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 refrigeration cycle, considering the operation cost and cooling efficiency, which can be controlled by $N$ and the qubit-qubit interaction strength. Besides, bounds on the achievable temperature are established. Such few-qubit compact quantum refrigerators can be significant to reduce dimensions of quantum technology applications, can be easy to integrate into all-qubit systems, and can increase the speed and power of quantum computing and thermal devices.
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 …
A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics, but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not need…
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…
A quantum absorption refrigerator driven by noise is studied with the purpose of determining the limitations of cooling to absolute zero. The model consists of a working medium coupled simultaneously to hot, cold and noise baths. Explicit expressions for the cooling power are obtained for Gaussian and Poisson white noise. The quantum model is consistent with the first and second laws of thermodynamics. The third law is quantified, the cooling power J_c vanishes as J_c proportional to T_c^{alpha}, when T_c approach 0, where alpha =d+1 for dissipation by emission and absorption of quanta describ…
The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as $T_c \to 0$. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature. The optimal cycle is characterized by linear relations between the heat extracted from the cold bath, the energy level spacing of the working medium and the temperature. The scaling of the optimal cooling rat…
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…
We comment that the model proposed in Phys. Rev. Lett. 108, 120603 (2012) violates the dynamical version of the third law of thermodynamics. We discuses the different formulations of the third law of thermodynamics and suggest a possible reason for the violation.
We investigate, theoretically and experimentally, the thermodynamic performance of a minimal three-qubit heat-bath algorithmic cooling refrigerator. We analytically compute the coefficient of performance, the cooling power and the polarization of the target qubit for an arbitrary number of cycles, taking realistic experimental imperfections into account. We determine their fundamental upper bounds in the ideal reversible limit and show that these values may be experimentally approached using a system of three qubits in a nitrogen-vacancy center in diamond.
We investigate the fundamental dimensional limits to thermodynamic machines. In particular we show that it is possible to construct self-contained refrigerators (i.e. not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbour interactions, and a single qutrit respectively. We then investigate fundamental limits to their performance; in particular we show that it is possible to cool towards absolute zero.
Results obtained recently in Phys. Rev. Lett. 108, 120603 (2012) by Cleuren et al. apparently contradict to the third law of thermodynamics. We discuss a scenario for resolving this contradiction, and show that this scenario is pertinent for clarifying the general message of the third law.
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, …
The extension of thermodynamics into the quantum regime has received much attention in recent years. A primary objective of current research is to find thermodynamic tasks which can be enhanced by quantum mechanical effects. With this goal in mind, we explore the finite-time dynamics of absorption refrigerators composed of three qubits. The aim of this finite-time cooling is to reach low temperatures as fast as possible and subsequently extract the cold particle to exploit it for information processing purposes. We show that the coherent oscillations inherent to quantum dynamics can be harness…
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 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 proposed a scheme to implement a self-contained quantum refrigerator system composed of three rf-SQUID qubits, or rather, flux-biased phase qubits. The three qubits play the roles of the target, the refrigerator and the heat engine respectively. We provide different effective temperatures for the three qubits, by imposing external current noises of different strengths. The differences of effective temperatures give rise to the flow of free energy and that drives the refrigerator system to cool down the target. We also show that the efficiency of the system approaches the Carnot efficiency.
We experimentally demonstrate the temporary removal of thermal photons from a microwave mode at 1.45 GHz through its interaction with the spin-polarized triplet states of photo-excited pentacene molecules doped within a p-terphenyl crystal at room temperature. The crystal functions electromagnetically as a narrow-band cryogenic load, removing photons from the otherwise room-temperature mode via stimulated absorption. The noise temperature of the microwave mode dropped to $50^{+18}_{-32}$ K (as directly inferred by noise-power measurements) while the metal walls of the cavity enclosing the mode…
We show that the lower levels of a large-spin network with a collective anti-ferromagnetic interaction and collective couplings to three reservoirs may function as a quantum absorption refrigerator. In appropriate regimes, the steady-state cooling current of this refrigerator scales quadratically with the size of the working medium, i.e., the number of spins. The same scaling is observed for the noise and the entropy production rate.
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 the asymptotic dynamics of arbitrary linear quantum open systems which are periodically driven while coupled with generic bosonic reservoirs. We obtain exact results for the heat flowing into the network, which are valid beyond the usual weak coupling or Markovian approximations. We prove the validity of the dynamical third law of thermodynamics (Nernst unattainability principle), showing that the ultimate limit for cooling is imposed by a fundamental heating mechanism which becomes dominant at low temperatures: the non resonant creation of pairs of excitations in the reservoirs induc…
Small self-contained quantum thermal machines function without external source of work or control, but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned---fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence a truly quantum refrigerator can outperform a classical one. Fu…
Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to the level of a single few level system coupled to the environment. Once the environment is split into three;a hot, cold and work reservoirs a heat engine can operate. The device converts the positive gain into power;where the gain is obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs is used as a template f…
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 consider fault-tolerant quantum computation in the context where there are no fresh ancilla qubits available during the computation, and where the noise is due to a general quantum channel. We show that there are three classes of noisy channels: In the first, typified by the depolarizing channel, computation is only possible for a logarithmic time. In the second class, of which the dephasing channel is an example, computation is possible for polynomial time. The amplitude damping channel is an example of the third class, and for this class of channels, it is possible to compute for an expon…
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…
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 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…
We propose a general method of cooling -- periodic driving generated by spatially deformed Hamiltonians -- and study it in general one-dimensional quantum critical systems described by a conformal field theory. Our protocol is able to efficiently cool a finite-temperature Gibbs (mixed) state down to zero temperature at prescribed sub-regions exponentially rapidly in Floquet time cycles. At the same time, entropy and energy are transferred and localized to the complementary regions that shrink with time. We derive these conclusions through an exact analytic solution of the full time evolution o…
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…
Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by 'reversing' the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fri…
We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realised in current experimental setups. We model the open-system dynamics with both a global and a local…
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 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 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.
Four stroke Otto refrigerator cycles with no classical analogue are studied. Extremely short cycle times with respect to the internal time scale of the working medium characterize these refrigerators. Therefore these cycles are termed sudden. The sudden cycles are characterized by the stable limit cycle which is the invariant of the global cycle propagator. During their operation the state of the working medium possesses significant coherence which is not erased in the equilibration segments due to the very short time allocated. This characteristic is reflected in a difference between the ener…
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…
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 combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born-Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and…
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…
Engineered two-photon dissipative confinement of a Kerr-cat qubit using SISIS quantum circuit refrigerator
National Institute of Advanced Industrial Science and Technology (AIST)（产业技术综合研究所）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CEA（法国原子能和替代能源委员会）；Grenoble INP（格勒诺布尔理工学院）；IRIG（研究信息与影像研究所）；PHELIQS（量子物理与化学研究所）；Institute for Solid State Physics, the University of Tokyo（东京大学固体物理研究所）；Department of Physics, Graduate School of Science, Tokyo University of Science（东京理科大学理学研究科物理学系）；Research Institute for Science and Technology, Tokyo University of Science（东京理科大学理工研究院）
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.
The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results which are model-independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for \textit{any} endoreversible quantum refrigerator.…
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 c…
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…
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 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…
