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arXiv:1604.04098 · Physical review. E

Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource

Ralph Silva, Gonzalo Manzano, Paul Skrzypczyk, Nicolas Brunner

Published Sep 16, 2016• 76 citations
arXivHTMLPDF

Abstract

Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

DOI
10.1103/physreve.94.032120

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Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.
We present a theoretical investigation of entanglement generation in an external quantum system during its interaction with a quantum autonomous thermal machine (QATM) under non-Markovian dynamics. The QATM, composed of two qubits each coupled to independent thermal reservoirs, interacts with an external system of two additional qubits. By analyzing the Hilbert space structure, energy level configurations, and temperature gradients, we define a common interaction between the QATM qubits and the external system qubits, which allows the definition of two thermodynamic cycles (A and B) governed by virtual temperatures and energy-conserving transitions. We demonstrate that the QATM can act as a structured reservoir able to induce non-Markovian memory effects highlighted by negative entropy production rates. Using mutual information and concurrence, we show that entanglement is generated only using cycle A, which is associated with stronger non-Markovian behavior and higher coherence correlations. Our results demonstrate that temperature differences, Hilbert space structure, and coherence serve as quantum resources for controlling and enhancing entanglement in quantum thermodynamic settings, with parameters consistent with experimental superconducting qubit platforms.
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-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.
Time remains one of the least well-understood concepts in physics, most notably in quantum mechanics.A central goal is to find the fundamental limits of measuring time.One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly.Here, we explore these questions by introducing a model of time measurements that is complete and autonomous.Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium-a prerequisite for any system to function as a clock-powered by minimal resources, namely, two thermal baths at different temperatures.Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock's performance in terms of its accuracy and resolution.Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power.More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.
Abstract We propose a model of two identical autonomous quantum refrigerators that interact through their qubits coupled to cold thermal baths. We consider the same specific disposition for each refrigerator related to a three-level system coupled to different thermal baths and, in turn, to a qubit as the object to be cooled. By coupling the two systems, we show that under certain conditions on the model parameters, the devices can operate in the regime of an independent autonomous quantum refrigerator or be subject to an adjustment of the thermodynamic performances. We further investigate the correlations induced by the interaction between the two refrigerators, and illustrate their behavior with respect to their thermodynamic performances. We have found that adjusting the different interaction constants of the model can lead to an evolution of the quantum correlations of the two machines that is inversely related to the behavior of the thermodynamic quantities of both refrigerators. However, this is not necessarily the case when the temperatures of the model are considered as the reference parameters.
We develop a physics-based model for classical computation based on autonomous quantum thermal machines. These machines consist of few interacting quantum bits (qubits) connected to several environments at different temperatures. Heat flows through the machine are here exploited for computing. The process starts by setting the temperatures of the environments according to the logical input. The machine evolves, eventually reaching a non-equilibrium steady state, from which the output of the computation can be determined via the temperature of an auxilliary finite-size reservoir. Such a machine, which we term a "thermodynamic neuron", can implement any linearly-separable function, and we discuss explicitly the cases of NOT, 3-majority and NOR gates. In turn, we show that a network of thermodynamic neurons can perform any desired function. We discuss the close connection between our model and artificial neurons (perceptrons), and argue that our model provides an alternative physics-based analogue implementation of neural networks, and more generally a platform for thermodynamic computing.
Quantum coherence has been shown to impact the operational capabilities of quantum systems performing thermodynamic tasks in a significant way, and yet the possibility and conditions for genuine coherence-enhanced thermodynamic operation remain unclear. Introducing a comparison with classical machines using the same set of thermodynamic resources, we show that for steady-state quantum thermal machines – both autonomous and externally driven – that interact weakly with thermal reservoirs and work sources, the presence of coherence induced by perturbations in the machine Hamiltonian guarantees a genuine thermodynamic advantage under mild conditions. This advantage applies to both cases where the induced coherence is between levels with different energies or between degenerate levels. On the other hand, we show that engines subjected to noise-induced coherence can be outperformed by classical stochastic engines using exactly the same set of (incoherent) resources. We illustrate our results with three prototypical models of heat engines and refrigerators: the three-level amplifier, the three-qubit autonomous refrigerator, and a noise-induced-coherence machine.