The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an introduction to the thermodynamics of small quantum systems. It is illustrated how the laws of thermodynamics emerge from quantum theory and how open quantum systems can be modeled by Markovian master equations. Quantum systems that are designed to perform a certain task, such as cooling or generating entanglement are considered. Finally, the effect of fluctuations on the thermodynamic description is discussed.

Color center spins in diamond nanostructures are a key resource for emerging quantum technologies. Their innate surface proximity makes precise control of diamond surface chemistry essential for optimizing their functionality and charge states. However, conventional surface functionalization methods typically lack the tunability and efficiency required for robust charge-state control. Here, we introduce a deterministic, nonvolatile technique for continuously and efficiently tuning diamond's surface termination via laser-induced oxidation of H-terminated diamond nanopillars. By tracking SiV$^-$ photoluminescence as a charge-state proxy, we uncover the microscopic mechanism of this photocatalytic process through a systematic photon-flux and -energy analysis, where we identify charge-cycling of native defects as sources of optically generated holes driving the desired surface oxidation. Our results suggest that our method applies broadly to other color centers and host materials, offering a versatile tool for on-demand charge-state control and surface engineering in solid-state quantum devices.

The laws of thermodynamics are a cornerstone of physics. At the nanoscale, where fluctuations and quantum effects matter, there is no unique thermodynamic framework because thermodynamic quantities such as heat and work depend on the accessibility of the degrees of freedom. We derive a thermodynamic framework for coherently driven systems, where the output light is assumed to be accessible. The resulting second law of thermodynamics is strictly tighter than the conventional one and it demands the output light to be more noisy than the input light. We illustrate our framework across several well-established models and we show how the three-level maser can be understood as an engine that reduces the noise of a coherent drive. Our framework opens a new avenue for investigating the noise properties of driven-dissipative quantum systems.

Highly transparent superconducting contacts to a topological insulator (TI) remain a persistent challenge on the route to engineer topological superconductivity. Recently, the higher-order TI WTe$_2$ was shown to turn superconducting when placed on palladium (Pd) bottom contacts, demonstrating a promising material system in pursuing this goal. Here, we report the diffusion of Pd into WTe$_2$ and the formation of superconducting PdTe$_x$ as the origin of observed superconductivity. We find an atomically sharp interface in vertical direction to the van der Waals layers between the diffusion crystal and its host crystal, forming state-of-the-art superconducting contacts to a TI. The diffusion is discovered to be non-uniform along the width of the WTe$_2$ crystal, with a greater extend along the edges compared to the bulk. The potential of this contacting method is highlighted in transport measurements on Josephson junctions by employing external superconducting leads.

The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In this work, we lay out a formalism for the laws of thermodynamics in an open quantum system under continuous measurement and feedback described by a Quantum Fokker Planck Master Equation. We derive expressions for work, heat, and measurement-induced energy changes, and we investigate entropy production and fluctuation theorems. We illustrate our results with a continuous version of a measurement-driven Szilard engine, as well as a work extraction scheme in a two-level system under bang-bang control. Our results provide insights into the energetics as well as the irreversibility of classical and quantum systems under continuous feedback control.

The inhomogeneous magnetic stray field of micromagnets has been extensively used to manipulate electron spin qubits. By means of micromagnetic simulations and scanning superconducting quantum interference device microscopy, we show that the polycrystallinity of the magnet and non-uniform magnetization significantly impact the stray field and corresponding qubit properties. We find that the random orientation of the crystal axis in polycrystalline Co magnets alters the qubit frequencies by up to 0.5 GHz, compromising single qubit addressability and single gate fidelities. We map the stray field of Fe micromagnets with an applied magnetic field of up to 500 mT (mimicking conditions when operating qubits), finding field gradients above 1 mT/nm. The measured gradients and the lower magnetocrystalline anisotropy of Fe demonstrate the advantage of using Fe instead of Co for magnets in spin qubit devices. These properties of Fe also enabled us to design a 2D arrangement of nanomagnets for driving spin qubits distributed on a 2D lattice.

We investigate experimentally the quantum coherence of an electronic two-level system in a double quantum dot under continuous charge detection. The charge-state of the two-level system is monitored by a capacitively coupled single quantum dot detector that imposes a back-action effect to the system. The measured back-action is well described by an additional decoherence rate, approximately linearly proportional to the detector electron tunneling rate. We provide a model for the decoherence rate arising due to level detuning fluctuations induced by detector charge fluctuations. The theory predicts a factor of two lower decoherence rate than observed in the experiment, suggesting the need for a more elaborate theory accounting for additional sources of decoherence.

Planar semiconductor heterostructures offer versatile device designs and are promising candidates for scalable quantum computing. Notably, heterostructures based on strained germanium have been extensively studied in recent years, with emphasis on their strong and tunable spin-orbit interaction, low effective mass, and high hole mobility. However, planar systems are still limited by the fact that the shape of the confinement potential is directly related to the density. In this work, we present the successful implementation of a backgate for a planar germanium heterostructure. The backgate, in combination with a topgate, enables independent control over the density and the electric field, which determines important state properties such as the effective mass, the $g$-factor and the quantum lifetime. This unparalleled degree of control paves the way towards engineering qubit properties and facilitates the targetted tuning of bilayer quantum wells, which promise denser qubit packing.

Metal-assisted chemical etching of silicon is a promising method for fabricating nanostructures with a high aspect ratio. To define a pattern for the catalyst, lift-off processes are commonly used. The lift-off step however is often a process bottle neck due to low yield, especially for smaller structures. To bypass the lift-off process, other methods such as electroplating can be utilized. In this paper, we suggest an electroplated bi-layer catalyst for vapour phase metal-assisted chemical etching as an alternative to the commonly utilised lift-off process. Samples were successfully etched in vapour, and resulting structures had feature sizes down to 10 nm.

Two-dimensional materials are extraordinarily sensitive to external stimuli, making them ideal for studying fundamental properties and for engineering devices with new functionalities. One such stimulus, strain, affects the magnetic properties of the layered magnetic semiconductor CrSBr to such a degree that it can induce a reversible antiferromagnetic-to-ferromagnetic phase transition. Given the pervasiveness of non-uniform strain in exfoliated two-dimensional magnets, it is crucial to understand its impact on their magnetic behavior. Using scanning SQUID-on-lever microscopy, we directly image the effects of spatially inhomogeneous strain on the magnetization of layered CrSBr as it is polarized by a field applied along its easy axis. The evolution of this magnetization and the formation of domains is reproduced by a micromagnetic model, which incorporates the spatially varying strain and the corresponding changes in the local interlayer exchange stiffness. The observed sensitivity to small strain gradients along with similar images of a nominally unstrained CrSBr sample suggest that unintentional strain inhomogeneity influences the magnetic behavior of exfoliated samples and must be considered in the design of future devices.

Holes in planar germanium (Ge) heterostructures show promise for quantum applications, particularly in superconducting and spin qubits, due to strong spin-orbit interaction, low effective mass, and absence of valley degeneracies. However, charge traps cause issues such as gate hysteresis and charge noise. This study examines the effect of surface treatments on the accumulation behaviour and transport properties of Ge-based two dimensional hole gases (2DHGs). Oxygen plasma treatment reduces conduction in a setting without applied top-gate voltage and improves the mobility and lowers the percolation density, while hydrofluoric acid (HF) etching provides no benefit. The results suggest that interface traps from the partially oxidised silicon (Si) cap pin the Fermi level, and that oxygen plasma reduces the trap density by fully oxidising the Si cap. Therefore, optimising surface treatments is crucial for minimising the charge traps and thereby enhancing the device performance.

A diffusive process that is reset to its origin at random times, so-called stochastic resetting (SR), is an ubiquitous expedient in many natural systems . Yet, beyond its ability to improve the efficiency of target searching, SR is a true non-equilibrium thermodynamic process that brings forward new and challenging questions . Here, we show how the recent developments of experimental information thermodynamics renew the way to address SR and can lead, beyond a new understanding, to better control on the non-equilibrium nature of SR. This thermodynamically controlled SR is experimentally implemented within a time-dependent optical trapping potential. We show in particular that SR converts heat into work from a single bath continuously and without feedback. This implements a Maxwell's demon that constantly erases information. In our experiments, the erasure takes the form of a protocol that allows to evaluate the true energetic cost of SR. We show that using an appropriate measure of the available information, this cost can be reduced to a reversible minimum while being bounded by the Landauer limit. We finally reveal that the individual trajectories generated by the demon all break ergodicity and thus demonstrate the non-ergodic nature of the demon's modus operandi. Our results offer new approaches to processes, such as SR, where the informational framework provides key experimental tools for their non-equilibrium thermodynamic control.

Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.

Seventeen-carbon-atom-wide armchair graphene nanoribbons (17-AGNRs) are promising candidates for high-performance electronic devices due to their narrow electronic bandgap. Atomic precision in edge structure and width control is achieved through a bottom-up on-surface synthesis (OSS) approach from tailored molecular precursors in ultra-high vacuum (UHV). This synthetic protocol must be optimized to meet the structural requirements for device integration, with ribbon length being the most critical parameter. Here, we report optimized OSS conditions that produce 17-AGNRs with an average length of approximately 17 nm. This length enhancement is achieved through a gradual temperature ramping during an extended annealing period, combined with a template-like effect driven by monomer assembly at high surface coverage. The resulting 17-AGNRs are comprehensively characterized in UHV using scanning probe techniques and Raman spectroscopy. Raman measurements following substrate transfer enabled the characterization of the length distribution of GNRs on the device substrate and confirmed their stability under ambient conditions and harsh chemical environments, including acid vapors and etchants. The increased length and ambient stability of the 17-AGNRs lead to their reliable integration into device architectures. As a proof of concept, we integrate 17-AGNRs into field-effect transistors (FET) with graphene electrodes and confirm that electronic transport occurs through the GNRs. This work demonstrates the feasibility of integrating narrow-bandgap GNRs into functional devices and contributes to advancing the development of carbon-based nanoelectronics.

The properties of functional oxide heterostructures are strongly influenced by the physics governing their interfaces. Modern deposition techniques allow us to accurately engineer the interface physics through the growth of atomically precise heterostructures. This enables minute control over the electronic, magnetic, and structural characteristics. Here, we investigate the magnetic properties of tailor-made superlattices employing the ferromagnetic and insulating double perovskites RE$_2$NiMnO$_6$ (RE = La, Nd), featuring distinct Curie temperatures. Adjusting the superlattice periodicity at the unit cell level allows us to engineer their magnetic phase diagram. Large periodicity superlattices conserve the individual para- to ferromagnetic transitions of the La$_2$NiMnO$_6$ and Nd$_2$NiMnO$_6$ parent compounds. As the superlattice periodicity is reduced, the Curie temperatures of the superlattice constituents converge and, finally, collapse into one single transition for the lowest period samples. This is a consequence of the magnetic order parameter propagating across the superlattice interfaces, as supported by a minimal Landau theory model. Further, we find that the Nd-Ni/Mn exchange interaction can be enhanced by the superlattice interfaces. This leads to a field-induced reversal of the Nd magnetic moments, as confirmed by synchrotron X-ray magnetic circular dichroism measurements and supported by first-principles calculations. Our work demonstrates how superlattice engineering can be employed to fine-tune the magnetic properties in oxide heterostructures and broadens our understanding of magnetic interfacial effects.

The molecular self-assembly and the magnetic properties of two cyclooctatetraenide (COT) - based single-ion magnets (SIM) adsorbed on Ag(100) in the sub-monolayer range are reported. Our study combines scanning-tunneling microscopy, X-ray photoemission spectroscopy and polarized X-ray absorption spectroscopy to show that Cp*ErCOT (Cp* = 1,2,3,4,5-pentamethylcyclopentadienide anion) SIMs self-assemble as alternating compact parallel rows including standing-up and lying-down conformations, following the main crystallographic directions of the substrate. Conversely, K[Er(COT)$_2$], obtained from subliming the [K(18-c-6)][Er(COT)$_2$]$\cdot$ 2THF salt, forms uniaxially ordered domains with the (COT)$^{2-}$ rings perpendicular to the substrate plane. The polarization-dependent X-ray absorption spectra reproduced by the multiX simulations suggest that the strong in-plane magnetic anisotropy of K[Er(COT)$_2$]/Ag(100) and the weak out-of-plane anisotropy of Cp*ErCOT/Ag(100) can be attributed to the strikingly different surface ordering of these two complexes. Compared to the bulk phase, surface-supported K[Er(COT)$_2$] exhibits a similarly large hysteresis opening, while the Cp*ErCOT shows a rather small opening. This result reveals that despite structural similarities, the two organometallic SMMs have strongly different magnetic properties when adsorbed on the metal substrate, attributed to the different orientations and the resulting interactions of the ligand rings with the surface.

We describe an apparatus for the implementation of hybrid optomechanical systems at 4 K. The platform is based on a high-finesse, micrometer-scale fiber Fabry-Perot cavity, which can be widely tuned using piezoelectric positioners. A mechanical resonator can be positioned within the cavity in the object-in-the-middle configuration by a second set of positioners. A high level of stability is achieved without sacrificing either performance or tunability, through the combination of a stiff mechanical design, passive vibration isolation, and an active Pound-Drever-Hall feedback lock incorporating a reconfigurable digital filter. The stability of the cavity length is demonstrated to be better than a few picometers over many hours both at room temperature and at 4 K.

We use a scanning superconducting quantum interference device (SQUID) to image the magnetic flux produced by a superconducting device designed for quantum computing. The nanometer-scale SQUID-on-tip probe reveals the flow of superconducting current through the circuit as well as the locations of trapped magnetic flux. In particular, maps of current flowing out of a flux-control line in the vicinity of a qubit show how these elements are coupled, providing insight on how to optimize qubit control.

Cold ions in traps are well-established, highly controllable quantum systems with a wide variety of applications in quantum information, precision spectroscopy, clocks and chemistry. Nanomechanical oscillators are used in advanced sensing applications and for exploring the border between classical and quantum physics. Here, we report on the implementation of a hybrid system combining a metallic nanowire with laser-cooled ions in a miniaturised ion trap. We demonstrate resonant and off-resonant coupling of the two systems and the coherent motional excitation of the ion by the mechanical drive of the nanowire. The present results open up avenues for mechanically manipulating the quantum motion of trapped ions, for the development of ion-mechanical hybrid quantum systems and for the sympathetic cooling of mechanical systems by trapped ions and vice versa.

We demonstrate the fabrication of scanning superconducting quantum interference devices (SQUIDs) on the apex of sharp quartz scanning probes -- known as SQUID-on-tip probes -- using conventional magnetron sputtering. We produce and characterize SQUID-on-tips made of both Nb and MoGe with effective diameters ranging from 50 to 80 nm, magnetic flux noise down to \SI{300}{\nano\Phi_{0}/\sqrt{\hertz}}, and operating fields as high as \SI{2.5}{\tesla}. Compared to the SQUID-on-tip fabrication techniques used until now, including thermal evaporation and collimated sputtering, this simplified method facilitates experimentation with different materials, potentially expanding the functionality and operating conditions of these sensitive nanometer-scale scanning probes.