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Quantum technologies

Dieter Meschede's research group
Theses - Quantum walks


  • C. Robens
    Testing the Quantumness of Atom Trajectories, (2017), PhD thesisBibTeXPDF

    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 thesisBibTeXPDF

    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.


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

    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 thesisBibTeXPDF

    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.


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

    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 thesisBibTeXPDF

    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.


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

    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 thesisBibTeXPDF
    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 thesisBibTeXPDF
    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.


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


  • M. Genske
    Electric Quantum Walks with Individual Atoms, (2012), Master thesisBibTeXPDF

    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.