In this Colloquium recent advances in the field of quantum heat transport are reviewed. This topic has been investigated theoretically for several decades, but only during the past twenty years have experiments on various mesoscopic systems become fe
asible. A summary of the theoretical basis for describing heat transport in one-dimensional channels is first provided. Then the main experimental investigations of quantized heat conductance due to phonons, photons, electrons, and anyons in such channels are presented. These experiments are important for understanding the fundamental processes that underly the concept of a heat conductance quantum for a single channel. Then an illustration on how one can control the quantum heat transport by means of electric and magnetic fields, and how such tunable heat currents can be useful in devices is given. This lays the basis for realizing various thermal device components such as quantum heat valves, rectifiers, heat engines, refrigerators, and calorimeters. Also of interest are fluctuations of quantum heat currents, both for fundamental reasons and for optimizing the most sensitive thermal detectors; at the end of the review the status of research on this intriguing topic is given.
We discuss the non-zero frequency noise of heat current with the explicit example of energy carried by thermal photons in a circuit. Instead of the standard circuit modelling that gives a convenient way of predicting time-averaged heat current, we de
scribe a setup composed of two resistors forming the heat baths by collections of bosonic oscillators. In terms of average heat transport this model leads to identical results with the conventional one, but besides this, it yields a convenient way of dealing with noise as well. The non-zero frequency heat current noise does not vanish in equilibrium even at zero temperature, the result that is known for, e.g., electron tunneling. We present a modulation method that can convert the difficult-to-measure high frequency quantum noise down to zero frequency.
We describe a qubit linearly coupled to a heat bath, either directly or via a cavity. The bath is formed of oscillators with a distribution of energies and coupling strengths, both for qubit-oscillator and oscillator-oscillator interaction. A direct
numerical solution of the Schrodinger equation for the full system including up to $10^6$ oscillators in the bath and analytic solutions are given, verifying quantum decay in short time quadratic (Zeno), long time exponential and eventually power law relaxation regimes. The main new results of the paper deal with applications and implications in quantum thermodynamics setups. We start by providing a correspondence of the oscillator bath to a resistor in a circuit. With the presented techniques we can then shed light on two topical questions of open quantum systems. First, splitting a quantum to uncoupled baths is presented as an opportunity for detection of low energy photons. Second, we address quantitatively the question of separation between a quantum system and its classical environment.
We investigate the basic charge and heat transport properties of charge neutral epigraphene at sub-kelvin temperatures, demonstrating nearly logarithmic dependence of electrical conductivity over more than two decades in temperature. Using graphenes
sheet conductance as in-situ thermometer, we present a measurement of electron-phonon heat transport at mK temperatures and show that it obeys the $T^4$ dependence characteristic for clean two-dimensional conductor. Based on our measurement we predict the noise-equivalent power of $sim 10^{-22}~{rm W}/sqrt{{rm Hz}}$ of epigraphene bolometer at the low end of achievable temperatures.
We apply quantum trajectory techniques to analyze a realistic set-up of a superconducting qubit coupled to a heat bath formed by a resistor, a system that yields explicit expressions of the relevant transition rates to be used in the analysis. We dis
cuss the main characteristics of the jump trajectories and relate them to the expected outcomes (clicks) of a fluorescence measurement using the resistor as a nanocalorimeter. As the main practical outcome we present a model that predicts the time-domain response of a realistic calorimeter subject to single microwave photons, incorporating the intrinsic noise due to the fundamental thermal fluctuations of the absorber and finite bandwidth of a thermometer.
We present a set of experiments to optimize the performance of the noninvasive thermometer based on proximity superconductivity. Current through a standard tunnel junction between an aluminum superconductor and a copper electrode is controlled by the
strength of the proximity induced to this normal metal, which in turn is determined by the position of a direct superconducting contact from the tunnel junction. Several devices with different distances were tested. We develop a theoretical model based on Usadel equations and dynamic Coulomb blockade which reproduces the measured results and yields a tool to calibrate the thermometer and to optimize it further in future experiments.
In miniaturising electrical devices down to nanoscales, heat transfer has turned into a serious obstacle but also potential resource for future developments, both for conventional and quantum computing architectures. Controlling heat transport in sup
erconducting circuits has thus received increasing attention in engineering microwave environments for circuit quantum electrodynamics (cQED) and circuit quantum thermodynamics experiments (cQTD). While theoretical proposals for cQTD devices are numerous, the experimental situation is much less advanced. There exist only relatively few experimental realisations, mostly due to the difficulties in developing the hybrid devices and in interfacing these often technologically contrasting components. Here we show a realisation of a quantum heat rectifier, a thermal equivalent to the electronic diode, utilising a superconducting transmon qubit coupled to two strongly unequal resonators terminated by mesoscopic heat baths. Our work is the experimental realisation of the spin-boson rectifier proposed by Segal and Nitzan.
We study the application of a counter-diabatic driving (CD) technique to enhance the thermodynamic efficiency and power of a quantum Otto refrigerator based on a superconducting qubit coupled to two resonant circuits. Although the CD technique is ori
ginally designed to counteract non-adiabatic coherent excitations in isolated systems, we find that it also works effectively in the open system dynamics, improving the coherence-induced losses of efficiency and power. We compare the CD dynamics with its classical counterpart, and find a deviation that arises because the CD is designed to follow the energy eigenbasis of the original Hamiltonian, but the heat baths thermalize the system in a different basis. We also discuss possible experimental realizations of our model.
Almost a century ago, Johnson and Nyquist presented evidence of fluctuating electrical current and the governing fluctuation dissipation theorem (FDT). Whether, likewise, temperature T can fluctuate is a controversial topic and has led to scientific
debates for several decades. To resolve this issue, there was an experiment initially in 1992 where the authors found good agreement between the FDT theory for heat and experiment on a macroscopic sample. A key question is what happens when we consider a nanoscale system with much fewer particles at 100 times lower temperatures. This challenge has not been addressed up to now, due to the demanding experimental requirement on fast and sensitive thermometry on a mesoscopic absorber. Here we observe equilibrium fluctuations of temperature in a canonical system of about 10^8 electrons exchanging energy with phonon bath at a fixed temperature. Moreover, temperature fluctuations under nonequilibrium conditions present a nontrivial dependence on the chemical potential bias of a hot electron source. These fundamental fluctuations of T set the ultimate lower bound of the energy resolution of a calorimeter.
Characterizing superconducting microwave resonators with highly dissipative elements is a technical challenge, but a requirement for implementing and understanding the operation of hybrid quantum devices involving dissipative elements, e.g. for therm
al engineering and detection. We present experiments on $lambda/4$ superconducting niobium coplanar waveguide (CPW) resonators, terminating at the antinode by a dissipative copper microstrip via aluminum leads, such that the resonator response is difficult to measure in a typical microwave environment. By measuring the transmission both above and below the superconducting transition of aluminum, we are able to isolate the resonance. We then experimentally verify this method with copper microstrips of increasing thicknesses, from 50 nm to 150 nm, and measure quality factors in the range of $10sim67$ in a consistent way.
