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Thermodynamics of a Two-Qubit Absorption-Driven Heat Pump

Gustav Seemann

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

Quantum thermal machines, a sub-field of quantum thermodynamics, are actively studied with the aim to understand the connection between quantum mechanics and thermodynamics. In this work, qubits are used as the active medium in an absorption driven heat pump. The dynamics of this thermal machine are computationally simulated by treating the qubits as an open quantum system interacting with three bosonic heat baths. Some thermodynamic bounds for the system parameters are derived and used in order to define a refrigerating regime for the system.

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Quantum thermal machines, a sub-field of quantum thermodynamics, are actively studied with the aim to understand the connection between quantum mechanics and thermodynamics. In this work, qubits are used as the active medium in an absorption driven heat pump. The dynamics of this thermal machine are computationally simulated by treating the qubits as an open quantum system interacting with three bosonic heat baths. Some thermodynamic bounds for the system parameters are derived and used in order to define a refrigerating regime for the system.
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.
We use the theory of open quantum systems to study quantum thermal machines, deriving their master equations to understand how they evolve in time. We consider three different working substances coupled to heat baths that may act as engines, refrigerators, accelerators or dissipators. The first is a network of driven quantum harmonic oscillators where we study the effect that the driving speed has on the operation of the system. We see how squeezing one of the baths may lead to a more efficient engine as well as the generation of entanglement within the system. We then investigate the use of coherence in the baths as a resource to improve the performance of a quantum thermal machine whose working substance consists of a single qubit. Finally, we introduce a rotor to a system of two qubits to create an autonomous quantum machine capable of converting heat flow into useful mechanical work. We also study both the heat and angular momentum rectification that may be accomplished by this machine.
Quantum mechanics has given us a new playground in which to experiment that boasts several unique features. In this thesis, we explore it in the context of thermodynamics: looking at what kind of thermal devices can be constructed and how quantum behaviour affects them. We consider three research strands. In the first part we formulate a selection of heat engines with two-qubit systems, utilising environments that induce quantum correlations into the system. We see that these correlations can have some effects on the work of the engine, but this effect is system dependent. Describing the dynamics of a quantum system in contact with an external environment is often achieved with a master equation. When considering systems comprised of multiple subsystems, the description becomes more complicated and some of the master equations that have been used previously produce unphysical results. In the second part of this thesis we show that if one does the proper analysis of the microscopic derivation of these master equations, then no thermodynamical inconsistencies occur. When one considers a system connected to three or more environments, a whole new set of possible thermodynamical machines becomes available. One notable case of these is the absorption refrigerator, which performs refrigeration without the need for an external work source. For the third part, we show how one can construct an absorption refrigerator using a three-qubit system with two-body interactions and describe its operation. We also show some thermal control properties of the three-qubit system.
Recent years have enjoyed an overwhelming interest in quantum thermodynamics, a field of research aimed at understanding thermodynamic tasks performed in the quantum regime.Further progress, however, seems to be obstructed by the lack of experimental implementations of thermal machines in which quantum effects play a decisive role.In this work, we introduce a blueprint of quantum field machines, which-once experimentally realized-would fill this gap.Even though the concept of the QFM presented here is very general and can be implemented in any many-body quantum system that can be described by a quantum field theory.We provide here a detailed proposal of how to realize a quantum machine in onedimensional ultracold atomic gases, which consists of a set of modular operations giving rise to a piston.These can then be coupled sequentially to thermal baths, with the innovation that a quantum field takes up the role of the working fluid.In particular, we propose models for compression on the system to use it as a piston, and coupling to a bath that gives rise to a valve controlling heat flow.These models are derived within Bogoliubov theory, which allows us to study the operational primitives numerically in an efficient way.By composing the numerically modeled operational primitives we design complete quantum thermodynamic cycles that are shown to enable cooling and hence giving rise to a quantum field refrigerator.The active cooling achieved in this way can operate in regimes where existing cooling methods become ineffective.We describe the consequences of operating the machine at the quantum level and give an outlook of how this work serves as a road map to explore open questions in quantum information, quantum thermodynamic, and the study of non-Markovian quantum dynamics.
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or more baths at different temperatures and continuously driven. To this end, we investigate parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and power of the working device, which can operate as an engine, refrigerator, or accelerator, and analyze the instantaneous and average efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to a dissipator. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle.
The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT(t)/dt∼-T^{ζ} when approaching absolute zero, T→0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ζ, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.