Quantum-limited heat conduction over macroscopic distances

Testing the Minimum System Entropy and the Quantum of Entropy

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.

The phonon quantum of thermal conductance: Are simulations and measurements estimating the same quantity?

The thermal conductance quantum is a fundamental quantity in quantum transport theory. However, two decades after its first reported measurements and calculations for phonons in suspended nanostructures, reconciling experiments and theory remains elusive. Our massively parallel calculations of phonon transport in micrometer-sized three-dimensional structures suggest that part of the disagreement between theory and experiment stems from the inadequacy of macroscopic concepts to analyze the data. The computed local temperature distribution in the wave ballistic nonequilibrium regime shows that the spatial placement and dimensions of thermometers, heaters, and supporting microbeams in the suspended structures can noticeably affect the thermal conductance's measured values. In addition, diffusive transport assumptions made in the data analysis may result in measured values that considerably differ from the actual thermal conductance of the structure. These results urge for experimental validation of the suitability of diffusive transport assumptions in measuring devices operating at sub-kelvin temperatures.

Measurement-Based Quantum Thermal Machines with Feedback Control

We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

Photonic heat transport in three terminal superconducting circuit

We report an experimental realization of a three-terminal photonic heat transport device based on a superconducting quantum circuit. The central element of the device is a flux qubit made of a superconducting loop containing three Josephson junctions, which can be tuned by magnetic flux. It is connected to three resonators terminated by resistors. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system and demonstrate their tunability by magnetic field at the level of 1 aW. We determine system parameters by performing microwave transmission measurements on a separate nominally identical sample and, in this way, demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. Our experiment is an important step towards realization of heat transistors, heat amplifiers, masers pumped by heat and other quantum heat transport devices.

Quantum heat transport devices are currently intensively studied. Here, the authors report the photonic heat transport modulated by superconducting qubit in a three-terminal device. Flux dependent heat power correlates with microwave measurements.

Strategies for Manipulating Phonon Transport in Solids

In this review, we summarize the recent efforts on manipulating phonon transport in solids by using specific techniques that modify their phonon thermal conductivity (i.e., specific heat, phonon group velocity, and mean free path) and phonon thermal conductance (i.e., transmission probability and density of states). The strategies discussed for tuning thermal conductivity are as follows: large unit cell approach and liquid-like conduction for maneuvering specific heat; rattler, mini-bandgap, and phonon confinement for manipulating phonon group velocity; nanoparticles, nanosized grains, coated grains, alloy (isotope) scattering, selection rules in phonon dispersion, Grüneisen parameter, lone-pair electronics, dynamic disorder, and local static distortion for restricting mean free path. We have also included the discussion on tuning phonon thermal conductance, as thermal conduction can be viewed as a transmission process. Additionally, phonon filtering, ballistic transport, and waveguiding are discussed to alter density of states and transmission probability. We hope this review can bring meaningful insights to the researchers in the field of phonon transport in solids.

Excitation Dynamics in Chain-Mapped Environments

The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.

Materials loss measurements using superconducting microwave resonators

The performance of superconducting circuits for quantum computing is limited by materials losses. In particular, coherence times are typically bounded by two-level system (TLS) losses at single photon powers and millikelvin temperatures. The identification of low loss fabrication techniques, materials, and thin film dielectrics is critical to achieving scalable architectures for superconducting quantum computing. Superconducting microwave resonators provide a convenient qubit proxy for assessing performance and studying TLS loss and other mechanisms relevant to superconducting circuits such as non-equilibrium quasiparticles and magnetic flux vortices. In this review article, we provide an overview of considerations for designing accurate resonator experiments to characterize loss, including applicable types of losses, cryogenic setup, device design, and methods for extracting material and interface losses, summarizing techniques that have been evolving for over two decades. Results from measurements of a wide variety of materials and processes are also summarized. Finally, we present recommendations for the reporting of loss data from superconducting microwave resonators to facilitate materials comparisons across the field.

Electric field control of radiative heat transfer in a superconducting circuit

Heat is detrimental for the operation of quantum systems, yet it fundamentally behaves according to quantum mechanics, being phase coherent and universally quantum-limited regardless of its carriers. Due to their robustness, superconducting circuits integrating dissipative elements are ideal candidates to emulate many-body phenomena in quantum heat transport, hitherto scarcely explored experimentally. However, their ability to tackle the underlying full physical richness is severely hindered by the exclusive use of a magnetic flux as a control parameter and requires complementary approaches. Here, we introduce a dual, magnetic field-free circuit where charge quantization in a superconducting island enables thorough electric field control. We thus tune the thermal conductance, close to its quantum limit, of a single photonic channel between two mesoscopic reservoirs. We observe heat flow oscillations originating from the competition between Cooper-pair tunnelling and Coulomb repulsion in the island, well captured by a simple model. Our results highlight the consequences of charge-phase conjugation on heat transport, with promising applications in thermal management of quantum devices and design of microbolometers.

Electronic heat flow and thermal shot noise in quantum circuits

When assembling individual quantum components into a mesoscopic circuit, the interplay between Coulomb interaction and charge granularity breaks down the classical laws of electrical impedance composition. Here we explore experimentally the thermal consequences, and observe an additional quantum mechanism of electronic heat transport. The investigated, broadly tunable test-bed circuit is composed of a micron-scale metallic node connected to one electronic channel and a resistance. Heating up the node with Joule dissipation, we separately determine, from complementary noise measurements, both its temperature and the thermal shot noise induced by the temperature difference across the channel. The thermal shot noise predictions are thereby directly validated, and the electronic heat flow is revealed. The latter exhibits a contribution from the channel involving the electrons' partitioning together with the Coulomb interaction. Expanding heat current predictions to include the thermal shot noise, we find a quantitative agreement with experiments.

Heat conduction measurements in ballistic 1D phonon waveguides indicate breakdown of the thermal conductance quantization

Emerging quantum technologies require mastering thermal management, especially at the nanoscale. It is now accepted that thermal metamaterial-based phonon manipulation is possible, especially at sub-kelvin temperatures. In these extreme limits of low temperatures and dimensions, heat conduction enters a quantum regime where phonon exchange obeys the Landauer formalism. Phonon transport is then governed by the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here we report on ultra-sensitive thermal experiments made on ballistic 1D phonon conductors using a micro-platform suspended sensor. Our thermal conductance measurements attain a power sensitivity of 15 attoWatts \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt {{\mathrm{Hz}}} \,^{ - 1}$$\end{document}Hz-1 around 100 mK. Ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. This limitation of heat transport in the quantum regime may have a significant impact on modern thermal management and thermal circuit design.

At low temperatures and dimensionality it has become possible to probe the quantum limits of heat transport. Tavakoli et al. show that heat transport through a one-dimensional device can be dominated by non-ideal transmission instead of reaching the regime of thermal conductance quantization.

Observation of microwave absorption and emission from incoherent electron tunneling through a normal-metal-insulator-superconductor junction

We experimentally study nanoscale normal-metal–insulator–superconductor junctions coupled to a superconducting microwave resonator. We observe that bias-voltage-controllable single-electron tunneling through the junctions gives rise to a direct conversion between the electrostatic energy and that of microwave photons. The measured power spectral density of the microwave radiation emitted by the resonator exceeds at high bias voltages that of an equivalent single-mode radiation source at 2.5 K although the phonon and electron reservoirs are at subkelvin temperatures. Measurements of the generated power quantitatively agree with a theoretical model in a wide range of bias voltages. Thus, we have developed a microwave source which is compatible with low-temperature electronics and offers convenient in-situ electrical control of the incoherent photon emission rate with a predetermined frequency, without relying on intrinsic voltage fluctuations of heated normal-metal components or suffering from unwanted losses in room temperature cables. Importantly, our observation of negative generated power at relatively low bias voltages provides a novel type of verification of the working principles of the recently discovered quantum-circuit refrigerator.

Manipulating the Flow of Thermal Noise in Quantum Devices

There has been significant interest recently in using complex quantum systems to create effective nonreciprocal dynamics. Proposals have been put forward for the realization of artificial magnetic fields for photons and phonons; experimental progress is fast making these proposals a reality. Much work has concentrated on the use of such systems for controlling the flow of signals, e.g., to create isolators or directional amplifiers for optical signals. In this Letter, we build on this work but move in a different direction. We develop the theory of and discuss a potential realization for the controllable flow of thermal noise in quantum systems. We demonstrate theoretically that the unidirectional flow of thermal noise is possible within quantum cascaded systems. Viewing an optomechanical platform as a cascaded system we show here that one can ultimately control the direction of the flow of thermal noise. By appropriately engineering the mechanical resonator, which acts as an artificial reservoir, the flow of thermal noise can be constrained to a desired direction, yielding a thermal rectifier. The proposed quantum thermal noise rectifier could potentially be used to develop devices such as a thermal modulator, a thermal router, and a thermal amplifier for nanoelectronic devices and superconducting circuits.

Towards phase-coherent caloritronics in superconducting circuits

The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) is based on the possibility of controlling heat currents by using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices that can control energy transfer with a degree of accuracy approaching that reached for charge transport by contemporary electronic components. This can be done by making use of the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson effect and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic nonlinear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.

Quantum-circuit refrigerator

Quantum technology promises revolutionizing applications in information processing, communications, sensing and modelling. However, efficient on-demand cooling of the functional quantum degrees of freedom remains challenging in many solid-state implementations, such as superconducting circuits. Here we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable electron tunnelling in a nanoscale refrigerator. This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even for an elevated electron temperature at the refrigerator. Our conclusions are verified by control experiments and by a good quantitative agreement between theory and experimental observations at various operation voltages and bath temperatures. In the future, we aim to remove spurious dissipation introduced by our refrigerator and to decrease the operational temperature. Such an ideal quantum-circuit refrigerator has potential applications in the initialization of quantum electric devices. In the superconducting quantum computer, for example, fast and accurate reset of the quantum memory is needed.

Efficient on-demand cooling of the functional degrees of freedom in solid-state implementations of quantum information processing devices remains a challenge. Here the authors demonstrate direct cooling of a photonic mode of a superconducting resonator using voltage-controllable electron tunnelling.

Thermal conductance of Nb thin films at sub-kelvin temperatures

We determine the thermal conductance of thin niobium (Nb) wires on a silica substrate in the temperature range of 0.1–0.6 K using electron thermometry based on normal metal-insulator-superconductor tunnel junctions. We find that at 0.6 K, the thermal conductance of Nb is two orders of magnitude lower than that of Al in the superconducting state, and two orders of magnitude below the Wiedemann-Franz conductance calculated with the normal state resistance of the wire. The measured thermal conductance exceeds the prediction of the Bardeen-Cooper-Schrieffer theory, and demonstrates a power law dependence on temperature as T^4.5, instead of an exponential one. At the same time, we monitor the temperature profile of the substrate along the Nb wire to observe possible overheating of the phonon bath. We show that Nb can be successfully used for thermal insulation in a nanoscale circuit while simultaneously providing an electrical connection.

Detection of Zeptojoule Microwave Pulses Using Electrothermal Feedback in Proximity-Induced Josephson Junctions

We experimentally investigate and utilize electrothermal feedback in a microwave nanobolometer based on a normal-metal (Au_{x}Pd_{1-x}) nanowire with proximity-induced superconductivity. The feedback couples the temperature and the electrical degrees of freedom in the nanowire, which both absorbs the incoming microwave radiation, and transduces the temperature change into a radio-frequency electrical signal. We tune the feedback in situ and access both positive and negative feedback regimes with rich nonlinear dynamics. In particular, strong positive feedback leads to the emergence of two metastable electron temperature states in the millikelvin range. We use these states for efficient threshold detection of coherent 8.4 GHz microwave pulses containing approximately 200 photons on average, corresponding to 1.1×10^{-21}  J≈7.0  meV of energy.