Quantum absorption refrigerator with trapped ions

Probing coherent quantum thermodynamics using a trapped ion

Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, where coherence and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we demonstrate the possibility to experimentally measure and benchmark a genuine quantum correction, induced by quantum friction, to the classical work fluctuation-dissipation relation. This is achieved by combining laser-induced coherent Hamiltonian rotations and energy measurements on a trapped ion. Our results demonstrate that recent developments in stochastic quantum thermodynamics can be used to benchmark and unambiguously distinguish genuine quantum coherent signatures generated along driving protocols, even in presence of experimental SPAM errors and, most importantly, beyond the regimes for which theoretical predictions are available (e.g., in slow driving).

Catalytic Advantage in Otto-like Two-Stroke Quantum Engines

We demonstrate how to incorporate a catalyst to enhance the performance of a heat engine. Specifically, we analyze efficiency in one of the simplest engine models, which operates in only two strokes and comprises of a pair of two-level systems, potentially assisted by a d-dimensional catalyst. When no catalysis is present, the efficiency of the machine is given by the Otto efficiency. Introducing the catalyst allows for constructing a protocol which overcomes this bound, while new efficiency can be expressed in a simple form as a generalization of Otto's formula: 1-(1/d)(ω_{c}/ω_{h}). The catalyst also provides a bigger operational range of parameters in which the machine works as an engine. Although an increase in engine efficiency is mostly accompanied by a decrease in work production (approaching zero as the system approaches Carnot efficiency), it can lead to a more favorable trade-off between work and efficiency. The provided example introduces new possibilities for enhancing performance of thermal machines through finite-dimensional ancillary systems.

Chiral quantum heating and cooling with an optically controlled ion

Quantum heat engines and refrigerators are open quantum systems, whose dynamics can be well understood using a non-Hermitian formalism. A prominent feature of non-Hermiticity is the existence of exceptional points (EPs), which has no counterpart in closed quantum systems. It has been shown in classical systems that dynamical encirclement in the vicinity of an EP, whether the loop includes the EP or not, could lead to chiral mode conversion. Here, we show that this is valid also for quantum systems when dynamical encircling is performed in the vicinity of their Liouvillian EPs (LEPs), which include the effects of quantum jumps and associated noise-an important quantum feature not present in previous works. We demonstrate, using a Paul-trapped ultracold ion, the first chiral quantum heating and refrigeration by dynamically encircling a closed loop in the vicinity of an LEP. We witness the cycling direction to be associated with the chirality and heat release (absorption) of the quantum heat engine (quantum refrigerator). Our experiments have revealed that not only the adiabaticity breakdown but also the Landau-Zener-Stückelberg process play an essential role during dynamic encircling, resulting in chiral thermodynamic cycles. Our observations contribute to further understanding of chiral and topological features in non-Hermitian systems and pave a way to exploring the relation between chirality and quantum thermodynamics.

Entanglement Growth via Splitting of a Few Thermal Quanta

Quanta splitting is an essential generator of Gaussian entanglement, exemplified by Einstein-Podolsky-Rosen states and apparently the most commonly occurring form of entanglement. In general, it results from the strong pumping of a nonlinear process with a highly coherent and low-noise external drive. In contrast, recent experiments involving efficient trilinear processes in trapped ions and superconducting circuits have opened the complementary possibility to test the splitting of a few thermal quanta. Stimulated by such small thermal energy, a strong degenerate trilinear coupling generates large amounts of nonclassicality, detectable by more than 3 dB of distillable quadrature squeezing. Substantial entanglement can be generated via frequent passive linear coupling to a third mode present in parallel with the trilinear coupling. This new form of entanglement, outside any Gaussian approximation, surprisingly grows with the mean number of split thermal quanta; a quality absent from Gaussian entanglement. Using distillable squeezing we shed light on this new entanglement mechanism for nonlinear bosonic systems.

Experimental Realization of Self-Contained Quantum Refrigeration

A fundamental challenge in quantum thermodynamics is the exploration of inherent dimensional constraints in thermodynamic machines. In the context of two-level systems, the most compact refrigerator necessitates the involvement of three entities, operating under self-contained conditions that preclude the use of external work sources. Here, we build such a smallest refrigerator using a nuclear spin system, where three distinct two-level carbon-13 nuclei in the same molecule are involved to facilitate the refrigeration process. The self-contained feature enables it to operate without relying on net external work, and the unique mechanism sets this refrigerator apart from its classical counterparts. We evaluate its performance under varying conditions and systematically scrutinize the cooling constraints across a spectrum of scenarios, which sheds light on the interplay between quantum information and thermodynamics.

Quantum Molecular Devices

Miniaturization has been the driving force in contemporary technologies. However, two main obstacles limit further progress: additional reduction in size has reached its quantum limit, and lithography has reached its threshold. Future progress requires tackling three challenges: chemical synthesis of a complete device, active cooling for exploiting quantum characteristics, and quantum coherent control for operation. Chemical synthesis replaces the current top-bottom approach to manufacturing with bottom-up synthesis from elementary building blocks. New ultracold synthetic methods should be developed. An additional challenge is the active cooling of molecules, where the bottleneck is entropy removal. Notably, the current solution, namely, diffusion, is too slow. A coherent approach offers a possible solution; specifically, quantum coherent control is the method of choice for manipulating ultracold matter. Finally, the many degrees of freedom of molecules should be an asset that allows the design and implementation of complex tasks such as sensing communication and computing.

Energy-Conversion Device Using a Quantum Engine with the Work Medium of Two-Atom Entanglement

Although entanglement is considered as an essential resource for quantum information processing, whether entanglement helps for energy conversion or output in the quantum regime is still lack of experimental witness. Here, we report on an energy-conversion device operating as a quantum engine with the working medium acted by two entangled ions confined in a harmonic potential. The two ions are entangled by virtually coupling to one of the vibrational modes shared by the two ions, and the quantum engine couples to a quantum load, which is another shared vibrational mode. We explore the energy conversion efficiency of the quantum engine and investigate the useful energy (i.e., the maximum extractable work) stored in the quantum load by tuning the two ions in different degrees of entanglement as well as detecting the change of the phonons in the load. Our observation provides, for the first time, quantitative evidence that entanglement fuels the useful energy produced by the quantum engine, but not helpful for the energy conversion efficiency. We consider that our results may be useful to the study of quantum batteries for which one of the most indexes is the maximum extractable energy.

Remote Charging and Degradation Suppression for the Quantum Battery

The quantum battery (QB) makes use of quantum effects to store and supply energy, which may outperform its classical counterpart. However, there are two challenges in this field. One is that the environment-induced decoherence causes the energy loss and aging of the QB, the other is that the decreasing of the charger-QB coupling strength with increasing their distance makes the charging of the QB become inefficient. Here, we propose a QB scheme to realize a remote charging via coupling the QB and the charger to a rectangular hollow metal waveguide. It is found that an ideal charging is realized as long as two bound states are formed in the energy spectrum of the total system consisting of the QB, the charger, and the electromagnetic environment in the waveguide. Using the constructive role of the decoherence, our QB is immune to the aging. Additionally, without resorting to the direct charger-QB interaction, our scheme works in a way of long-range and wireless-like charging. Effectively overcoming the two challenges, our result supplies an insightful guideline to the practical realization of the QB by reservoir engineering.

Thermodynamics of hybrid quantum rotor devices

We investigate the thermodynamics of a hybrid quantum device consisting of two qubits collectively interacting with a quantum rotor and coupled dissipatively to two equilibrium reservoirs at different temperatures. By modeling the dynamics and the resulting steady state of the system using a collision model, we identify the functioning of the device as a thermal engine, a refrigerator, or an accelerator. In addition, we also look into the device's capacity to operate as a heat rectifier and optimize both the rectification coefficient and the heat flow simultaneously. Drawing an analogy to heat rectification and since we are interested in the conversion of energy into the rotor's kinetic energy, we introduce the concept of angular momentum rectification, which may be employed to control work extraction through an external load.

Atom-doped photon engine: Extracting mechanical work from a quantum system via radiation pressure

The possibility of efficiently converting heat into work at the microscale has triggered an intense research effort to understand quantum heat engines, driven by the hope of quantum superiority over classical counterparts. In this work, we introduce a model featuring an atom-doped optical quantum cavity propelling a classical piston through radiation pressure. The model, based on the Jaynes-Cummings Hamiltonian of quantum electrodynamics, demonstrates the generation of mechanical work through thermal energy injection. We establish the equivalence of the piston expansion work with Alicki's work definition, analytically for quasistatic transformations and numerically for finite-time protocols. We further employ the model to construct quantum Otto and Carnot engines, comparing their performance in terms of energetics, work output, efficiency, and power under various conditions. This model thus provides a platform to extract useful work from an open quantum system to generate net motion, and it sheds light on the quantum concepts of work and heat.

Universal quantum Otto heat machine based on the Dicke model

In this paper we study a quantum Otto thermal machine where the working substance is composed of N identical qubits coupled to a single mode of a bosonic field, where the atoms and the field interact with a reservoir, as described by the so-called open Dicke model. By controlling the relevant and experimentally accessible parameters of the model we show that it is possible to build a universal quantum heat machine (UQHM) that can function as an engine, refrigerator, heater, or accelerator. The heat and work exchanges are computed taking into account the growth of the number N of atoms as well as the coupling regimes characteristic of the Dicke model for several ratios of temperatures of the two thermal reservoirs. The analysis of quantum features such as entanglement and second-order correlation shows that these quantum resources do not affect either the efficiency or the performance of the UQHM based on the open Dicke model. In addition, we show that the improvement in both efficiency and coefficient of performance of our UQHM occurs for regions around the critical value of the phase transition parameter of the model.

Full statistics of nonequilibrium heat and work for many-body quantum Otto engines and universal bounds: A nonequilibrium Green's function approach

We consider a generic four-stroke quantum Otto engine consisting of two unitary and two thermalization strokes with an arbitrary many-body working medium. Using the Schwinger-Keldysh nonequilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of nonequilibrium work and heat. The obtained result is valid up to the second order of the external driving amplitude. We then focus on the linear response limit and obtained Onsager's transport coefficients for the generic Otto cycle and show that the traditional fluctuation-dissipation relation for the total work is violated in the quantum domain, whereas for heat it is preserved. This leads to remarkable consequences in obtaining universal constraints on heat and work fluctuations for engine and refrigerator regimes of the Otto cycle and further allows us to make connections to the thermodynamic uncertainty relations. These findings are illustrated using a paradigmatic model that can be feasibly implemented in experiments.

Thermodynamic uncertainty theorem

Thermodynamic uncertainty relations (TURs) express a fundamental lower bound on the precision (inverse scaled variance) of any thermodynamic charge-e.g., work or heat-by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend TUR inequalities by incorporating and analyzing the impact of higher statistical cumulants of the entropy production itself within the general framework of time-symmetrically-controlled computation. We derive an exact expression for the charge that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name the thermodynamic uncertainty theorem (TUT). Importantly, both the minimum scaled variance charge and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any charge's precision. This is made explicit via a thorough numerical analysis of "swap" and "reset" computations that quantitatively compares the TUT against previous generalized TURs.

Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning

A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on reinforcement learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal tradeoffs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.

Bounds on nonequilibrium fluctuations for asymmetrically driven quantum Otto engines

For a four-stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on nonequilibrium fluctuations of work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regimes. Focusing on the engine regime, we show that the ratio of nonequilibrium fluctuations of output work to input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish a hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relations. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reverse cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine.

Enhancement of Quantum Heat Engine by Encircling a Liouvillian Exceptional Point

Quantum heat engines are expected to outperform the classical counterparts due to quantum coherences involved. Here we experimentally execute a single-ion quantum heat engine and demonstrate, for the first time, the dynamics and the enhanced performance of the heat engine originating from the Liouvillian exceptional points (LEPs). In addition to the topological effects related to LEPs, we focus on thermodynamic effects, which can be understood by the Landau-Zener-Stückelberg process under decoherence. We witness a positive net work from the quantum heat engine if the heat engine cycle dynamically encircles a LEP. Further investigation reveals that a larger net work is done when the system is operated closer to the LEP. We attribute the enhanced performance of the quantum heat engine to the Landau-Zener-Stückelberg process, enabled by the eigenenergy landscape in the vicinity of the LEP, and the exceptional point-induced topological transition. Therefore, our results open new possibilities toward LEP-enabled control of quantum heat engines and of thermodynamic processes in open quantum systems.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

Nonequilibrium thermodynamics in cavity optomechanics

Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium. As an emerging field, nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes, particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations. Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability, excellent mechanical performance, and ability to operate deep in the quantum regime. Here, we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems. The experimental results in entropy production assessment, fluctuation theorems, heat transfer, and heat engines are highlighted.

Stroboscopic thermally-driven mechanical motion

Unstable nonlinear systems can produce a large displacement driven by a small thermal initial noise. Such inherently nonlinear phenomena are stimulating in stochastic physics, thermodynamics, and in the future even in quantum physics. In one-dimensional mechanical instabilities, recently made available in optical levitation, the rapidly increasing noise accompanying the unstable motion reduces a displacement signal already in its detection. It limits the signal-to-noise ratio for upcoming experiments, thus constraining the observation of such essential nonlinear phenomena and their further exploitation. An extension to a two-dimensional unstable dynamics helps to separate the desired displacement from the noisy nonlinear driver to two independent variables. It overcomes the limitation upon observability, thus enabling further exploitation. However, the nonlinear driver remains unstable and rapidly gets noisy. It calls for a challenging high-order potential to confine the driver dynamics and rectify the noise. Instead, we propose and analyse a feasible stroboscopically-cooled driver that provides the desired detectable motion with sufficiently high signal-to-noise ratio. Fast and deep cooling, together with a rapid change of the driver stiffness, are required to reach it. However, they have recently become available in levitating optomechanics. Therefore, our analysis finally opens the road to experimental investigation of thermally-driven motion in nonlinear systems, its thermodynamical analysis, and future quantum extensions.

Dynamical control of quantum heat engines using exceptional points

A quantum thermal machine is an open quantum system coupled to hot and cold thermal baths. Thus, its dynamics can be well understood using the concepts and tools from non-Hermitian quantum systems. A hallmark of non-Hermiticity is the existence of exceptional points where the eigenvalues of a non-Hermitian Hamiltonian or a Liouvillian superoperator and their associated eigenvectors coalesce. Here, we report the experimental realization of a single-ion heat engine and demonstrate the effect of Liouvillian exceptional points on the dynamics and the performance of a quantum heat engine. Our experiments have revealed that operating the engine in the exact- and broken-phases, separated by a Liouvillian exceptional point, respectively during the isochoric heating and cooling strokes of an Otto cycle produces more work and output power and achieves higher efficiency than executing the Otto cycle completely in the exact phase where the system has an oscillatory dynamics and higher coherence. This result opens interesting possibilities for the control of quantum heat engines and will be of interest to other research areas that are concerned with the role of coherence and exceptional points in quantum processes and in work extraction by thermal machines.

Bath Engineering Enhanced Quantum Critical Engines

Driving a quantum system across quantum critical points leads to non-adiabatic excitations in the system. This in turn may adversely affect the functioning of a quantum machine which uses a quantum critical substance as its working medium. Here we propose a bath-engineered quantum engine (BEQE), in which we use the Kibble-Zurek mechanism and critical scaling laws to formulate a protocol for enhancing the performance of finite-time quantum engines operating close to quantum phase transitions. In the case of free fermionic systems, BEQE enables finite-time engines to outperform engines operating in the presence of shortcuts to adiabaticity, and even infinite-time engines under suitable conditions, thus showing the remarkable advantages offered by this technique. Open questions remain regarding the use of BEQE based on non-integrable models.

Experimental Realization of a Quantum Refrigerator Driven by Indefinite Causal Orders

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 and the heat energy extracted from the low-temperature reservoir. Unlike classical refrigerators in which the coefficient of performance (COP) is perversely higher the closer the temperature of the high-temperature and low-temperature reservoirs are to each other, the ICO refrigerator's COP is always bounded to small values due to the nonunit success probability in projecting the ancillary qubit to the preferable subspace. To enhance the COP, we propose and experimentally demonstrate a general framework based on the density matrix exponentiation (DME) approach, as an extension to the ICO refrigeration. The COP is observed to be enhanced by more than 3 times with the DME approach. Our Letter demonstrates a new way for nonclassical heat exchange, and paves the way towards construction of quantum refrigerators on a quantum system.

Extractable work in quantum electromechanics

Recent experiments have demonstrated the generation of coherent mechanical oscillations in a suspended carbon nanotube, which are driven by an electric current through the device above a certain voltage threshold, in close analogy with a lasing transition. We investigate this phenomenon from the perspective of work extraction, by modeling a nanoelectromechanical device as a quantum flywheel or battery that converts electrical power into stored mechanical energy. We introduce a microscopic model that qualitatively matches the experimental finding, and we compute the Wigner function of the quantum vibrational mode in its nonequilibrium steady state. We characterize the threshold for self-sustained oscillations using two approaches to quantifying work deposition in nonequilibrium quantum thermodynamics: the ergotropy and the nonequilibrium free energy. We find that ergotropy serves as an order parameter for the phonon lasing transition. The framework we employ to describe work extraction is general and widely transferable to other mesoscopic quantum devices.

Floquet quantum thermal transistor

We apply periodic control to realize a quantum thermal transistor, which we term as the Floquet quantum thermal transistor. Periodic modulation allows us to control the heat flows and achieve large amplification factors even for fixed bath temperatures. Importantly, this transistor effect persists in the cutoff region, where traditional quantum thermal transistors operating in the absence of periodic modulation, fail to act as viable heat modulation devices.

Controlling thermodynamics of a quantum heat engine with modulated amplitude drivings

External driving of bath temperatures with a phase difference of a nonequilibrium quantum engine leads to the emergence of geometric effects on the thermodynamics. In this work we modulate the amplitude of the external driving protocols by introducing envelope functions and study the role of geometric effects on the flux, noise, and efficiency of a four-level driven quantum heat engine coupled with two thermal baths and a unimodal cavity. We observe that having a finite width of the modulation envelope introduces an additional control knob for studying the thermodynamics in the adiabatic limit. The optimization of the flux as well as the noise with respect to thermally induced quantum coherences becomes possible in the presence of geometric effects, which hitherto has not been possible with sinusoidal driving without an envelope. We also report the deviation of the slope and generation of an intercept in the standard expression for efficiency at maximum power as a function of Carnot efficiency in the presence of geometric effects under the amplitude modulation. Further, a recently developed universal bound on the efficiency obtained from the thermodynamic uncertainty relation is shown not to hold when a small width of the modulation envelope along with a large value of cavity temperature is maintained.

Collective effects on the performance and stability of quantum heat engines

Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.

Quantum Non-Gaussianity of Multiphonon States of a Single Atom

Quantum non-Gaussian mechanical states are already required in a range of applications. The discrete building blocks of such states are the energy eigenstates-Fock states. Despite progress in their preparation, the remaining imperfections can still invisibly cause loss of the aspects critical for their applications. We derive and apply the most challenging hierarchy of quantum non-Gaussian criteria on the characterization of single trapped-ion oscillator mechanical Fock states with up to 10 phonons. We analyze the depth of these quantum non-Gaussian features under intrinsic mechanical heating and predict their requirement for reaching quantum advantage in the sensing of a mechanical force.

Nanotubes as sinks for quantum particles

Nanotubes with proper thickness, size, and texture make ultra-efficient sinks for quantum particles traveling into specific background media. Several optimal semiconducting cylindrical layers are reported to achieve enhancement in the trapping of matter waves by two to three orders of magnitude. The identified shells can be used as pieces in quantum devices that involve the focusing of incident beams, spanning from charge pumps and superconducting capacitors to radiation pattern controllers and matter-wave lenses.

Detecting Heat Leaks with Trapped Ion Qubits

The concept of passivity has been conceived to set bounds on the evolution of microscopic systems initialized in thermal states. We experimentally demonstrate the utility of two frameworks, global passivity and passivity deformation, for the detection of coupling to a hidden environment. We employ a trapped-ion quantum processor, where system qubits undergoing unitary evolution may optionally be coupled to an unobserved environment qubit, resulting in a heat leak. Evaluating the measurement data from the system qubits only, we show that global passivity can verify the presence of a heat leak, which is not detectable by a microscopic equivalent of the second law of thermodynamics. Furthermore, we experimentally show that passivity deformation allows for even more sensitive detection of heat leaks, as compared to global passivity, and detect a heat leak with an error margin of 5.3 standard deviations, in a scenario where other tests fail.

Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators

For steady-state autonomous absorption refrigerators operating in the linear response regime, we show that there exists a hierarchy between the relative fluctuation of currents for cold, hot, and work terminals. Our proof requires the Onsager reciprocity relation along with the refrigeration condition that sets the direction of the mean currents for each terminal. As a consequence, the universal bounds on the mean cooling power, obtained following the thermodynamic uncertainty relations, follow a hierarchy. Interestingly, within this hierarchy, the tightest bound is given in terms of the work current fluctuation. Furthermore, the relative uncertainty hierarchy introduces a bound on cooling efficiency that is tighter than the bound obtained from the thermodynamic uncertainty relations. Interestingly, all of these bounds saturate in the tight-coupling limit. We test the validity of our results for two paradigmatic absorption refrigerator models: (i) a four-level working fluid and (ii) a two-level working fluid, operating in the weak (additive) and strong (multiplicative) system-bath interaction regimes, respectively.

Strong system-bath coupling effects in quantum absorption refrigerators

We study the performance of three-level quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we demonstrate that in a broad range of parameters the cooling window at strong coupling can be captured by a weak-coupling theory, albeit with parameters renormalized by the system-bath coupling energy. As a result, at strong system-bath couplings the window of cooling is significantly reshaped compared to predictions of weak-coupling treatments. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance as one increases system-bath coupling-when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operational window.

Common Environmental Effects on Quantum Thermal Transistor

Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three strong-coupling qubits. It is shown that the functions of the thermal transistor can be maintained and the amplification rate can be modestly enhanced by the skillfully designed common environments. In particular, the presence of a dark state in the case of the completely correlated transitions can provide an additional external channel to control the heat currents without any disturbance of the amplification rate. These results show that common environmental effects can offer new insights into improving the performance of quantum thermal devices.

Universal Bounds on Fluctuations in Continuous Thermal Machines

We study bounds on ratios of fluctuations in steady-state time-reversal energy conversion devices. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.

Quantum Heat Engines with Complex Working Media, Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.

Many-body quantum thermal machines

Thermodynamics of quantum systems and quantum thermal machines are rapidly developing fields, which have already delivered several promising results, as well as raised many intriguing questions. Many-body quantum machines present new opportunities stemming from many-body effects. At the same time, they pose new challenges related to many-body physics. In this short review we discuss some of the recent developments on technologies based on many-body quantum systems. We mainly focus on many-body effects in quantum thermal machines. We also briefly address the role played by many-body systems in the development of quantum batteries and quantum probes.

Two coupled double quantum-dot systems as a working substance for heat machines

This paper presents a conceptual design for quantum heat machines using a pair of coupled double quantum dots (DQDs), each DQD with an excess electron to interact, as an working substance. We define a compression ratio as the ratio between the Coulomb couplings which describes the interaction between the electrons during the isochoric processes of the quantum Otto cycle and then we analyze the arising of different regimes of operations of our thermal machine. We also show that we may change the operation mode of an Otto engine when considering the effects due to the quantum tunneling of a single electron between each individual DQD.

Bounds on fluctuations for finite-time quantum Otto cycle

For quantum Otto engine driven quasistatically, we provide exact full statistics of heat and work for a class of working fluids that follow a scale-invariant energy eigenspectra under driving. Equipped with the full statistics we go on to derive a universal expression for the ratio of nth cumulant of output work and input heat in terms of the mean Otto efficiency. Furthermore, for nonadiabatic driving of quantum Otto engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasistatic limit of the engine.

Few-qubit quantum refrigerator for cooling a multi-qubit system

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 to be used as refrigerant by means of short interactions with a many-qubit system to be cooled. 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. We summarize how preparing the refrigerant qubits using the spin-star model paves the way for the cooling of a many-qubit system by means of a collisional route to thermalization. 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.

Maximum efficiency of absorption refrigerators at arbitrary cooling power

We consider absorption refrigerators consisting of simultaneously operating Carnot-type heat engine and refrigerator. Their maximum efficiency at given power (MEGP) is given by the product of MEGPs for the internal engine and refrigerator. The only subtlety of the derivation lies in the fact that the maximum cooling power of the absorption refrigerator is not limited just by the maximum power of the internal refrigerator, but, due to the first law, also by that of the internal engine. As a specific example, we consider the simultaneous absorption refrigerators composed of low-dissipation (LD) heat engines and refrigerators, for which the expressions for MEGPs are known. The derived expression for maximum efficiency implies bounds on the MEGP of LD absorption refrigerators. It also implies that a slight decrease in power of the absorption refrigerator from its maximum value results in a large nonlinear increase in efficiency, observed in heat engines, whenever the ratio of maximum powers of the internal engine and the refrigerator does not diverge. Otherwise, the increase in efficiency is linear as observed in LD refrigerators. Thus, in all practical situations, the efficiency of LD absorption refrigerators significantly increases when their cooling power is slightly decreased from its maximum.

Dissipatively Controlled Optomechanical Interaction via Cascaded Photon-Phonon Coupling

In an optomechanical system, we experimentally engineer the optical density of state to reduce or broaden the effective linewidth of the optical mode by introducing an ancillary mechanical mode, which has a large decay rate, i.e., stimulated backward Brillouin scattering. Based on this dissipation engineering, we could engineer the optical mode linewidth by one order of magnitude. In addition, we can either enhance or suppress the optomechanical cooling and amplification of the target mechanical oscillations. Our scheme demonstrates the cascaded photon-phonon coupling to control the mechanical interactions, and also presents a novel approach for engineering coherent light-matter interaction in hybrid systems, which consist of different types of nonlinear interactions and multiple modes, and promote the performance of quantum devices.

Fluctuations in irreversible quantum Otto engines

We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent work fluctuations, average work, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency, work fluctuations, and relative power fluctuations are discussed.

Analog of a Quantum Heat Engine Using a Single-Spin Qubit

A quantum two-level system with periodically modulated energy splitting could provide a minimal universal quantum heat machine. We present the experimental realization and the theoretical description of such a two-level system as an impurity electron spin in a silicon tunnel field-effect transistor. In the incoherent regime, the system can behave analogously to either an Otto heat engine or a refrigerator. The coherent regime could be described as a superposition of those two regimes, producing specific interference fringes in the observed source-drain current.

Quantum Otto engine working with interacting spin systems: Finite power performance in stochastic thermodynamics

A quantum Otto engine using two-interacting spins as its working medium is analyzed within framework of stochastic thermodynamics. The time-dependent power fluctuations and average power are explicitly derived for a complete cycle of engine operation. We find that the efficiency and power fluctuations are affected significantly by interparticle interactions, but both of them become interaction-independent under maximal power via optimizing the external control parameter. The behavior of the efficiency at maximum power is further explained by analyzing the optimal protocol of the engine.

Thermodynamic optimization subsumed in stability phenomena

In the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. This feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. Furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. Endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the Pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the Omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

Optimal performance of a three-level quantum refrigerator

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 can be maximized with respect to one control frequency, while χ function can be maximized globally with respect to two control frequencies. Additionally, we show that in the low-temperature regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and χ function can be maximized, we compare the cooling power of the quantum refrigerator at maximum χ function with the maximum cooling power.

Quantum Photovoltaic Cells Driven by Photon Pulses

We investigate the quantum thermodynamics of two quantum systems, a two-level system and a four-level quantum photocell, each driven by photon pulses as a quantum heat engine. We set these systems to be in thermal contact only with a cold reservoir while the heat (energy) source, conventionally given from a hot thermal reservoir, is supplied by a sequence of photon pulses. The dynamics of each system is governed by a coherent interaction due to photon pulses in terms of the Jaynes-Cummings Hamiltonian together with the system-bath interaction described by the Lindblad master equation. We calculate the thermodynamic quantities for the two-level system and the quantum photocell including the change in system energy, the power delivered by photon pulses, the power output to an external load, the heat dissipated to a cold bath, and the entropy production. We thereby demonstrate how a quantum photocell in the cold bath can operate as a continuum quantum heat engine with a sequence of photon pulses continuously applied. We specifically introduce the power efficiency of the quantum photocell in terms of the ratio of output power delivered to an external load with current and voltage to the input power delivered by the photon pulse. Our study indicates a possibility that a quantum system driven by external fields can act as an efficient quantum heat engine under non-equilibrium thermodynamics.

Quantum Statistical Enhancement of the Collective Performance of Multiple Bosonic Engines

We consider an ensemble of indistinguishable quantum machines and show that quantum statistical effects can give rise to a genuine quantum enhancement of the collective thermodynamic performance. When multiple indistinguishable bosonic work resources are coupled to an external system, the internal energy change of the external system exhibits an enhancement arising from permutation symmetry in the ensemble, which is absent when the latter consists of distinguishable work resources.

Three-qubit refrigerator with two-body interactions

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 realized in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.

Cooling condition for multilevel quantum absorption refrigerators

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 nonideality (heat leakage, competition between different cooling pathways) and examine the cooling current with different designs. This study assists in identifying the cooling window of imperfect thermal machines.

Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs

In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.