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Millikelvin confocal microscopy of electrostatic exciton traps and filter-function description of noisy quantum dynamics

Tobias Hangleiter

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum technology promises to be a paradigm shift in the precision, speed, and breadth of application of technology. Recent advances in the fields of quantum computing, quantum networks, and quantum sensing have been rapid, but large-scale utilization is still out of reach. This is largely due to the fragility of the individual quantum systems that this technology seeks to control and manipulate. While small demonstrators have by now shown these novel machines to work in principle, the task in the coming years will be to make them reproducible at scale. Leveraging the advanced semiconductor fabrication technology of today's classical computers, spin qubits in semiconductors such as Si/SiGe or GaAs/AlGaAs are hoped to meet this challenge. In this thesis, I present contributions in four different areas towards this overarching goal. I present an open-source software tool for Fourier-transform noise spectroscopy, improvements and characterization of a Millikelvin confocal microscope, optical measurements of electrostatic exciton traps, and a general filter-function formalism for the description of noisy quantum dynamics. I review the theory of noise spectroscopy based on Welch's method of overlapping periodograms and lay out the design of the hardware-agnostic, open-source python_spectrometer software package that facilitates interactive noise spectroscopy in everyday use. In a didactic fashion, I explore the features and capabilities of the tool and guide the reader through its operation. I then characterize a confocal microscope incorporated in a cryogen-free dilution refrigerator, applying the aforementioned noise spectroscopy tool to evaluate the displacement noise power spectral density of the system. I develop an optical technique based on a knife-edge reflectance contrast to measure the displacement noise reaching a shot-noise floor of 1 nm/√Hz. Using this technique, I determine a displacement noise RMS of 100 nm. I measure the electron temperature of a GaAs/AlGaAs quantum dot in the microscope, finding 76 mK, and demonstrate at hand of a second-order correlation measurement of a self-assembled quantum dot the setup's optical capabilities. In the experimental part of this thesis, I first provide an introduction to photoluminescence and the quantum-confined Stark effect in semiconductor quantum wells, appealing to simple analytical theory to develop an intuition for the relevant effects. I then describe the mjolnir measurement framework developed to conduct optical measurements of electrostatic exciton traps in semiconductor membranes, and present extensive measurements in search of signatures of single-photon emitters. Finally, I develop a comprehensive theoretical formalism for describing and analyzing the noisy dynamics of quantum systems based on filter functions. There, I combine the Magnus and cumulant expansions to derive a quantum-operations formulation of the dynamics under arbitrary classical noise that can be expressed in terms of filter functions capturing the susceptibility of a quantum system in response to noise at a given frequency. I present the filter_functions software package that implements the formalism and demonstrate its efficacy using several examples.

DOI
10.18154/rwth-2026-04707

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Cryogenic confocal microscopy is a powerful method for studying solid state quantum devices such as single photon sources and optically controlled qubits. While the vast majority of such studies have been conducted at temperatures of a few Kelvin, experiments involving fragile quantum effects often require lower operating temperatures. To also allow for electrical dynamic control, microwave connectivity is required. For polarization-sensitive studies, free space optical access is advantageous compared to fiber coupling. Here we present a confocal microscope in a dilution refrigerator providing all the above features at temperatures below 100 mK. The installed high frequency cabling meets the requirements for state-of-the-art spin qubit experiments. As another unique advantage of our system, the sample fitting inside a large puck can be exchanged while keeping the cryostat cold with minimal realignment. Assessing the performance of the instrument, we demonstrate confocal imaging, sub-nanosecond modulation of the emission wavelength of a suitable sample, and an electron temperature of 76 mK. While the instrument was constructed primarily with the development of optical interfaces to electrically controlled qubits in mind, it can be used for many experiments involving quantum transport, solid state quantum optics, and microwave-optical transducers.
Cryogenic confocal microscopy is a powerful method for studying solid state quantum devices such as single photon sources and optically controlled qubits. While the vast majority of such studies have been conducted at temperatures of a few Kelvin, experiments involving fragile quantum effects often require lower operating temperatures. To also allow for electrical dynamic control, microwave connectivity is required. For polarization-sensitive studies, free space optical access is advantageous compared to fiber coupling. Here we present a confocal microscope in a dilution refrigerator providing all the above features at temperatures below 100 mK. The installed high frequency cabling meets the requirements for state of the art spin qubit experiments. As another unique advantage of our system, the sample fitting inside a large puck can be exchanged while keeping the cryostat cold with minimal realignment. Assessing the performance of the instrument, we demonstrate confocal imaging, sub-nanosecond modulation of the emission wavelength of a suitable sample and an electron temperature of 76 mK. While the instrument was constructed primarily with the development of optical interfaces to electrically controlled qubits in mind, it can be used for many experiments involving quantum transport, solid state quantum optics and microwave-optical transducers.
This thesis reports the development of a quantum enhanced microparticle tracking technique, which applied to measurements within living cells, allowed the first demonstrations of both biological measurements beyond the quantum noise limit and quantum enhanced spatial resolution within biology. The sensitivity of any optical measurement is limited by noise which follows from quantization of the electromagnetic field. This thesis theoretically characterizes the resulting quantum limit on particle tracking precision; both in the limit of perfect measurements and for the measurements used in real experiments, and theoretically establishes an experimental strategy which could allow the quantum limit to be surpassed via the application of non-classical light. Further, a computational tool is developed which allows rapid characterization of particle tracking experiments, thus providing researchers the benefit of rigorous theoretical predictions without requiring detailed calculations. Following this, classical technologies are developed which can improve microparticle tracking sensitivity and which are enabling steps toward integration of non-classical light. An interferometric strategy is described whereby signal-to-noise is improved by removing unwanted light from the detector. An optical lock-in technique is developed which eliminates low-frequency noise, thus allowing quantum noise limited performance at low frequencies. This is a crucial requirement for quantum enhanced measurements, and can also improve precision in classical experiments. Dark-field illumination is also explored as a method to remove unwanted background light, and the optimal illumination angle is calculated for our intended experiments. These advances are then applied in the development of the first quantum enhanced particle tracking apparatus. Squeezed states of light are used to improve particle tracking precision by 2.7 dB, demonstrating quantum enhanced microscopy for the first time. This was applied to perform the first measurements of living systems with quantum enhanced precision. Naturally occurring lipid particles were tracked within the cytoplasm of Saccharomyces cerevisiae yeast cells, with squeezed light enhancing precision by 2.4 dB. The thermal motion of these particles could then be analyzed to infer the viscosity and elasticity of the local environment, with squeezed light allowing 64% faster observations, thus improving the sensitivity to dynamic biological changes. This experiment was then extended to spatially resolved quantum imaging, with lipid particles used as scanning probes in a technique called photonic force microscopy. The particles sample variations in the local environment with resolution limited by measurement precision rather than the diffraction limit. The use of squeezed light was found to enhance spatial resolution by 14% at an absolute resolution level of 10 nm, comparable to leading classical experiments. This was the first demonstration of both sub-diffraction limited resolution and quantum enhanced resolution in biology, and places practical applications of quantum imaging within reach. Finally, the future challenges and prospects of quantum enhanced particle tracking are outlined.n
The electromagnetic manipulation of isolated ions has led to many advances in atomic physics, from laser cooling to precision metrology and quantum control. As technical capability in this area has grown, so has interest in building miniature electromagnetic traps for the development of large-scale quantum information processors. This thesis will primarily focus on using microfabrication techniques to build arrays of miniature ion traps, similar to techniques used in fabricating high component density microprocessors. A specific focus will be on research using a gallium arsenide/aluminum gallium arsenide heterostructure as a trap architecture, as well as the recent testing of different ion traps fabricated at outside foundries. The construction and characterization of a conventional ceramic trap capable of shuttling an ion through a junction will also be detailed, and reveal the need for moving towards lithographically fabricated traps. Combined, these serve as a set of proof-of-principle experiments pointing to methods for designing and building large scale arrays of ion traps capable of constituting a quantum information processor. As traps become smaller, electrical potentials on the electrodes have greater influence on the ion. This not only pertains to intentionally applied voltages, but also to deleterious noise sources, such as thermal Johnson noise and the more significant ``patch potential" noise, which both cause motional heating of the ion. These problematic noise sources dovetail with my thesis research into trap miniaturization since their effects become more pronounced and impossible to ignore for small trap sizes. Therefore characterizing them and investigating ways to suppress them have become an important component of my research. I will describe an experiment using a pair of movable needle electrodes to measure the ion heating rate corresponding to the harmonic frequency of the trap, the ion-electrode distance, and the electrode temperature. This information is used for characterizing the fluctuating potentials and exploring the possibility of suppressing motional heating by cooling the trap electrodes. This source of noise is also observed in other systems, and its characterization could potentially improve other precision experiments, such as those measuring deviations in the gravitational inverse square law with proximate masses.
Second generation quantum technologies aim to outperform classical alternatives by utilizing engineered quantum systems. Maintaining the coherence required to enable any quantum advantage requires detailed knowledge and control over the noise that the hosting system is subjected to. Characterizing noise processes via their power spectral density is routinely done throughout science and technology and can be a demanding task. Determining the phase noise power spectrum in leading quantum technology platforms, for example, can be either outside the reach of many phase noise analyzers or prohibitively expensive. In this work, we present and characterize a low-complexity, low-cost optical phase noise analyzer based on the short-delay optical self-heterodyne measurements for quantum technology applications. Using this setup, we compare two ≈1 Hz linewidth ultra-stable oscillators near 729 nm. Their measurements are used as a baseline to determine and discuss the noise floor achieved in this measurement apparatus with a focus on limitations and their tradeoffs. The achieved noise floor in this all-stock-component implementation of an optical phase noise analyzer compares favorably with commercial offerings. This setup can be used particularly without a more stable reference or operational quantum system as a sensor as would be the case for many component manufacturers.