production of the probes is inspired by methods of optical microscopy in the nano-scale regime like Total-Internal-Reflexion-Fluorescence- and Scanning-Nearfield-Optical-Microscopy. Self-written MATLAB-routines are used to extract quantitative information on the imaging system. The analysis in this work shows that the objective can operate close to diffraction limit with a numerical aperture of 0.9. Numerically calculated point-spread-functions are compared to the measurements to explain the small deviations to the perfect Airy pattern. A very good agreement has been found between the point-spread-function calculated numerically and that measured in the characterization set-up.

• J. Zopes
  Sorting atoms in spin-dependent optical lattices, (2014), Master thesisBibTeX
  ABSTRACT »

  This work reports on the implementation of feedback methods for position control of single Cesium atoms in spin-dependent optical lattices. For this purpose a new control software has been developed. It encapsulates experimental control, fluorescence image acquisition and analysis into a single program. Combining the new software with spin-dependent transport and position-dependent addressing, we have developed a versatile feedback algorithm to deterministically arrange arbitrary patterns of up to 6 atoms. In addition, we have prepared two atoms in a common lattice site. We observed light-assisted collisions between both atoms and thereby characterized the preparation effciency of 83 ± 4 %. The results pave the way for the study of controlled interactions between precisely two atoms in a single well of the optical lattice potential, enabling the realization of a fundamental quantum logic gate.

• I. Boventer
  Characterisation of Phase Noise for the Preparation of Atoms in the Motional Ground State, (2014), Master thesisBibTeX
  ABSTRACT »

  Contents 1 Introduction 1 2 Setup for Raman Sideband Cooling with Phase Noise Characterisation 2.1 The optical dipole potential 2.2 The motional groundstate 2.3 Raman Transitions 2.4 Stabilization of the Phase 2.5 Phase Noise by a Quadrature Measurement 2.6 Experimental Setup 2.7 Cooling into the ground state 2.8 Summary 3 Common Mode OpticalPhase Noise of the Optical Lattice 3.1 Experimental Setup 3.2 The Interferometer 3.3 Generation of the Beat Signal 3.4 Power Spectral Density (PSD) 3.5 Measurements and Results 3.6 Analysis of Displacements of Atoms 4 Quadrature Interferometer 4.1 Experimental test apparatus 4.2 Stability and temporal drifts 4.3 Considerations for experimental realization in SDT 4.4 Outlook 5 Conclusion and Outlook 6 Appendix 6.1 Schematic of Lead-Lag Filter in OPLL 6.2 Relation between fraction of total power below carrier and RMS phase noise 6.3 Required sensitivity for quadrature interferometer

• S. Shestovyy
  Entwicklung eines hochstabilen optischen Phasendetektors für Licht-Polarisationssynthese, (2014), Diplom thesisBibTeX
  ABSTRACT »

  Diese Arbeit beschäftigt sich mit der Optimierung der elektronischen Elemente für eine optische Phasenregelschleife, welche ein zweidimensionales Dipolgitter regeln soll. Insbesondere wird ein hochstabiler optischer Phasendetektor entwickelt und charakterisiert. Dieser wird in dem entstehendem zweidimensionalen Digitalen Quantensimulator eingesetzt. Mit DQSIM werden einige neue Simulationsmöglichkeiten gegenüber dem bestehendem eindimensionalen Digitalen Quantensimulator eröffnet, wie z.B. Simulation künstlicher Magnetfelder oder Untersuchung eines zweidimensionalen Systems wie Graphen.

• S. Reichel
  Mikroprozessorgesteuerte Fasereinkopplung, (2014), Bachelor thesisBibTeX

2013

• A. Steffen
  Single atom interferometers and Bloch oscillations in quantum walks, (2013), PhD thesisBibTeX
  ABSTRACT »

  This thesis deals with the digital manipulation of the position and spin of neutral Caesium atoms in an optical lattice. I investigate coherent phenomena based on interferences between the trajectories of a single atom. Individual atoms are split by making use of our state-dependent lattice to shift different spin states in opposite directions, leading to coherent superpositions of spin and position state. This offers many possibilities; in this work, we chose to investigate atom interferometry and quantum walks in potential gradients. Chapter 1 is a brief introduction to the importance of phase in quantum mechanics. In chapter 2, I provide an introduction to our experimental apparatus with particular focus on state-dependent shifting and correct alignment procedures. Our model for decoherence in the lattice is also presented, with emphasis on the polarization state of the lattice lasers. Chapter 3 presents the first of two measurement campaigns, which employs a single atom interferometer with a flexible geometry. We investigate a laser intensity gradient present in the system and demonstrate how several interferometer geometries can be compared to glean extra information about the symmetries of a potential gradient, such as its spin state dependence. A deliberately applied inertial force serves as a proof-of-principle for accelerometry and is correctly measured. Chapter 4 contains the results of the second measurement campaign, which focussed on quantum walks. Quantum walks are a quantum analog to classical random walks and possess remarkable spreading properties. A theoretical model is presented, including a band structure picture of the walk. Unlike previous experiments, the walk can now be performed in a potential gradient, giving rise to new physics, in particular Bloch oscillations, which manifest as oscillations of the distribution width. Experimental results first confirm the predictions made by our model and show quantum walks of up to 100 steps with coherent behaviour. Walks in potential gradients are measured and indeed show clear signatures of Bloch oscillations. This is particularly remarkable because the quantum walk is effectively mimicking an electron in a solid, forming a basic quantum simulator. Chapter 5 is a conclusion and a preview on ongoing technical improvements that stand to significantly extend the experimental capabilities.

• J. Huisman
  State-dependent Atom Transport in Polarization Synthesized Optical Lattices: An Estimation of Dephasing Inlfuences, (2013), Bachelor thesisBibTeX

2012

• A. Hambitzer
  Direct Synthesis of Light Polarization for State-Dependent Transport, (2012), Master thesisBibTeX
  ABSTRACT »

  This master-thesis investigates a new approach for state-dependent transport of atoms in an optical lattice. It is based on a direct synthesis of light polarization by superimposing two circular polarized beams and employing RF sources integrated with acousto-optic modulators for phase control. An interferometrically stable phase between the two beams is achieved by locking them actively with a heterodyne technique. The influence of polarization crosstalk and erroneous components on the optical lattice and the phase locked loop are investigated and the quality of the phase locked loop is analyzed.

  Compared to conventional methods [25] the direct synthesis method avoids the need of an electro-optic modulator, where rotations on the Poincare sphere are limited by the applicable voltage and restrictions on manufacturing and crystal quality exist. Overcoming these limitations it is expected to reach higher polarization purity and larger shift distances in the new design.

• M. Genske
  Electric Quantum Walks with Individual Atoms, (2012), Master thesisBibTeX
  ABSTRACT »

  The experimental realisation of electric quantum walks, i.e. quantum walks that are subject to a force, is presented with individual caesium atoms. Hereby, the behaviour of a charged quantum particle in a static electric eld is simulated in a time as well as space discrete system. Building on previous achievements [1], the demonstration of ordinary quantum walks of up to 100 steps is shown. Further thorough theoretical studies expose the underlying simulator properties of such a quantum walk system experiencing a force. Similarities to the continuous time analogue as well as characteristic features that are indebted to the discrete evolution of the system are presented. The implementation of a direct digital synthesizer allows the experimental application of discrete forces in the system by employing frequency ramps, and thus leads to the realisation of electric walks. Results are given for selected force parameters, showing the phenomenon of Bloch oscillations. Additionally, pure ballistic transport of the electric quantum walk due to strong Landau-Zener tunnelling in the strong force regime is demonstrated.

• D. Kim
  Quantum Register Initialization via Deterministic Atom Sorting in Optical Lattices, (2012), Master thesisBibTeX

• J. Zopes
  Einzelplatz-Detektion im optischen Gitter unterhalb des Beugungslimits, (2012), Bachelor thesisBibTeX

• S. Arnoldt
  Rotating Quarter-Wave Plate Stokes Polarimeter, (2012), Bachelor thesisBibTeX

2011

• S. Hild
  Resolved Raman sideband cooling in a doughnut-shaped optical trap, (2011), Master thesisBibTeX

2010

• A. Mawardi
  Generation of a donut beam for a tight radial confinement of atoms in a one-dimensional optical lattice, (2010), Master thesisBibTeX

• M. Karski
  State-selective transport of single neutral atoms, (2010), PhD thesisBibTeX
  ABSTRACT »

  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.

• L. Förster
  Microwave control of atomic motion in a spin dependent optical lattice, (2010), PhD thesisBibTeX
  ABSTRACT »

  In this thesis I present my results concerning the coherent control of the quantized motional state of trapped neutral Cesium atoms. This is accomplished using microwave radiation in combination with a spin dependent potential conning the atoms. I present both cooling of atoms close to the motional ground state and the preparation of nonclassical motional states. In total, our apparatus is thus capable to control the spin, the position along the periodic potential and the vibrational state of the atoms. In chapter 1 I give an overview of the experimental apparatus. Our setup is designed to trap and to store on the order of ten atoms in a one dimensional optical lattice. Fluorescence imaging in conjunction with a microscope lens system is used to determine both the number and the position of the atoms. The spin degree of freedom is manipulated using microwave radiation and the trapping potential allows to shift the atoms to the 'left' or to the 'right' along the potential axis, depending on their spin orientation. In chapter 2 I discuss the coupling mechanism between the spin and the motional degree of freedom. A microwave spectrum with a slightly displaced lattice exhibits sideband peaks corresponding to a change of the vibrational quantum number. For the full quantitative understanding I compare the experimental results with a theoretical model, which is also used to quantify possible decoherence mechanisms. Based on this investigations, in chapter 3 I present the results for our ground state cooling scheme, whereby the focuss lies on the peculiarities of our system. A model based on master equations is used to analyze the present cooling limits. In chapter 4, nally, two detection schemes for arbitrary motional states of an atomic ensemble are presented. In particular, they are employed to verify the preparation of nonclassical states.

• K. Katayama
  Optical Phase Lock Loops and Raman-Cooling, (2010), Master thesisBibTeX

2008

• F. Grenz
  Ein System zur entarteten Raman-Seitenbandkühlung einzelner Cäsium-Atome , (2008), Diplom thesisBibTeX

2007

• D. Döring
  Ein Experiment zum zustandsabhängigen Transport einzelner Atome, (2007), Diplom thesisBibTeX

• A. Härter
  Ein Aufbau zur kohärenten Manipulation und zum zustandsabhängigen Transport einzelner Atome, (2007), Diplom thesisBibTeX