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We use trajectory averaging to show that the energy dissipated in the nonequilibrium energy-state transitions of a driven two-state system satisfies a fluctuation-dissipation relation. This connection between the average energy dissipation induced by external driving and its fluctuations about equilibrium is preserved by an adiabatic approximation scheme. We use this scheme to obtain the heat statistics of a single-electron box with superconducting leads in the slow-driving regime, where the dissipated heat becomes normally distributed with a relatively high probability to be extracted from the environment rather than dissipated. We also discuss heat fluctuation relations for driven two-state transitions., Comment: References corrected

Accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunnelling in the wrong direction. Increasing the barrier transparency between the island and the leads, and the source-drain bias helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunnelling in the wrong direction hence extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional AC signal applied to the bias with twice the frequency as the one applied to the gate electrode. This allows additional modulation of the island chemical potential. By using the new approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally-contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors $\sim 10^{-3}$ at high frequencies and can bring them under $5\times 10^{-4}$., Comment: 11 pages

openaire: EC/H2020/824109/EU//EMP Funding Information: We thank Joonas T Peltonen for useful discussions. This work was supported by Academy of Finland Grant 312057 (QTF Centre of Excellence), European Microkelvin Platform (EMP, No. 824109 EU Horizon 2020) and Real-K Project (Grant No. 18SIB02). Real-K received funding from the European Metrology Programme for Innovation and Research (EMPIR) co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. The numerical calculations were performed using the computer infrastructure within the Aalto University School of Science (Science-IT). Publisher Copyright: © 2022 BIPM & IOP Publishing Ltd. We investigate temperature uncertainty of Coulomb blockade thermometer (CBT) arising from inevitable non-uniformities in tunnel junction arrays. The corrections are proportional to the junction resistance variance in the linear operation regime and this result holds approximately also beyond this originally studied high temperature range. We present both analytical and numerical results, and discuss briefly their implications on achievable uniformity based on state-of-the-art fabrication of sensors.

Funding Information: We thank Dmitry Golubev for many useful discussions. This work was supported by Academy of Finland (Grant No. 312057). Publisher Copyright: © 2022 American Physical Society. We analyze theoretically the properties of the recently introduced and experimentally demonstrated converter of frequency to power. The system is composed of a hybrid single-electron box with normal island and superconducting lead, and the detector of the energy flow using a thermometer on a normal metal bolometer. Here, we consider its potential for metrology. The errors in power arise mainly from inaccuracy of injecting electrons at the precise energy equal to the energy gap of the superconductor. We calculate the main systematic error in the form of the excess average energy of the injected electrons and its cumulants, and that due to subgap leakage. We demonstrate by analytic and numerical calculations that the systematic error in detection can, in principle, be made much smaller than the injection errors, which also, with proper choice of system parameters, can be very small

Superconducting circuits present a promising platform with which to realize a quantum refrigerator. Motivated by this, we fabricate and perform spectroscopy of a gated Cooper-pair box, capacitively coupled to two superconducting coplanar waveguide resonators with different frequencies. We experimentally demonstrate the strong coupling of a charge qubit to two superconducting resonators, with the ability to perform voltage driving of the qubit at GHz frequencies. We go on to discuss how the measured device could be modified to operate as a cyclic quantum refrigerator by terminating the resonators with normal-metal resistors acting as heat baths.

Funding Information: We received funding from the Academy of Finland under Grant 312057. We acknowledge the provision of facilities and technical support by Aalto University at the OtaNano—Micronova Nanofabrication Center and through the low temperature laboratory (LTL) infrastructure, which is part of the EU Horizon 2020 European Microkelvin Platform (EMP), No. 824109. Publisher Copyright: © 2022, The Author(s). We discuss the temperature dependence of a common low temperature local thermometer, a tunnel junction between a superconductor and a normal metal (NIS junction). Towards the lowest temperatures its characteristics tend to saturate, which is usually attributed to selfheating effects. In this technical note, we reanalyze this saturation and show that the temperature independent subgap current of the junction alone explains in some cases the low temperature behavior quantitatively.

Funding Information: We acknowledge Fredrik Brange, Christian Flindt, Martin Leijnse, and Claes Thelander for fruitful discussions and the QuantERA project “2D hybrid materials as a platform for topological quantum computing,” Swedish National Science Foundation (Dnr 2018-00099 and 2019-04111), NanoLund, Academy of Finland Grant No. 312057 and QTF Centre of Excellence for financial support. We acknowledge the provision of facilities by Aalto University at OtaNano—Micronova Nanofabrication Centre. We measure the rates and coupling coefficients for local Andreev, nonlocal Andreev, and elastic cotunneling processes. The nonlocal Andreev process, giving rise to Cooper pair splitting, exhibits the same coupling coefficient as the elastic cotunneling whereas the local Andreev process is more than 2 orders of magnitude stronger than the corresponding nonlocal one. Theory estimates describe the findings and explain the large difference in the nonlocal and local coupling arising from competition between electron diffusion in the superconductor and tunnel junction transparency.

Funding Information: This work was supported by Academy of Finland Grant No. 312057 (QTF Centre of Excellence) and by the European Metrology Programme for Innovation and Research (EMPIR) program co-financed by the Participating States and by the European Union Horizon 2020 research and innovation program. We acknowledge the provision of facilities and technical support by Aalto University at the OtaNano—Micronova Nanofabrication Center and through the low temperature laboratory (LTL) infrastructure, which is part of the EU Horizon 2020 European Microkelvin Platform (EMP), No. 824109. Publisher Copyright: © 2022 American Physical Society. We present a scheme and demonstrate measurements of a Coulomb-blockade thermometer (CBT) in a microwave-transmission setup. The sensor is embedded in an LCR resonator, where R is determined by the conductance of the junction array of the CBT. A transmission measurement yields a signal that is directly proportional to the conductance of the CBT, thus enabling the calibration-free operation of the thermometer. This is verified by measuring an identical sensor simultaneously in the usual dc setup. The important advantage of the rf measurement is its speed: the whole bias dependence of the CBT conductance can now be measured in a time of about 100 ms, which is 1000 times faster than in a standard dc measurement. The achieved noise-equivalent temperature of this rf primary measurement is about 1mK/Hz at the bath temperature T=200mK.

We demonstrate a genuine quantum feature of heat: the power emitted by a qubit (quantum two-level system) into a reservoir under continuous driving shows peaks as a function of frequency $f$. These resonant features appear due to the accumulation of the dynamical phase during the driving. The position of the $n$th maximum is given by $f=f_{\rm M}/n$, where $f_{\rm M}$ is the mean frequency of the qubit in the cycle, and their positions are independent of the form of the drive and the number of heat baths attached, and even the presence or absence of spectral filtering. We show that the waveform of the drive determines the intensity of the peaks, differently for odd and even resonances. This quantum heat is expected to play a crucial role in the performance of driven thermal devices such as quantum heat engines and refrigerators. We also show that by optimizing the cycle protocol, we recover the favorable classical limit in fast driven systems without the use of counter-diabatic drive protocols and we demonstrate an entropy preserving non-unitary process. We propose that this non-trivial quantum heat can be detected by observing the steady-state power absorbed by a resistor acting as a bolometer attached to a driven superconducting qubit., Comment: 6 pages, 3 figures, comments welcome

Hybrid turnstiles have proven to generate accurate single-electron currents. The usual operation consists of applying a periodic modulation to a capacitively coupled gate electrode and requires a non-zero DC source-drain bias voltage. Under this operation, a current of the same magnitude and opposite direction can be generated by flipping the polarity of the bias. Here, we demonstrate that accurate single-electron currents can be generated under zero average bias voltage. We achieve this by applying an extra periodic modulation with twice the frequency of the gate signal and zero DC level to the source electrode. This creates a time interval, which is otherwise zero, between the crossings of tunnelling thresholds that enable single-electron tunnelling. Furthermore, we show that within this operation the current direction can be reversed by only shifting the phase of the source signal., Comment: 5 pages

We report on a robust method to achieve strong coupling between a superconducting flux qubit and a high-quality quarter-wavelength coplanar waveguide resonator. We demonstrate the progression from the strong to ultrastrong coupling regime by varying the length of a shared inductive coupling element, ultimately achieving a qubit-resonator coupling strength of 655 MHz, $10\%$ of the resonator frequency. We derive an analytical expression for the coupling strength in terms of circuit parameters and also discuss the maximum achievable coupling within this framework. We experimentally characterize flux qubits coupled to superconducting resonators using one and two-tone spectroscopy methods, demonstrating excellent agreement with the proposed theoretical model., Comment: 9 pages, 6 figures

Funding Information: Academy of Finland Horizon 2020 Framework Programme Russian Science Foundation Foundational Questions Institute Fund Funding Information: This work was supported by Academy of Finland Grant No. 312057, the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie actions (Grant Agreement No. 766025), the Russian Science Foundation (Grant No. 20-62-46026), and the Foundational Questions Institute Fund (FQXi) via Grant No. FQXi-IAF19-06. Publisher Copyright: © 2021 American Physical Society 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 20 years have experiments on various mesoscopic systems become feasible. A summary of the theoretical basis for describing heat transport in one-dimensional channels is first provided. The main experimental investigations of quantized heat conductance due to phonons, photons, electrons, and anyons in such channels are then presented. These experiments are important for understanding the fundamental processes that underlie the concept of a heat conductance quantum for a single channel. An illustration of 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 first 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 Colloquium the status of research on this topic is given.

We propose and experimentally demonstrate a self-calibrating detector of Cooper pair depairing in a superconductor based on a mesoscopic superconducting island coupled to normal metal leads. On average, exactly one electron passes through the device per broken Cooper pair, independent of the absorber volume, device or material parameters. The device operation is explained by a simple analytical model and verified with numerical simulations in quantitative agreement with experiment. In a proof-of-concept experiment, we use such a detector to measure the high-frequency phonons generated by another, electrically decoupled superconducting island, with a measurable signal resulting from less than 10 fW of dissipated power., 5 pages, 3 figures; supplementary material included

Low temperature phenomena and methods are quantum thermodynamics per se. Modern engineered quantum systems, for instance those used for superconducting quantum information processing and mesoscopic electron transport, provide working media for realizing devices such as quantum heat engines and refrigerators and a testbed for fundamental principles and phenomena in thermodynamics of quantum systems and processes.

Single-electron transport relates an operation frequency f to the emitted current I through the electron charge e as I = ef (refs.

Direct frequency to power conversion (FPC), to be presented here, links both quantities through a known energy, like single-electron transport relates an operation frequency $f$ to the emitted current $I$ through the electron charge $e$ as $I=ef$. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt -- energy, which is traceable to Planck's constant $h$, emitted per unit of time. This time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom $\Delta\nu_\mathrm{Cs}$; hence, FPC comprises a simple and elegant way to realize the watt. In this spirit, single-photon emission and detection at known rates have been proposed and experimented as radiometric standard. However, nowadays power standards are only traceable to electrical units, i.e., volt and ohm. In this letter, we demonstrate the feasibility of an alternative proposal based on solid-state direct FPC using a SINIS (S = superconductor, N = normal metal, I = insulator) single-electron transistor (SET) accurately injecting $N$ (integer) quasiparticles (qps) per cycle to both leads with discrete energies close to their superconducting gap $\Delta$, even at zero drain-source voltage. Furthermore, the bias voltage plays an important role in the distribution of the power among the two leads, allowing for an almost equal injection $N\Delta f$ to the two. We estimate that under appropriate conditions errors can be well below $1\%$., Comment: Includes supplementary information

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.

We perform direct thermovoltage measurements in a single-electron transistor, using on-chip local thermometers, both in the linear and non-linear regimes. Using a model which accounts for co-tunneling, we find excellent agreement with the experimental data with no free parameters even when the temperature difference is larger than the average temperature (far-from-linear regime). This allows us to confirm the sensitivity of the thermovoltage on co-tunneling and to find that in the non-linear regime the temperature of the metallic island is a crucial parameter. Surprisingly, the metallic island tends to overheat even at zero net charge current, resulting in a reduction of the thermovoltage., 10 pages, 4 figures

openaire: EC/H2020/766025/EU//QuESTech We investigate the basic charge and heat transport properties of charge neutral epigraphene at sub-kelvin temperatures, demonstrating a nearly logarithmic dependence of electrical conductivity over more than two decades in temperature. Using graphene's sheet conductance as an in situ thermometer, we present a measurement of electron-phonon heat transport at mK temperatures and show that it obeys the T4 dependence characteristic for a clean two-dimensional conductor. Based on our measurement, we predict the noise-equivalent power of ∼ 10 - 22 W / Hz of the epigraphene bolometer at the low end of achievable temperatures.

The Coulomb Blockade Thermometer (CBT) is a primary thermometer for cryogenic temperatures, with demonstrated operation from below 1 mK up to 60 K. Its performance as a primary thermometer has been verified at temperatures from 20 mK to 200 mK at uncertainty level below 1 % (k = 2). In a new project, our aim is to extend the metrologically verified temperature range of the primary CBT up to 25 K. We also demonstrate close-to-ideal operation of a CBT with only two tunnel junctions when the device is embedded in a low-impedance environment., 2 pages, 3 figures, 2020 Conference on Precision Electromagnetic Measurements (CPEM), Denver (Aurora), CO, USA, 2020

openaire: EC/H2020/742559/EU//SQH | openaire: EC/H2020/766025/EU//QuESTech We discuss the nonzero frequency noise of heat current with the explicit example of energy carried by thermal photons in a circuit. Instead of the standard circuit modeling that gives a convenient way of predicting timeaveraged heat current, we describe 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 nonzero-frequency heat current noise does not vanish in equilibrium even at zero temperature, a 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 present a theoretical model of an on-chip three-level maser in a superconducting circuit based on a single artificial atom and pumped by a temperature gradient between thermal baths coupled to different interlevel transitions. We show that maser powers of the order of a few femtowatts, well exceeding the resolution of the sensitive bolometry, can be achieved with typical circuit parameters. We also demonstrate that population inversion in the artificial atom can be detected without measuring coherent radiation output of the maser. For that purpose, the system should operate as a three-terminal heat transport device. The hallmark of population inversion is the influx of heat power into the weakly coupled output terminal even though its temperature exceeds the temperatures of the two other terminals. The proposed method of on-chip conversion of heat into microwave radiation and control of energy-level populations by heating provide additional useful tools for circuit quantum electrodynamics experiments., 9 pages, 3 figures

Trabajo presentado en la 3rd Conference on Statistical Physics (2021), celebrada en Miramare (Italia) del 8 al 10 de septiembre de 2021., The stochastic nature of games at the casino allows lucky players to make profit by means of gambling. Like games of chance and stocks, small physical systems are subject to fluctuations, thus their energy and entropy become stochastic, following an unpredictable evolution. In this context, information about the evolution of a thermodynamic system can be used by Maxwell's demons to extract work using feedback control. This is not always the case, and a challenging task is then to develop efficient thermodynamic protocols achieving work extraction in situations where feedback control cannot be realized, in the same spirit as it is done on a daily basis in casinos and financial markets. We introduce and realize gambling demons who, following a customary gambling strategy to stop a nonequilibrium process at stochastic times, are able to extract more average work than the free energy change. We derive second laws in the presence of gambling, and a set of universal stopping-time fluctuation relations for the work done in classical and quantum stochastic non-stationary processes. We test experimentally our results in a single-electron box, where an electrostatic potential is used to drive the dynamics of individual electrons tunneling into a metallic island.

openaire: EC/H2020/766025/EU//QuESTech Shot-noise measurements are widely used for the characterization of nonequilibrium configurations in electronic conductors. The recently introduced quantum tomography approach was implemented for the studies of electronic wave functions of few-electron excitations created by periodic voltage pulses in phase-coherent ballistic conductors based on the high-quality GaAs two-dimensional electron gas. Still relying on the manifestation of Fermi correlations in noise, we focus on the simpler and more general approach beneficial for local measurements of energy distribution (ED) in electronic systems with arbitrary excitations with well-defined energies and random phases. Using biased diffusive metallic wire as a test bed, we demonstrate the power of this approach and extract the well-known double-step ED from the shot noise of a weakly coupled tunnel junction. Our experiment paves the way for local measurements of generic nonequilibrium configurations applicable to virtually any conductor.

openaire: EC/H2020/766025/EU//QuESTech | openaire: EC/H2020/742559/EU//SQH We present a set of experiments to optimize the performance of a 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 are tested. We develop a theoretical model based on Usadel equations and dynamic Coulomb blockade that reproduces the measured results and yields a tool to calibrate the thermometer and to optimize it further in future experiments. We also propose an analytic formula that reproduces the experimental data for a wide range of temperatures.

Weak electron-phonon interaction in metals at low temperatures forms the basis of operation for cryogenic hot-electron bolometers and calorimeters. Standard power laws, describing the heat flow in the majority of experiments, have been identified and derived theoretically. However, a full picture encompassing experimentally relevant effects such as reduced dimensionality, material interfaces, and disorder is in its infancy, and has not been tested extensively. Here, we study the electron-phonon heat flow in a thin gold film on a SiO${}_2$ platform below 100 mK using supercurrent thermometry. We find the power law exponent to be modified from 5.1 to 4.6 as the platform is micromachined and released from its substrate. We attribute this change to a modified phonon spectrum. The findings are compared to past experiments and theoretical models., Comment: 9 pages, 6 figures

openaire: EC/H2020/742559/EU//SQH | openaire: EC/H2020/766025/EU//QuESTech We apply quantum trajectory techniques to analyze a realistic setup 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 discuss 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.

Unveiling the impact in thermodynamics of the phenomena specific to quantum mechanics is a crucial step to identify fundamental costs for quantum operations and quantum advantages in heat engines. We propose a two-reservoir setup to detect the quantum component in the heat flow exchanged by a coherently driven atom with its thermal environment. Tuning the driving parameters switches on and off the quantum and classical contributions to the heat flows, enabling their independent characterization. We demonstrate the feasibility of the measurement in a circuit-QED setup. Our results pave the road towards the first experimental verification of this quantum thermodynamic signature ubiquitous in quantum technologies., 5 pages, 3 figures, Supplement included. Comments welcome

We propose a method to perform accurate and fast charge pumping in superconducting nanocircuits. Combining topological properties and quantum control techniques based on shortcuts to adiabaticity, we show that it is theoretically possible to achieve perfectly quantised charge pumping at any finite-speed driving. Model-specific errors may still arise due the difficulty of implementing the exact control. We thus assess this and other practical issues in a specific system comprised of three Josephson junctions. Using realistic system parameters, we show that our scheme can improve the pumping accuracy of this device by various orders of magnitude. Possible metrological perspectives are discussed., 13 pages, 6 figures

We demonstrate a novel approach to thermometry at the nanoscale exploiting a superconducting weak link. Such a weak link probed with nanosecond current pulses serves as a temperature sensing element and, due to the fast inherent dynamics, is capable of delivering unprecedented temporal resolution. We employ the thermometer to measure dynamic temperature of electrons in a long superconducting wire relaxing to the bath temperature after application of the heating pulse. Our measurement delivers nanosecond resolution thus providing the proof-of-concept of the fastest-todate all-solid-state thermometry. Our method improves the state-of-the-art temporal resolution of mesoscopic thermometry by at least two orders of magnitude, extending temporal resolution of existing experiments and introducing new possibilities for ultra-sensitive calorimeters and radiation detectors.

We report on a device that integrates eight superconducting transmon qubits in lambda/4 superconducting coplanar waveguide resonators fed from a common feedline. Using this multiplexing architecture, each resonator and qubit can be addressed individually thus reducing the required hardware resources and allowing their individual characterisation by spectroscopic methods. The measured device parameters agree with the designed values and the resonators and qubits exhibit excellent coherence properties and strong coupling, with the qubit relaxation rate dominated by the Purcell effect when brought in resonance with the resonator. Our analysis shows that the circuit is suitable for generation of single microwave photons on demand with an efficiency exceeding 80%., 16 pages, 8 figures

We present a measurement and analysis scheme for determining traceable thermodynamic temperature at cryogenic temperatures using Coulomb blockade thermometry. The uncertainty of the electrical measurement is improved by utilizing two sampling digital voltmeters instead of the traditional lock-in technique. The remaining uncertainty is dominated by that of the numerical analysis of the measurement data. Two analysis methods are demonstrated: numerical fitting of the full conductance curve and measuring the height of the conductance dip. The complete uncertainty analysis shows that using either analysis method the relative combined standard uncertainty (k = 1) in determining the thermodynamic temperature in the temperature range from 20 mK to 200 mK is below 0.5 %. In this temperature range, both analysis methods produced temperature estimates that deviated from 0.39 % to 0.67 % from the reference temperatures provided by a superconducting reference point device calibrated against the Provisional Low Temperature Scale of 2000., Comment: 11 pages

We observe a crossover from electron-phonon (ep) coupling limited energy relaxation to that governed by thermal boundary resistance (pp) in copper films at sub-kelvin temperatures. Our measurement yields a quantitative picture of heat currents, in terms of temperature dependences and magnitudes, in both ep and pp limited regimes, respectively. We show that by adding a third layer in between the copper film and the substrate, the thermal boundary resistance is increased fourfold, consistent with an assumed series connection of thermal resistances., Comment: 4 figures

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 originally 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., Comment: 9 pages, 8 figures

We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kHz. We demonstrate that the pair breaking is caused by the backaction of the single-electron transistor used as a charge detector. With sufficiently low probing currents, our superconducting island is free of quasiparticles 97% of the time., Supplementary material included

We experimentally realize protocols that allow to extract work beyond the free energy difference from a single electron transistor at the single thermodynamic trajectory level. With two carefully designed out-of-equilibrium driving cycles featuring kicks of the control parameter, we demonstrate work extraction up to large fractions of $k_BT$ or with probabilities substantially greater than 1/2, despite zero free energy difference over the cycle. Our results are explained in the framework of nonequilibrium fluctuation relations. We thus show that irreversibility can be used as a resource for optimal work extraction even in the absence of feedback from an external operator., Comment: Submitted, SI included

The electronic structure of the giant vortex states in a mesoscopic superconducting disk is studied in a dirty limit using the Usadel approach. The local density of states profiles are shown to be strongly affected by the effect of quasiparticle (QP) tunneling between the states localized in the vortex core and the ones bound to the sample edge. Decreasing temperature leads to a crossover between the edge-dominated and core-dominated regimes in the magnetic field dependence of the tunneling conductance. This crossover is discussed in the context of the efficiency of quasiparticle cooling by the magnetic field induced QP traps in various mesoscopic superconducting devices., 10 pages, 7 figures, 59 references

Ongoing experimental activity aims at calorimetric measurements of thermodynamic indicators of quantum integrated systems. We study a model of a driven qubit in contact with a finite-size thermal electron reservoir. The temperature of the reservoir changes due to energy exchanges with the qubit and an infinite-size phonon bath. Under the assumption of weak coupling and weak driving, we model the evolution of the qubit-electron-temperature as a hybrid master equation for the density matrix of the qubit at different temperatures of the calorimeter. We compare the temperature evolution with an earlier treatment of the qubit-electron model, where the dynamics were modelled by a Floquet master equation under the assumption of drive intensity much larger than the qubit-electron coupling squared. We numerically and analytically inquire the predictions of the two mathematical models of dynamics in the weak-drive parametric region. We numerically determine the parametric regions where the two models of dynamics give distinct temperature predictions and those where their predictions match., 11 pages, 4 figures