Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Optimization of the Mechanical and Optical Properties of Tunable Optical Sensor Arrays (TOSA) for a Nanospectrometer in the Visible and Near Infrared Spectral Range

Tunable Optical Sensor Arrays (TOSA) based on Fabry-Pérot (FP) filters, for high quality spectroscopic applications in the visible and near infrared spectral range are investigated within this work. The optical performance of the FP filters is improved by using ion beam sputtered niobium pentoxide (Nb2O5) and silicon dioxide (SiO2) Distributed Bragg Reflectors (DBRs) as mirrors. Due to their high refractive index contrast, only a few alternating pairs of Nb2O5 and SiO2 films can achieve DBRs with high reflectivity in a wide spectral range, while ion beam sputter deposition (IBSD) is utilized due to its ability to produce films with high optical purity. However, IBSD films are highly stressed; resulting in stress induced mirror curvature and suspension bending in the free standing filter suspensions of the MEMS (Micro-Electro-Mechanical Systems) FP filters. Stress induced mirror curvature results in filter transmission line degradation, while suspension bending results in high required filter tuning voltages. Moreover, stress induced suspension bending results in higher order mode filter operation which in turn degrades the optical resolution of the filter. Therefore, the deposition process is optimized to achieve both near zero absorption and low residual stress. High energy ion bombardment during film deposition is utilized to reduce the film density, and hence the film compressive stress. Utilizing this technique, the compressive stress of Nb2O5 is reduced by ~43%, while that for SiO2 is reduced by ~40%. Filters fabricated with stress reduced films show curvatures as low as 100 nm for 70 μm mirrors. To reduce the stress induced bending in the free standing filter suspensions, a stress optimized multi-layer suspension design is presented; with a tensile stressed metal sandwiched between two compressively stressed films. The stress in Physical Vapor Deposited (PVD) metals is therefore characterized for use as filter top-electrode and stress compensating layer. Surface micromachining is used to fabricate tunable FP filters in the visible spectral range using the above mentioned design. The upward bending of the suspensions is reduced from several micrometers to less than 100 nm and 250 nm for two different suspension layer combinations. Mechanical tuning of up to 188 nm is obtained by applying 40 V of actuation voltage. Alternatively, a filter line with transmission of 65.5%, Full Width at Half Maximum (FWHM) of 10.5 nm and a stopband of 170 nm (at an output wavelength of 594 nm) is achieved. Numerical model simulations are also performed to study the validity of the stress optimized suspension design for the near infrared spectral range, wherein membrane displacement and suspension deformation due to material residual stress is studied. Two bandpass filter designs based on quarter-wave and non-quarter-wave layers are presented as integral components of the TOSA. With a filter passband of 135 nm and a broad stopband of over 650 nm, high average filter transmission of 88% is achieved inside the passband, while maximum filter transmission of less than 1.6% outside the passband is achieved.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

Auf Basis umfangreicher Messdatensätze experimentell und numerisch validierte Regeln zur optimierten Auslegung von Luft-Erdwärmetauschern

Ein Luft-Erdwärmetauscher (L-EWT) kommt wegen seines niedrigen Energiebedarfs und möglicher guter Aufwandszahlen als umweltfreundliche Versorgungskomponente für Gebäude in Betracht. Dabei ist besonders vorteilhaft, dass ein L-EWT die Umgebungsluft je nach Jahreszeit vorwärmen oder auch kühlen kann. Dem zufolge sind L-EWT zur Energieeinsparung nicht nur für den Wohnhausbau interessant, sondern auch dort, wo immer noch große Mengen an fossiler Energie für die Raumkühlung benötigt werden, im Büro- und Produktionsgebäudesektor. Der Einsatzbereich eines L-EWT liegt zwischen Volumenströmen von 100 m3/h und mehreren 100.000 m3/h. Aus dieser Bandbreite und den instationären Randbedingungen entstehen erhebliche Schwierigkeiten, allgemeingültige Aussagen über das zu erwartende thermische Systemverhalten aus der Vielzahl möglicher Konstruktionsvarianten zu treffen. Hauptziel dieser Arbeit ist es, auf Basis umfangreicher, mehrjähriger Messungen an einer eigens konzipierten Testanlage und eines speziell angepassten numerischen Rechenmodells, Kennzahlen zu entwickeln, die es ermöglichen, die Betriebseigenschaften eines L-EWT im Planungsalltag zu bestimmen und ein technisch, ökologisch wie ökonomisch effizientes System zu identifizieren. Es werden die Kennzahlen elewt (Aufwandszahl), QV (Netto-Volumenleistung), ME (Meterertrag), sowie die Kombination aus v (Strömungsgeschwindigkeit) und VL (Metervolumenstrom) definiert, die zu wichtigen Informationen führen, mit denen die Qualität von Systemvarianten in der Planungsphase bewertet werden können. Weiterführende Erkenntnisse über die genauere Abschätzung von Bodenkennwerten werden dargestellt. Die hygienische Situation der durch den L-EWT transportierten Luft wird für die warme Jahreszeit, aufgrund auftretender Tauwasserbildung, beschrieben. Aus diesem Grund werden alle relevanten lufthygienischen Parameter in mehreren aufwendigen Messkampagnen erfasst und auf pathogene Wirkungen überprüft. Es wird über Sensitivitätsanalysen gezeigt, welche Fehler bei Annahme falscher Randbedingungen eintreten. Weiterhin werden in dieser Arbeit wesentliche, grundsätzliche Erkenntnisse aufbereitet, die sich aus der Betriebsbeobachtung und der Auswertung der umfangreich vorliegenden Messdaten mehrerer Anlagen ergeben haben und für die praktische Umsetzung und die Betriebsführung bedeutend sind. Hinweise zu Materialeigenschaften und zur Systemwirtschaftlichkeit sind detailliert aufgeführt.