Quantum heat engines are novel technologies that leverage quantum mechanical principles alongside thermodynamic theory to generate useful work. While experimental realizations of such devices have existed since the 1950s, they require continuous drive by an external control field. Autonomous quantum heat engines offer an alternate approach where the heat engine cycle is driven from within the device itself. Without being superimposed onto an external control field, the generated work from an autonomous quantum heat engine can more easily be observed and extracted. This thesis studies the low-frequency, energy-storing resonator in a superconducting circuit sample proposed as one such autonomous quantum heat engine. Transmission line measurements are performed to characterize the resonator while also analyzing its behavior in the time domain. When thermal-like noise is introduced to the system, the resonance dip is enhanced by up to 4.5 dB. However, the resonator rapidly decays, exhibiting bare resonance behavior after 6 µs without noise. Furthermore, this thesis finds that the intrinsic dissipation rate of the resonator is greater than the photon generation rate of the system. The internal quality factor peaks at 2.1×10^4, higher than the expected values for the type of resonator utilized and four times higher than the bare noiseless resonance. The total quality factor reaches 1.8×10^4 at ideal noise temperatures.
Quantum heat engines are novel technologies that leverage quantum mechanical principles alongside thermodynamic theory to generate useful work. While experimental realizations of such devices have existed since the 1950s, they require continuous drive by an external control field. Autonomous quantum heat engines offer an alternate approach where the heat engine cycle is driven from within the device itself. Without being superimposed onto an external control field, the generated work from an autonomous quantum heat engine can more easily be observed and extracted. This thesis studies the low-frequency, energy-storing resonator in a superconducting circuit sample proposed as one such autonomous quantum heat engine. Transmission line measurements are performed to characterize the resonator while also analyzing its behavior in the time domain. When thermal-like noise is introduced to the system, the resonance dip is enhanced by up to 4.5 dB. However, the resonator rapidly decays, exhibiting bare resonance behavior after 6 µs without noise. Furthermore, this thesis finds that the intrinsic dissipation rate of the resonator is greater than the photon generation rate of the system. The internal quality factor peaks at 2.1×10^4, higher than the expected values for the type of resonator utilized and four times higher than the bare noiseless resonance. The total quality factor reaches 1.8×10^4 at ideal noise temperatures.
Quantum thermodynamics sits at the intersection of quantum mechanics and thermodynamics, aiming to understand how key thermodynamic concepts such as heat, work, and entropy behave in quantum systems. A primary interest in this field is the study and development of quantum heat engines, devices that convert the flow of thermal energy into work using a quantum system as the working medium. Conventional quantum heat engines require consistent external control to drive their operating cycle. In contrast, autonomous quantum heat engines operate without such external control, instead, their cyclic behavior emerges entirely from internal dynamics and the coupling to thermal reservoirs. In this thesis, we study an autonomous quantum heat engine circuit based on superconducting quantum circuits, in which thermal noise from heat reservoirs drives cyclic energy exchange between two superconducting resonators coupled with a superconducting quantum interference device (SQUID). In this thesis, classical circuit simulations of the autonomous quantum heat engine are implemented in AWR Design Environment using lumped-element resonators, coupling capacitors, and Josephson junction models. By mapping quantum components to their classical analogues and varying the external magnetic flux threading the superconducting quantum interference device, the resonance frequencies, quality factors, and coupling dynamics of the circuit are analyzed across two parameter sets. The simulated quality factor of the second resonator exceeded the threshold required for negative dissipation in both parameter sets, consistent with conditions favorable for coherent microwave generation. Transient simulations further revealed that above a threshold drive power, energy builds up at the second resonator’s resonance frequency through SQUID-mediated coupling. This provides qualitative evidence that the classical model captures the essential inter-resonator coupling mechanism. However, systematic quantitative discrepancies in resonance frequencies and dissipation rates are identified, attributed primarily to the linearized SQUID representation used in the classical model. These results demonstrate that classical circuit simulations can qualitatively reproduce key dynamical features of the studied autonomous quantum heat engine, while also revealing the limitations of classical approximations in capturing its full quantum behavior.
Quantum heat engines provide attractive means in quantum thermodynamics for studying the fundamentals of the flow of heat and work. Previous experimental implementations of heat engines operating at the level of a few excitation quanta have utilized external driving, which has made the observation of the produced work challenging. Conversely, autonomous quantum heat engines only require a flow of heat to operate and generate work. However, autonomous quantum heat engines have not yet been experimentally demonstrated in any system despite numerous theoretical investigations. Here, we experimentally realize an autonomous quantum heat engine based on superconducting circuits. We construct the engine circuit implementing an approximate Otto cycle by coupling two superconducting resonators with a superconducting quantum interference device, and coupling this system to spectrally filtered hot and cold reservoirs. By varying the experimental conditions, we observe coherent microwave power generation arising from the internal dynamics of the system driven only by the thermal reservoirs. Our results validate previous theoretical predictions for this circuit and pave the way for detailed studies of quantum effects in heat engines and for using heat-generated coherent microwaves in circuit quantum electrodynamics.
As superconducting quantized electric circuits continue to emerge as an exceptionally versatile and powerful platform for quantum computing and other quantum technologies, they also provide a rich foundation for exploring quantum thermodynamics. The study of heat transport in these circuits offers invaluable synergy as understanding the impact of thermal fluctuations becomes increasingly important for their operation. Heat engines represent one of the most fundamental classes of thermal devices, whether regarding classical or quantum applications. Although heat transport in superconducting circuits has been extensively studied, quantum heat engines (QHE) operating at the limit of a few excitation quanta had not been experimentally realized prior to this work. These engines offer valuable insight into the quantum thermodynamics of superconducting circuits. Beyond fundamental research, the beseeching goal is to develop integrated QHEs which generate useful work in conjunction with other quantum technologies. In this context, autonomous QHEs, capable of operating without coherent external control, are particularly compelling. In this thesis, we explore thermodynamics and quantum heat engines, with a particular focus on engineering quantum heat engines using superconducting circuits as our experimental platform. The presented research includes both experimental and theoretical advancements, focusing on driven and autonomous QHEs, respectively. First, we demonstrate that engineered environments in superconducting circuits can serve as effective thermal reservoirs for externally driven quantum heat engines. Experimentally, we show that a quantum-circuit refrigerator (QCR) can be used not only for cooling but also for heating the coupled circuit. This discovery imminently leads to the experimental realization of a quantum heat engine, where a quantum Otto cycle is driven in a transmon qubit coupled to the QCR. Second, regarding autonomous quantum heat engines, we theoretically show that non-linear optomechanical coupling can eliminate the need for external driving while providing a method for directly observing the work output. These promising theoretical results suggest that the experimental realization of an autonomous QHE is ultimately a matter of careful circuit engineering. However, achieving this experimentally remains a tantalising challenge for future research, beyond the scope of the present work.
Superconducting microwave circuits are a ubiquitous and important tool for devices that exploit the phenomena of superconductivity and cryogenic temperatures as an environment for achieving the generation, manipulation, and detection of quantum states - required for the ongoing development of quantum technologies. In particular, superconducting circuits are a promising platform for the universal quantum computer, which will require an unprecedented density of quantum-coherent elements to perform large-scale quantum-enhanced calculations and simulations, using the framework of cavity quantum lectrodynamics.Dissipation and heat in these superconducting circuits is a key source of error and inefficiency, however the thermodynamics in this regime is poorly understood despite its increasing relevancy.This thesis describes the integration of superconducting resonators and artificial atoms derived from superconducting quantum circuits with ultra-sensitive bolometry, for looking at heat transport through superconducting circuits. We will describe the physics and operation of each of these elements, before combining and utilising them to perform heat transport measurements through a superconducting artificial atom coupled to two resonators, each terminated by a normal-metal mesoscopic resistor, with the resistor temperature measured and temperature gradients across the circuit induced by superconducting tunnel-probes. We will present tunable heat transport through this system, firstly when the resonators are symmetric, allowing us to observe the role of dissipation-limited coupling of the resonators to the artificial atom on the locality of the heat transport, then on an asymmetric system, demonstrating a directional rectification of the heat transport. Additionally, we will discuss how each element of the system can be individually characterised, in particular the quality factor of superconducting resonators in the highly-dissipative limit, by exploiting the superconducting transition to perform a background reference. It is suggested that this hybrid quantum system, and these initial experiments provide a promising platform in the emergent field of circuit quantum thermodynamics. We believe that the techniques and tools developed during this thesis present key steps towards the understanding of the thermodynamics of quantum circuits, towards the realisation of devices that can explore heat transport in the quantum limit, such as a quantum heat engine.
A central building block of a heat engine is the working fluid, which mediates the conversion of heat into work. In nanoscale heat engines, the working fluid can be a quantum system whose behavior and dynamics are non-classical. A particularly versatile realization is a quantum resonator, which allows for precise control and coupling to thermal reservoirs, making it an ideal platform for exploring quantum thermodynamic processes. Here, we investigate the thermodynamic properties of a driven quantum resonator whose temperature is controlled by modulating its natural frequency. We evaluate the work performed by the external drive and the resulting heat flow between the resonator and its environment, both within linear response and beyond. To further elucidate these processes, we determine the full distribution of photon exchanges between the resonator and its environment, characterized by its first few cumulants. Our results provide quantitative insights into the interplay between heat, work, and fluctuations, and may help in designing future heat engines.
Superconducting circuits provide a controllable and versatile platform for studying quantum phenomena and advancing quantum technologies. Josephson junctions and resonators are the central circuit elements, as they enable the realization of macroscopic quantum systems—such as qubits—that can be conveniently controlled, probed, and integrated with non-superconducting components. The implementation of a thermal reservoir through the integration of a dissipative element, such as a normal-metal resistor, offers an experimental platform for investigating quantum thermodynamics, heat management in circuits, on-chip thermal detectors, and the realization of quantum thermal machines. In this thesis, we integrate a mesoscopic normal metal and its associated thermometers as an on-chip bolometer within circuit quantum electrodynamics devices for thermal detection and quantum thermodynamics experiments. The on-chip bolometer is utilized as a sensitive and broadband thermal spectrometer to characterize the properties of a superconducting resonator and to investigate its dominant loss channels. We demonstrate the capability of our thermal detector to resolve the resonator modes over a wide frequency range extending above 20 GHz. When two thermal baths are connected through a qubit–resonator system, a quantum heat valve can be realized. This device has been demonstrated using both transmon and flux qubits. Photonic heat transport between the two baths is controlled by tuning the qubit energy via an applied static magnetic field. To model these experiments, we propose an approach based on electromagnetic simulation and microwave circuit theory, restricted to the linear-response regime. Despite this limitation, the method successfully captures the experimental observations and provides a practical tool for analysing and designing circuits for future experiments. A periodically driven qubit coupled to two unequal resonators, each terminated by a heat reservoir, enables the realization of a quantum Otto refrigerator. The use of a transmon qubit for this purpose is limited by its weak anharmonicity. We therefore explore alternative platforms for the experimental implementation of a quantum refrigerator based on charge and flux qubits, which exhibit strong anharmonicity. As an important step, we perform experiments on a driven flux qubit galvanically coupled to a resonator that is, in turn, weakly capacitively coupled to a heat reservoir. We observe interference patterns in the heat current arising from driving-induced coherence. In particular, resonance peaks in the heat transferred to the bath appear at driving frequencies that are integer fractions of the resonator frequency. These quantum features are governed by the relative phase accumulated by the qubit states under driving.