The quantum reservoirs commonly considered in open-quantum systems theory are those modeled by quantum harmonic oscillators, which are called bosonic reservoirs. Recently, quantum reservoirs modeled by two-level systems, the so-called fermionic reservoirs, have received attention due to their features. Given that the components of these reservoirs have a finite number of energy levels, unlike bosonic reservoirs, some studies are being carried out to explore the advantages of using this type of reservoir, especially in the operation of heat machines. In this paper, we carry out a case study of a quantum refrigerator operating in the presence of bosonic or fermionic thermal reservoirs, and we show that fermionic baths have advantages over bosonic ones.
The quantum reservoirs commonly considered in open-quantum systems theory are those modeled by quantum harmonic oscillators, which are called bosonic reservoirs. Recently, quantum reservoirs modeled by two-level systems, the so-called fermionic reservoirs, have received attention due to their features. Given that the components of these reservoirs have a finite number of energy levels, unlike bosonic reservoirs, some studies are being carried out to explore the advantages of using this type of reservoir, especially in the operation of heat machines. In this paper, we carry out a case study of a quantum refrigerator operating in the presence of bosonic or fermionic thermal reservoirs, and we show that fermionic baths have advantages over bosonic ones.
We developed this work at the moment with the objective to resolver the master equation for both thermal reservoir: bosonic and fermionic, as well as the master equation in reservoirs of vacuum and of Fock compressed . the bosonic thermal reservoir is modeled by a collection of coupled harmonic oscillators and the fermionic reservoir by a collection of two-level atoms. We made use of the Jaynes-Cummings model and the Bohr, Bohr-Markov and Markov approaches. In the end we discussed the application to the master equation for two distinct phenomena, Cooling by Heating (CBH) analyzing average energy graphs to the atomic system versus number of photons, and the average energy of the bosonic system as a function of the mean number of phonons, we observed the negative temperature in the absolute scale due to the inversion of population of states in function of cooperativity, we also analyzed a signature of negative response in a three level system interacting in a optical cavity, that comes as a result of decrease in the output field intensity when the input field intensity is increased.
We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also operate in a parameter regime where no or negligible steady-state cooling is achieved, but there is considerable transient cooling. The steady-state temperature can be lowered significantly by an increase in the strength of the few-body interaction terms existing due to the use of the common bath in the refrigerator setup. The proposed refrigerator built with three qubits and two baths is shown to provide steady-state cooling for both Markovian qubit-bath interactions between the qubits and canonical bosonic thermal reservoirs, and a simpler reset model for the qubit-bath interactions.
The study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.
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.
Abstract In this work, we study and find that the performance of an autonomous refrigerator can be improved by means of collective dissipations of common reservoirs. The refrigerator is based on a four-level system with two degenerate levels, coupled to three thermal reservoirs with different temperatures. Our study reveals that utilizing only one common reservoir can not significantly enhance the refrigerator’s performance. However, when two reservoirs are shared simultaneously, the performance improvement becomes more evident. Furthermore, we find that the refrigerator’s performance can be further enhanced by operating in a regime where the decoherence-free subspace is present. Our results indicate that careful engineering is essential to maximize the benefits of common reservoirs in enhancing the performance of quantum thermal machines.
We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.