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arXiv:2103.12678 · Journal of Physics A Mathematical and Theoretical

Quantum thermodynamics aspects with a thermal reservoir based on PT -symmetric Hamiltonians

Jonas F. G. Santos, Fabricio S Luiz

Published Jul 13, 2021• 4 citations
arXivHTMLPDF

Abstract

Abstract We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on PT -symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the PT -symmetric features of the reservoir allows to reverse the heat flow between system and reservoir, as well as to preserve the coherence over a longer period of time and reduce the entropy production. Furthermore, we considered a modified quantum Otto cycle in which the standard hot thermal reservoir is replaced by the thermal reservoir based on PT -symmetric Hamiltonians. By defining an effective temperature depending on the PT -symmetric parameter, it is possible to interchange the quantum Otto cycle configuration from engine to refrigerator by varying the PT -symmetric parameter. Our results indicate that PT -symmetric effects could be useful to achieve an improvement in quantum thermodynamics protocols such as coherence protection and entropy production reduction.

DOI
10.1088/1751-8121/ac13de

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Abstract We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on PT -symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the PT -symmetric features of the reservoir allows to reverse the heat flow between system and reservoir, as well as to preserve the coherence over a longer period of time and reduce the entropy production. Furthermore, we considered a modified quantum Otto cycle in which the standard hot thermal reservoir is replaced by the thermal reservoir based on PT -symmetric Hamiltonians. By defining an effective temperature depending on the PT -symmetric parameter, it is possible to interchange the quantum Otto cycle configuration from engine to refrigerator by varying the PT -symmetric parameter. Our results indicate that PT -symmetric effects could be useful to achieve an improvement in quantum thermodynamics protocols such as coherence protection and entropy production reduction.
Recent advances in the study of thermodynamics of microscopic processes have driven the search for new developments in energy converters utilizing quantum effects. Here we propose a modified Otto cycle to design an engine fueled by quantum projective measurements. Standard quantum thermal machines operating in a finite-time regime with a driven Hamiltonian that does not commute at different times have their performance decreased by the presence of coherence, which is associated with a larger entropy production and irreversibility degree. However, we show that replacing the standard hot thermal reservoir by a projective measurement operation with a general basis in the Bloch sphere and controlling the basis angles suitably could improve the performance of the quantum engine as well as decrease the entropy change during the measurement process. Our results follow a generalization of quantum thermal machine models where the fuel comes from general sources beyond the standard thermal reservoir.
The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero.
We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
Abstract Based on a recently developed non-perturbative platform designed to simulate the full quantum dynamics of quantum thermal machines, the situation of a quantum refrigerator operating according to an Otto cycle is studied. The periodic steady-state dynamics is discussed in detail as well as the key thermodynamic quantities work, heat, and entropy. A particular benefit of the formulation is that it allows to access explicitly the work required for switching on and off the interaction with the respective thermal reservoirs in a consistent way. The domains in which the device operates in refrigerator mode are characterized.
The extension of quantum thermodynamics to situations that go beyond standard thermodynamic settings comprises an important and interesting aspect of its development. One such situation is the analysis of the thermodynamic consequences of structured environments that induce a non-Markovian dynamics. We study a quantum Otto refrigerator where the standard Markovian cold reservoir is replaced by a specific engineered cold reservoir which may induce a Markovian or non-Markovian dynamics on the quantum refrigerant system. The two dynamical regimes can be interchanged by varying the coupling between the refrigerant and the reservoir. An increase of non-Markovian effects will be related to an increase of the coupling strength, which in turn will make the energy stored in the interaction Hamiltonian, the interaction energy, increasingly relevant. We show how the figures of merit, the coefficient of performance, and the cooling power change for non-negligible interaction energies, discussing how neglecting this effect would lead to an overestimation of the refrigerator performance. Finally, we also consider a numerical simulation of a spin quantum refrigerator with experimentally feasible parameters to better illustrate the non-Markovian effects induced by the engineered cold reservoir. We argue that a moderate non-Markovian dynamics performs better than either a Markovian or a strong non-Markovian regime of operation.