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 a major challenge in many solid-state implementations, such as superconducting circuits. Here, we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable quantum tunneling of electrons in a nanoscale refrigerator. This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even when the electrons in the refrigerator itself are at an elevated temperature. Our conclusions are verified by control experiments and by a good quantitative agreement between a detailed theoretical model and the direct experimental observations in a broad range of operation voltages and phonon bath temperatures. In the future, the introduced refrigerator can be integrated with different quantum electric devices, potentially enhancing their performance. For the superconducting quantum computer, for example, it may provide an efficient way of initializing the quantum bits.
The emerging quantum technological applications call for fast and accurate initialization of the corresponding devices to low-entropy quantum states. To this end, we theoretically study a recently demonstrated quantum-circuit refrigerator in the case of non-linear quantum electric circuits such as superconducting qubits. The maximum refrigeration rate of transmon and flux qubits is observed to be roughly an order of magnitude higher than that of usual linear resonators, increasing flexibility in the design. We find that for typical experimental parameters, the refrigerator is suitable for rese…
An implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson unction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that signi…
Multi-terminal multi-dot devices have been put forward as versatile and performant setups for thermoelectric energy harvesting at the nanoscale. With a technique that encompasses and overtakes several of the usual theoretical tools used in this context, we explore a three-terminal Coulomb-coupled-dot device for refrigeration purposes. The refrigerator is monitored by either a voltage or a thermal bias. This comparative study shows that heat driven refrigerator is much underperforming than the power driven one, due to scarce on-dot charge fluctuations.
A simplified analytical model of single-level quantum dot (QD) refrigerator was studied without considering the electron spin and Coulomb interaction. Based on the ballistic transport of electrons between two reservoirs across the QD, the Joule heat of the system was assumed to be generated from the Ohmic contacts between the QD and reservoirs. By using the transition rate equation, the performance of the QD refrigerator was studied with respect to the electron transmission probability and the partition ratio (i.e., the fraction of Joule heat generated in the system that releases into the cold…
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 resonato…
Experiments performed at a temperature of a few millikelvin require effective thermalization schemes, low-pass filtering of the measurement lines and low-noise electronics. Here, we report on the modifications to a commercial dilution refrigerator with a base temperature of 3.5 mK that enable us to lower the electron temperature to 6.7 mK measured from the Coulomb peak width of a quantum dot gate-defined in an [Al]GaAs heteostructure. We present the design and implementation of a liquid $^4$He immersion cell tight against superleaks, implement an innovative wiring technology and develop optimi…
We investigate a mesoscopic refrigerator based on chiral quantum Hall edge channels. We discuss a three-terminal cooling device in which charge transport occurs between a pair of voltage-biased terminals only. The third terminal, which is to be cooled, is set as a voltage probe with vanishing particle flux. This largely prevents the generation of direct Joule heating which ensures a high coefficient of performance. Cooling operation is based on energy-dependent quantum transmissions. The latter are implemented with the aid of two tunable scattering resonances (quantum dots). To find the optima…
Absorption refrigerators are autonomous thermal machines that harness the spontaneous flow of heat from a hot bath into the environment in order to perform cooling. Here we discuss quantum realizations of absorption refrigerators in two different settings: namely, cavity and circuit quantum electrodynamics. We first provide a unified description of these machines in terms of the concept of virtual temperature. Next, we describe the two different physical setups in detail and compare their properties and performance. We conclude with an outlook on future work and open questions in this field of…
Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. We manifest that eigenbasis quantum coherences within this system generally suppress the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-…
Fluctuations are significant in mesoscopic systems and of particular importance in understanding quantum transport. Here, we show that fluctuations can be considered as a resource for the operations of open quantum systems as functional devices. We derive the statistics of the thermal transistor amplification factor and the cooling-by-heating refrigerator efficiency under the Gaussian fluctuation framework. Statistical properties of the stochastic thermal transistor and the cooling-by-heating efficiency are revealed in the linear-response regime. We clarify the unique role of inelastic process…
Models for quantum absorption refrigerators serve as test beds for exploring concepts and developing methods in quantum thermodynamics. Here, we depart from the minimal, ideal design and consider a generic multilevel model for a quantum absorption refrigerator, which potentially suffers from lossy processes. Based on a full-counting statistics approach, we derive a formal cooling condition for the refrigerator, which can be feasibly evaluated analytically and numerically. We exemplify our approach on a three-level model for a quantum absorption refrigerator that suffers from different forms of…
Absorption refrigerators transfer thermal energy from a cold bath to a hot bath without input power by utilizing heat from an additional "work" reservoir. Particularly interesting is a three-level design for a quantum absorption refrigerator, which can be optimized to reach the maximal (Carnot) cooling efficiency. Previous studies of three-level chillers focused on the behavior of the averaged cooling current. Here, we go beyond that and study the full counting statistics of heat exchange in a three-level chiller model. We explain how to obtain the complete cumulant generating function of the …
We investigate the performance of a quantum Otto refrigerator operating in finite time and exploiting local counterdiabatic techniques. We evaluate its coefficient of performance and cooling power when the working medium consists a quantum harmonic oscillator with a time-dependent frequency. We find that the quantum refrigerator outperforms its conventional counterpart, except for very short cycle times, even when the driving cost of the local counterdiabatic driving is included. We moreover derive upper bounds on the performance of the thermal machine based on quantum speed limits and show th…
We consider a quantum Otto refrigerator cycle of a time-dependent harmonic oscillator. We investigate the coefficient of performance at maximum figure of merit for adiabatic and nonadiabatic frequency modulations. We obtain analytical expressions for the optimal performance both in the high-temperature (classical) regime and in the low-temperature (quantum) limit. We moreover analyze the breakdown of the cooling cycle for strongly nonadiabatic driving protocols and derive analytical estimates for the minimal driving time allowed for cooling.
Two qubits form a quantum four-level system. The golden-rule based transition rates between these states are determined by the coupling of the qubits to noise sources. We demonstrate that depending on whether the noise acting on the two qubits is correlated or not, these transitions are governed by different selection rules. In particular, we find that for fully correlated or anticorrelated noise, there is a protected state, and the dynamics of the system depends then on its initialization. For nearly (anti)correlated noise, there is a long time scale determining the temporal evolution of the …
We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also o…
We analyse a quantum Otto refrigerator based on a superconducting qubit coupled to two LC-resonators each including a resistor acting as a reservoir. We find various operation regimes: nearly adiabatic (low driving frequency), ideal Otto cycle (intermediate frequency), and non-adiabatic coherent regime (high frequency). In the nearly adiabatic regime, the cooling power is quadratic in frequency, and we find substantially enhanced coefficient of performance $ε$, as compared to that of an ideal Otto cycle. Quantum coherent effects lead invariably to decrease in both cooling power and $ε$ as comp…
Revealing the fuel of a quantum continuous measurement-based refrigerator
Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Tata Institute of Fundamental Research（塔塔基础研究所）；Nordita（北欧理论天体物理学研究所）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Institute for Quantum Studies, Chapman University（查普曼大学量子研究学院）；Chapman University（查普曼大学）；University of Rochester（罗切斯特大学）；Department of Applied Physics, University of Geneva（日内瓦大学应用物理系）
Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, on the other hand, have attracted a great deal of attention in the last few years. In this article, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a trade-off relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the ste…
Micro-refrigerators that operate in the sub-kelvin regime are a key device in quantum technology. A well-studied candidate, an electronic cooler using Normal metal - Insulator - Superconductor (NIS) tunnel junctions offers substantial performance and power. However, its superconducting electrodes are severely overheated due to exponential suppression of their thermal conductance towards low temperatures, and the cooler performs unsatisfactorily - especially in powerful devices needed for practical applications. We employ a second NIS cooling stage to thermalize the hot superconductor at the ba…
We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and $χ$-function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power is optimizable only in the local region with respect to one control frequency, while $χ$-function can be optimized globally with respect to…
We demonstrate that a quantum absorption refrigerator can be realized from the smallest quantum system, a qubit, by coupling it in a non-additive (strong) manner to three heat baths. This function is un-attainable for the qubit model under the weak system-bath coupling limit, when the dissipation is additive. In an optimal design, the reservoirs are engineered and characterized by a single frequency component. We obtain then closed expressions for the cooling window and refrigeration efficiency, as well as bounds for the maximal cooling efficiency and the efficiency at maximal power. Our resul…
We propose a quantum absorption refrigerator using the quantum physics of resonant tunneling through quantum dots. The cold and hot reservoirs are fermionic leads, tunnel coupled via quantum dots to a central fermionic cavity, and we propose configurations in which the heat absorbed from the (very hot) central cavity is used as a resource to selectively transfer heat from the cold reservoir on the left, to the hot reservoir on the right. The heat transport in the device is particle---hole symmetric; we find two regimes of cooling as a function of the energy of the dots---symmetric with respect…
We report a scanning superconducting quantum interference device (SQUID) microscope in a cryogen-free dilution refrigerator with a base temperature at the sample stage of at least 30 mK. The microscope is rigidly mounted to the mixing chamber plate to optimize thermal anchoring of the sample. The microscope housing fits into the bore of a superconducting vector magnet, and our design accommodates a large number of wires connecting the sample and sensor. Through a combination of vibration isolation in the cryostat and a rigid microscope housing, we achieve relative vibrations between the SQUID …
We analyze a simple implementation of an absorption refrigerator, a system that requires heat and not work to achieve refrigeration, based on two Coulomb coupled single-electron systems. We analytically determine the general condition to achieve cooling-by-heating, and we determine the system parameters that simultaneously maximize the cooling power and cooling coefficient of performance (COP) finding that the system displays a particularly simple COP that can reach Carnot's upper limit. We also find that the cooling power can be indirectly determined by measuring a charge current. Analyzing t…
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a trade-off relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where no…
We present a microwave quantum refrigeration principle based on the Josephson effect. When a superconducting quantum interference device (SQUID) is pierced by a time-dependent magnetic flux, it induces changes in the macroscopic quantum phase and an effective finite bias voltage appears across the SQUID. This voltage can be used to actively cool well below the lattice temperature one of the superconducting electrodes forming the interferometer. The achievable cooling performance combined with the simplicity and scalability intrinsic to the structure pave the way to a number of applications in …
Refrigerators soak up heat energy from a low-temperature region and dump it into a higher temperature region using external work done on the system. Refrigerators are useful in cooling down a system to very low temperatures. In this letter, we show that a monolayer of strained graphene can be used in designing a quantum refrigerator with an excellent coefficient of performance and large cooling power. The operating point at which the strained graphene device works best as a quantum refrigerator is derived and the effects of strain and temperature on cooling are discussed.
We study universal aspects of fluctuations in an ensemble of noninteracting continuous quantum thermal machines in the steady state limit. Considering an individual machine, such as a refrigerator, in which relative fluctuations (and high order cumulants) of the cooling heat current to the absorbed heat current, $η^{(n)}$, are upper-bounded, $η^{(n)}\leq η_C^n$ with $n\geq 2$ and $η_C$ the Carnot efficiency, we prove that an {\it ensemble} of $N$ distinct machines similarly satisfies this upper bound on the relative fluctuations of the ensemble, $η_N^{(n)}\leq η_C^n$. For an ensemble of distin…
We study the phenomenon of absorption refrigeration, where refrigeration is achieved by heating instead of work, in two different setups: a minimal set up based on coupled qubits, and two non-linearly coupled resonators. Considering ZZ interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of XX type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of non-linearly coupled resonators (multi-level system…
Refrigerators use a thermodynamic cycle to move thermal energy from a cold reservoir to a hot one. Implementing this operation principle with mesoscopic components has recently emerged as a promising strategy to control heat currents in micro and nano systems for quantum technological applications. Here, we combine concepts from stochastic and quantum thermodynamics with advanced methods of optimal control theory to develop a universal optimization scheme for such small-scale refrigerators. Covering both the classical and the quantum regime, our theoretical framework provides a rigorous proced…
We propose a solid state refrigeration technique based on repeated adiabatic magnetization/demagnetization cycles of a superconductor which acts as the working substance. The gradual cooling down of a substrate (normal metal) in contact with the working substance is demonstrated for different initial temperatures of the substrate. Excess heat is given to a hot large-gap superconductor. The on-chip refrigerator works in a cyclic manner because of an effective thermal switching mechanism: Heat transport between N/N versus N/S junctions is asymmetric because of the appearance of the energy gap. T…
High-fidelity single-shot readout of spin qubits requires distinguishing states much faster than the T1 time of the spin state. One approach to improving readout fidelity and bandwidth (BW) is cryogenic amplification, where the signal from the qubit is amplified before noise sources are introduced and room-temperature amplifiers can operate at lower gain and higher BW. We compare the performance of two cryogenic amplification circuits: a current-biased heterojunction bipolar transistor circuit (CB-HBT), and an AC-coupled HBT circuit (AC-HBT). Both circuits are mounted on the mixing-chamber sta…
A robust cryogenic infrastructure in form of a wired, thermally optimized dilution refrigerator is essential for present and future solid-state based quantum processors. Here, we engineer an extensible cryogenic setup, which minimizes passive and active heat loads, while guaranteeing rapid qubit control and readout. We review design criteria for qubit drive lines, flux lines, and output lines used in typical experiments with superconducting circuits and describe each type of line in detail. The passive heat load of stainless steel and NbTi coaxial cables and the active load due to signal dissi…
We focus on a recently experimentally realized scenario of normal-metal-insulator-superconductor tunnel junctions coupled to a superconducting resonator. We develop a first-principles theory to describe the effect of photon-assisted electron tunneling on the quantum state of the resonator. Our results are in very good quantitative agreement with the previous experiments on refrigeration and heating of the resonator using the photon-assisted tunneling, thus providing a stringent verification of the developed theory. Importantly, our results provide simple analytical estimates of the voltage-tun…
Thermoelectric (TE) refrigeration such as Peltier cooler enables a unique opportunity in electric energy to directly convert thermal energy. Here, we propose a TE module with both refrigeration and power generation modes by utilizing asymmetric surfaces of a magnetic topological insulator (quantum anomalous Hall insulator) with a periodic array of hollows filled with two different dielectrics. Based on the Boltzmann transport theory, we show that its efficiency, i.e., the dimensionless figure of merit ZT exceeds 1 in the low-temperature regime below 300 K. The proposed device could be utilized…
We present a unified approach to study continuous measurement based quantum thermal machines in static as well as adiabatically driven systems. We investigate both steady state and transient dynamics for the time-independent case. In the adiabatically driven case, we show how measurement based thermodynamic quantities can be attributed geometric characteristics. We also provide the appropriate definition for heat transfer and dissipation owing to continous measurement in the presence and absence of adiabatic driving. We illustrate the aforementioned ideas and study the phenomena of refrigerati…
Quantum physics emerge and develop as temperature is reduced. Although mesoscopic electrical circuits constitute an outstanding platform to explore quantum behavior, the challenge in cooling the electrons impedes their potential. The strong coupling of such micrometer-scale devices with the measurement lines, combined with the weak coupling to the substrate, makes them extremely difficult to thermalize below 10 mK and imposes in-situ thermometers. Here we demonstrate electronic quantum transport at 6 mK in micrometer-scale mesoscopic circuits. The thermometry methods are established by the com…
The emerging field of phase-coherent caloritronics (from the Latin word "calor", i.e., heat) is based on the possibility to control heat currents using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices able to master energy transfer with a degree of accuracy approaching the one reached for charge transport by contemporary electronic components. This can be obtained by exploiting the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson and the proximity effect. Here, we…
We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently-developed quantum-circuit refrigerator (QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active rese…
