A reciprocating quantum refrigerator is studied with the purpose of determining the limitations of cooling to absolute zero. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, then there is a minimum achievable temperature above zero. Such a gap, combined with a negligible amount of noise, prevents adiabatic following during the demagnetization stage which is the necessary condition for reaching $T_c \to 0$. The refrigerator is based on an Otto cycle where the working medium is an interacting spin system with an energy gap. For this system the external control Hamiltonian does not commute with the internal interaction. As a result during the demagnetization and magnetization segments of the operating cycle the system cannot follow adiabatically the temporal change in the energy levels. We connect the nonadiabatic dynamics to quantum friction. An adiabatic measure is defined characterizing the rate of change of the Hamiltonian. Closed form solutions are found for a constant adiabatic measure for all the cycle segments. We have identified a family of quantized frictionless cycles with increasing cycle times. These cycles minimize the entropy production. Such frictionless cycles are able to cool to $T_c=0$. External noise on the controls eliminates these frictionless cycles. The influence of phase and amplitude noise on the demagnetization and magnetization segments is explicitly derived. An extensive numerical study of optimal cooling cycles was carried out which showed that at sufficiently low temperature the noise always dominates restricting the minimum temperature.
We revisit the self-contained quantum refrigerator in the strong-internal-coupling regime by employing the quantum optical master equation. It is shown that strong internal coupling reduces the cooling ability of the refrigerator. In contrast to the weak-coupling case, strong internal coupling could lead to quite different and even converse thermodynamic behaviors.
We discuss a quantum refrigerator to increase the ground state probability of a target qubit whose energy difference between the ground and excited states is less than the thermal energy of the environment. We consider two types of quantum refrigerators: (1) one extra qubit with frequent pulse operations and (2) two extra qubits without them. These two types of refrigerators are evaluated from the viewpoint of quantum thermodynamics. More specifically, we calculate the heat removed from the target qubit, the work done for the system, and the coefficient of performance (COP), the ratio between …
We explore a thermodynamical effect of anharmonicity in quantum mechanical oscillators. We show that small quartic perturbations to the oscillator potential lead to an enhancement of performance of quantum refrigerators for both the Otto and Stirling cycles. A similar nonlinearity driven enhancement of performance is also observed for an analogous spin-qubit model of quantum refrigerators. We further demonstrate the robustness of improvement of the coefficient of performance versus the energy cost for creating anharmonicity. It is shown that the anharmonicity driven improvement in performance …
We propose to use a few-qubit system as a compact quantum refrigerator for cooling an interacting multi-qubit system. We specifically consider a central qubit coupled to $N$ ancilla qubits in a so-called spin-star model as our quantum refrigerator. We first show that if the interaction between the qubits is of the longitudinal and ferromagnetic Ising model form, the central qubit is colder than the environment. The colder central qubit is then proposed to be used as the refrigerant interface of the quantum refrigerator to cool down general quantum many-qubit systems. We discuss a simple refrig…
Various quantum systems are considered as the working substance for the analysis of quantum heat cycles and quantum refrigerators. The ongoing technological challenge is how efficiently can a heat engine convert thermal energy to mechanical work. The seminal work of Carnot has proposed a fundamental upper limit-the Carnot limit on the efficiency of the heat engine. However, the heat engines can be operated beyond the fundamental upper limit by exploiting non-equilibrium reservoirs. Here, the change in the space structure introduces the non-equilibrium effect. So, a question arises whether a ch…
We consider a quantum Otto cycle operating between two squeezed thermal reservoirs. The influences of the squeezing degree on the optimization performance of quantum Otto heat engines and refrigerators are investigated. We demonstrate that under symmetric condition, the efficiency at maximum power (EMP) of heat engines and the coefficient of performance (COP) at maximum \c{hi} criterion of refrigerators are equal to Curzon-Ahlborn (CA) efficiency and CA COP, respectively. We also found that under asymmetric condition, the EMP of heat engines can be improved when the squeezing degree of hot the…
Refrigeration is an important enabler for quantum technology. The very low energy of the fundamental excitations typically utilized in quantum technology devices and systems requires temperature well below 1 K. Expensive cryostats are utilized in reaching sub-1 K regime and solid-state cooling solutions would revolutionize the field. New electronic micro-coolers based on phonon-blocked semiconductor-superconductor junctions could provide a viable route to such miniaturization. Here, we investigate the performance limits of these junction refrigerators.
We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhi…
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.
Indefinite causal order (ICO) is playing a key role in recent quantum technologies. Here, we experimentally study quantum thermodynamics driven by ICO on nuclear spins using the nuclear magnetic resonance system. We realize the ICO of two thermalizing channels to exhibit how the mechanism works, and show that the working substance can be cooled or heated albeit it undergoes thermal contacts with reservoirs of the same temperature. Moreover, we construct a single cycle of the ICO refrigerator based on the Maxwell's demon mechanism, and evaluate its performance by measuring the work consumption …
We show that one can construct a quantum absorption refrigerator that provides refrigeration only in the transient regime, by using three interacting qubits, each of which is also interacting with local heat-bath. The machine either does not provide cooling in the steady state, or the steady state is achieved after a long time. We propose a canonical form of qubit-bath interaction parameters that generates transient cooling without steady-state cooling, and claim that such a phenomenon is generic to small-scale quantum absorption refrigerators. We also show that it is generically possible to h…
We study a quantum absorption refrigerator, in which a target qubit is cooled by two machine qubits in a nonequilibrium steady state. It is realized by a strong internal coupling in the two-qubit fridge and a vanishing tripartite interaction among the whole system. The coherence of a \emph{machine virtual qubit} is investigated as quantumness of the fridge. A necessary condition for cooling shows that the quantum coherence is beneficial to the nonequilibrium fridge, while it is detrimental as far as the maximum coefficient of performance (COP) and the COP at maximum power are concerned. Here, …
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…
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…
We analyze the performance of a quantum Otto cycle, employing time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with the earlier studies claiming unit efficiency under the effect of squeezed reservoir. Then, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independen…
We study the thermodynamics of a quantum system interacting with different baths in the repeated interaction framework. In an appropriate limit, the evolution takes the Lindblad form and the corresponding thermodynamic quantities are determined by the state of the full system plus baths. We identify conditions under which the thermodynamics of the open system can be described only by system properties and find a quantum local detailed balance condition with respect to an equilibrium state that may not be a Gibbs state. The three-qubit refrigerator introduced in [N. Linden, S. Popescu and P. Sk…
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…
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…
Quantum refrigerators pump heat from a cold to a hot reservoir. In the few-particle regime, counter-diabatic (CD) driving of, originally adiabatic, work-exchange strokes is a promising candidate to overcome the bottleneck of vanishing cooling power. Here, we present a finite-time many-body quantum refrigerator that yields finite cooling power at high coefficient of performance, that considerably outperforms its non-adiabatic counterpart. We employ multi-spin CD driving and numerically investigate the scaling behavior of the refrigeration performance with system size. We further prove that opti…
We study the optimal performance of a three-level quantum refrigerator using a trade-off objective function, $Ω$ function, which represents a compromise between the energy benefits and the energy losses of a thermal device. First, we optimize the performance of our refrigerator by employing a two-parameter optimization scheme and show that the first two-terms in the series expansion of the obtained coefficient of performance (COP) match with those of some classical models of refrigerator. Then, in the high-temperature limit, optimizing with respect to one parameter while constraining the other…
The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal absorption machines are a particularly interesting class of device that operate autonomously and use only heat flows to perform a useful task. In the quantum regime, this provides a natural setting in which to quantify the thermodynamic cost of various operations such as cooling, timekeeping or entanglement generation. This article presents a pedagogical introd…
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…
Quantum absorption refrigerator (QAR) autonomously extracts heat from a cold bath and dumps into a hot bath by exploiting the input heat from a higher temperature reservoir. QARs typically require three-body interactions. We propose and examine a two-body QAR model based upon optomechanical-like coupling in the working medium composed of either two two-level systems or two harmonic oscillators or one two-level atom and a harmonic oscillator. In the ideal case without internal dissipation, within the experimentally realizable parameters, our model can attain the coefficient of performance that …
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…
In this work, we solve the quantum absorption refrigerator analytically in the space of holomorphic functions with Gaussian measure . Our approach simplifies the calculations since for a given quantum system the coordinate representation of any quantum state is always more complicated than its corresponding expression written with respect to the phase-space coordinate $z_{i}$. We finally discuss the computational complexity of the holomorphic representation and compare it with the computational complexity of the standard operator method and prove the efficiency of the holomorphic representatio…
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 how to achieve the ultimate power in the simplest, yet non trivial, model of a thermal machine, namely a two-level quantum system coupled to two thermal baths. Without making any prior assumption on the protocol, via optimal control we show that, regardless of the microscopic details and of the operating mode of the thermal machine, the maximum power is universally achieved by a fast Otto-cycle like structure in which the controls are rapidly switched between two extremal values. A closed formula for the maximum power is derived, and finite-speed effects are discussed. We also analyse…
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…
We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced pe…
An autonomous quantum thermal machine comprising a trapped atom or ion placed inside an optical cavity is proposed and analysed. Such a machine can operate as a heat engine whose working medium is the quantised atomic motion, or as an absorption refrigerator which cools without any work input. Focusing on the refrigerator mode, we predict that it is possible with state-of-the-art technology to cool a trapped ion almost to its motional ground state using a thermal light source such as sunlight. We nonetheless find that a laser or similar reference system is necessary to stabilise the cavity fre…
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 investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum $Ω$-function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet…
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…
Thermodynamics is one of the oldest and well-established branches of physics that sets boundaries to what can possibly be achieved in macroscopic systems. While it started as a purely classical theory, it was realized in the early days of quantum mechanics that large quantum devices, such as masers or lasers, can be treated with the thermodynamic formalism. Remarkable progress has been made recently in the miniaturization of heat engines all the way to the single Brownian particle as well as to a single atom. However, despite several theoretical proposals, the implementation of heat machines i…
The extension of quantum thermodynamics to situations that go beyond standard thermodynamic settings comprises an important and interesting aspect of its development. One such situation is the analysis of the thermodynamic consequences of structured environments that induce a non-Markovian dynamics. We study a quantum Otto refrigerator where the standard Markovian cold reservoir is replaced by a specific engineered cold reservoir which may induce a Markovian or non-Markovian dynamics on the quantum refrigerant system. The two dynamical regimes can be interchanged by varying the coupling betwee…
