The quantum-mechanical and thermodynamic properties of a 3-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir. This additional coupling need not be dissipative, and can provide a thermal driving force - the quantum analog of classical absorption chillers. The dependence of the maximum attainable cooling rate on temperature, at ultra-low temperatures, is determined and shown to respect the recently-established fundamental bound based on the second and third laws of thermodynamics.
Ground-state cooling of mechanical motion by coupling to a driven optical cavity has been demonstrated in various optomechanical systems. In our work, we provide a so far missing thermodynamic performance analysis of optomechanical sideband cooling in terms of a heat valve. As performance quantifiers, we examine not only the lowest reachable effective temperature (phonon number) but also the evacuated-heat flow as an equivalent to the cooling power of a standard refrigerator, as well as appropriate thermodynamic efficiencies, which all can be experimentally inferred from measurements of the ca…
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 study the quantum mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric process, such as quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in 1D box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum mechanical) foun…
Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical relation called thermo-majorization. But incorporating coherence has turned out to be challenging, even under the relatively tractable model wherein all Gibbs state-preserving quantum channels are included. Here we find a mathematical generalization of thermal operations at low temperatures, "cooling maps", for which we derive the necessary and sufficient state tr…
We discuss the possibility of existence of entanglement in biological systems. Our arguments centre on the fact that biological systems are thermodynamic open driven systems far from equilibrium. In such systems error correction can occur which may maintain entanglement despite high levels of de-coherence. We also discuss the possibility of cooling (classical or quantum) at molecular level.
From the thermodynamic equilibrium properties of a two-level system with variable energy-level gap $Δ$, and a careful distinction between the Gibbs relation $dE = T dS + (E/Δ) dΔ$ and the energy balance equation $dE = δQ^\leftarrow - δW^\to$, we infer some important aspects of the second law of thermodynamics and, contrary to a recent suggestion based on the analysis of an Otto-like thermodynamic cycle between two values of $Δ$ of a spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the celebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in principle with …
Exploring Noisy Quantum Thermodynamical Processes via the Depolarizing-Channel Approximation
Technische Universität Wien（维也纳工业大学）；Vienna Center for Quantum Science and Technology (VCQ)（维也纳量子科学与技术中心）；University of Vienna（维也纳大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）
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 demonstrate sympathetic cooling of a 43Ca+ trapped-ion "memory" qubit by a 40Ca+ "coolant" ion near the ground state of both axial motional modes, whilst maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during 10 cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O(0.01%) infidelity per cooling cycl…
We analyze the lowest achievable temperature for a mechanical oscillator (representing, for example, the motion of a single trapped ion) which is coupled with a driven quantum refrigerator. The refrigerator is composed of a parametrically driven system (which we also consider to be a single oscillator in the simplest case) which is coupled to a reservoir where the energy is dumped. We show that the cooling of the oscillator (that can be achieved due to the resonant transport of its phonon excitations into the environment) is always stopped by a fundamental heating process that is always domina…
The purity of quantum states is a key requirement for many quantum applications. Improving the purity is limited by fundamental laws of thermodynamics. Here we are probing the fundamental limits for a natural approach to this problem, namely heat-bath algorithmic cooling(HBAC). The existence of the cooling limit for HBAC techniques was proved by Schulman et al. in, the limit however remained unknown for the past decade. Here for the first time we find this limit. In the context of quantum thermodynamics, this corresponds to the maximum extractable work from the quantum system.
In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quan…
A cavity optomechanical system is initiated by a radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as cooling its effective temperature. Here we show that by properly engineering the spectral density of a thermal heat bath that interacts with a quantum system, the evolution of the quantum system can be effectively turned on and off. Inside a cavity optomechanical system, when the heat bath is realized by a multi-mode oscillator modeling of the mirror, this …
Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, which states that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilized? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure …
We suggest alternative quantum Otto engines, using heat bath algorithmic cooling with partner pairing algorithm instead of isochoric cooling. Liquid state nuclear magnetic resonance systems in one entropy sink are considered as working fluids. Then, the extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke type of quantum Otto engines. The role of heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two. Also, this cooling algorithm increases the power of engines reducing the time required for one cycle.
We propose a cooling scheme to prepare stationary entanglement of neutral atoms in the Rydberg blockade regime by combination of periodically collective laser pumping and dissipation. In each cycle, the controlled unitary dynamics process can selectively pump atoms away from the non-target state while maintaining the target state unchanged. The subsequent dissipative process redistributes the populations of ground states through the engineered spontaneous emission. After a number of cycles, the system will be eventually stabilized into the desired steady state independent of the initial state.…
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.
Traditional refrigeration is driven either by external force or an information-feedback mechanism. Surprisingly, the quantum measurement and collapse, which are generally detrimental, can also be used to power a cooling engine even without requiring any feedback mechanism. In this work, we experimentally demonstrate quantum measurement cooling (QMC) powered by entangled measurement by using a novel linear optical simulator. In the simulator, different thermodynamic processes can be simulated by adjusting the energy-level spacing of working substance and the temperature of thermal bath. We show…
Practical implementations of quantum technologies require preparation of states with a high degree of purity---or, in thermodynamic terms, very low temperatures. Given finite resources, the Third Law of thermodynamics prohibits perfect cooling; nonetheless, attainable upper bounds for the asymptotic ground state population of a system repeatedly interacting with quantum thermal machines have been derived. These bounds apply within a memoryless (Markovian) setting, in which each refrigeration step proceeds independently of those previous. Here, we expand this framework to study the effects of m…
Heat engines are fundamental physical objects to develop nonequilibrium thermodynamics. The thermodynamic performance of the heat engine is determined by the choice of cycle and time-dependence of parameters. Here, we propose a systematic numerical method to find a heat engine cycle to optimize some target functions. We apply the method to heat engines with slowly varying parameters and show that the method works well. Our numerical method is based on the genetic algorithm which is widely applied to various optimization problems.
Despite its simplicity, it seems to my best of knowledge that the possibly simplest approach towards deriving equations governing irreversible thermodynamics from gas-kinetic considerations within the framework of classical mechanics has never been pursued. In this paper we address this omission and derive the equations describing the irreversible thermodynamics of a gas in a piston and associated thermodynamic cycles performed in finite time. What we find is a thermodynamic action principle: The irreversible work we require for performing a thermodynamic cycle in finite time times the time we…
Heat-Bath Algorithmic Cooling is a set of techniques for producing highly pure quantum systems by utilizing a surrounding heat-bath and unitary interactions. These techniques originally used the thermal environment only to fully thermalize ancillas at the environment temperature. Here we extend HBAC protocols by optimizing over the thermalization strategy. We find, for any $d$-dimensional system in an arbitrary initial state, provably optimal cooling protocols with surprisingly simple structure and exponential convergence to the ground state. Compared to the standard ones, these schemes can us…
To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between t…
This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined. The connection that these paradigms have with other existing refrigeration techniques such as heat bath algorithmic cooling (HBAC), the resource theoretic approach to quantum thermodynamics, and autonomous cooling is then made. Each paradigm is then investigated on its own. This in particular allows for the derivation of a general and attainable bound. The bound is striking in its simplicity: it…
With the Lipkin-Meshkov-Glick (LMG) model as an illustration, we construct a thermodynamic cycle composed of two isothermal processes and two isomagnetic field processes and study the thermodynamic performance of this cycle accompanied by the quantum phase transition (QPT). We find that for a finite particle system working below the critical temperature, the efficiency of the cycle is capable of approaching the Carnot limit when the external magnetic field λ_{1} corresponding to one of the isomagnetic processes reaches the crosspoint of the ground states' energy level, which can become critica…
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…
We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\rm min}>0$ reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir, and over the reservoir energy spectrum. The minimal work needed to reach $T_{\rm min}$ grows as $1/T_{\rm min}$. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above $T_{\rm min}$. Our results …
Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this letter we derive a u…
Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to th…
We introduce quantum heat engines that perform quantum Otto cycle and the quantum Stirling cycle by using a coupled pair of harmonic oscillator as its working substance. In the quantum regime, different working medium is considered for the analysis of the engine models to boost the efficiency of the cycles. In this work, we present Otto and Stirling cycle in the quantum realm where the phase space is non-commutative in nature. By using the notion of quantum thermodynamics we develop the thermodynamic variables in non-commutative phase space. We encounter a catalytic effect (boost) on the effic…
There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics. Autonomous models, which do not rely on any external time-dependence, and models that make use of time-dependent control fields, often combined with dividing the control protocol into idealized strokes of a thermodynamic cycle. While the latter paradigm offers theoretical simplifications, its utility in practice has been questioned due to the involved approximations. Here, we bridge the two paradigms by constructing an autonomous model, which implements a thermodynamic cycle in a certain parameter regi…
Solids can be cooled by driving impurity ions with lasers, allowing them to transfer heat from the lattice phonons to the electromagnetic surroundings. This exemplifies a quantum thermal machine, which uses a quantum system as a working medium to transfer heat between reservoirs. We review the derivation of the Bloch-Redfield equation for a quantum system coupled to a reservoir, and its extension, using counting fields, to calculate heat currents. We use the full form of this equation, which makes only the weak-coupling and Markovian approximations, to calculate the cooling power for a simple …
The efficiency of laser-cooling relies on the existence of an almost closed optical-transition cycle in the energy spectrum of the considered species. In this respect rare-earth elements exhibit many transitions which are likely to induce noticeable leaks from the cooling cycle. In this work, to determine whether laser-cooling of singly-ionized erbium Er$^+$ is feasible, we have performed accurate electronic-structure calculations of energies and spontaneous-emission Einstein coefficients of Er$^+$, using a combination of \textit{ab initio} and least-square-fitting techniques. We identify five…
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. \jona{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. h…
A solar cell is a heat engine, but textbook treatments are not wholly satisfactory from a thermodynamic standpoint, since they present solar cells as directly converting the energy of light into electricity, and the current in the circuit as maintained by an electrostatic potential. We propose a thermodynamic cycle in which the gas of electrons in the p phase serves as the working substance. The interface between the p and n phases acts as a self-oscillating piston that modulates the absorption of heat from the photons so that it may perform a net positive work during a complete cycle of its m…
The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered so as to realize virtually any thermodynamic cycle. In spite of their versatility such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their …
The third law of thermodynamics in the form of the unattainability principle states that exact ground-state cooling requires infinite resources. Here we investigate the amount of non-equilibrium resources needed for approximate cooling. We consider as resource any system out of equilibrium, allowing for resources beyond the i.i.d. assumption and including the input of work as a particular case. We establish in full generality a sufficient and a necessary condition for cooling and show that for a vast class of non-equilibrium resources these two conditions coincide, providing a single necessary…
The ability to initialize quantum registers in pure states lies at the core of many applications of quantum technologies, from sensing to quantum information processing and computation. In this paper, we tackle the problem of increasing the polarization bias of an ensemble of two-level register spins by means of joint coherent manipulations, involving a second ensemble of ancillary spins and energy dissipation into an external heat bath. We formulate this spin refrigeration protocol, akin to algorithmic cooling, in the general language of quantum feedback control, and identify the relevant the…
Closed cycle $He^{3}-He^{4}$ dilution cryostats became the platform of choice in quantum sciences in the era of helium shortage. However, in many experiments, the mechanical vibrations induced by the pulsed cryocoolers present a significant drawback reflected both in electronic and mechanical noises. Here, we present a hybrid dilution cryostat platform; we have automated a commercial closed-cycle system to operate on a cryocooler or on a liquid helium battery. We implemented a scanning SQUID microscope in the hybrid dilution refrigerator. In this work we show the design of the hybrid setup and…
We analyze a steady-state thermoelectric engine, whose working substance consists of two capacitively coupled quantum dots. One dot is tunnel-coupled to a hot reservoir serving as a heat source, the other one to two electrically biased reservoirs at a colder temperature, such that work is extracted under the form of a steady-state current against the bias. In single realizations of the dynamics of this steady-state engine autonomous, 4-stroke cycles can be identified. The cycles are purely stochastic, in contrast to mechanical autonomous engines which exhibit self-oscillations. In particular, …
We study the physical mechanism of Maxwell's Demon (MD) helping to do extra work in thermodynamic cycles, by describing measurement of position, insertion of wall and information erasing of MD in a quantum mechanical fashion. The heat engine is exemplified with one molecule confined in an infinitely deep square potential inserted with a movable solid wall, while the MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. It is discovered that the the MD with quantum coherence or on a lower temperature than that of the heat bath of the particle would …
Improving Quantum Machine Learning via Heat-Bath Algorithmic Cooling
Atominstitut, Technische Universität Wien（维也纳技术大学原子研究所）；Miller Institute for Basic Research in Science, University of California Berkeley（加州大学伯克利分校米勒基础科学研究所）；Yonsei University（延世大学）
