Performance of quantum Otto refrigerators with squeezing

Quantum Otto-type heat engine with fixed frequency

In this work we analyze an Otto-type cycle operating with a working substance composed of a quantum harmonic oscillator (QHO). Unlike other studies in which the work extraction is done by varying the frequency of the QHO and letting it thermalize with a squeezed reservoir, here we submit the QHO to a parametric pumping controlled by the squeezing parameter and let it thermalize with a thermal reservoir. We then investigate the role of the squeezing parameter in our Otto-type engine powered by parametric pumping and show that it is possible to reach the Carnot limit by arbitrarily increasing the squeezing parameter. Notably, for certain squeezing parameters r, e.g., r=0.4, the quasistatic Otto limit can be reached even at nonzero power. We also investigated the role of entropy production in the efficiency behavior during the unitary strokes, showing that positive (negative) changes in entropy production correspond to increases (decreases) in engine efficiency, as expected. Furthermore, we show that under thermal reservoirs a work extraction process that is more efficient than the Carnot engine is impossible, regardless of the quantum resource introduced via the Hamiltonian of the system.

Geometrical Bounds on Irreversibility in Squeezed Thermal Bath

Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

Quantum-parametric-oscillator heat engines in squeezed thermal baths: Foundational theoretical issues

In this paper we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of four stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. The HPZ equation is an exact non-Markovian equation which preserves the positivity of the density operator and is valid for (1) all temperatures, (2) arbitrary spectral density of the bath, and (3) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This includes (1) the non-Markovian regimes for non-Ohmic, low-temperature baths, (2) what to expect in nonadiabatic frequency modulations, (3) strong system-bath coupling, as well as (4) the proper junction conditions between these two phases. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces that we hope are of use for exploring such possibilities.

Quantum Heat Engines with Complex Working Media, Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.

Performance bounds of nonadiabatic quantum harmonic Otto engine and refrigerator under a squeezed thermal reservoir

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.

Universal two-level quantum Otto machine under a squeezed reservoir

We study an Otto heat machine whose working substance is a single two-level system interacting with a cold thermal reservoir and with a squeezed hot thermal reservoir. By adjusting the squeezing or the adiabaticity parameter (the probability of transition) we show that our two-level system can function as a universal heat machine, either producing net work by consuming heat or consuming work that is used to cool or heat environments. Using our model we study the performance of these machine in the finite-time regime of the isentropic strokes, which is a regime that contributes to make them useful from a practical point of view.

Bosons outperform fermions: The thermodynamic advantage of symmetry

We examine a quantum Otto engine with a harmonic working medium consisting of two particles to explore the use of wave function symmetry as an accessible resource. It is shown that the bosonic system displays enhanced performance when compared to two independent single particle engines, while the fermionic system displays reduced performance. To this end, we explore the trade-off between efficiency and power output and the parameter regimes under which the system functions as engine, refrigerator, or heater. Remarkably, the bosonic system operates under a wider parameter space both when operating as an engine and as a refrigerator.

Entropy generation and unified optimization of Carnot-like and low-dissipation refrigerators

The connection between Carnot-like and low-dissipation refrigerators is proposed by means of their entropy generation and the optimization of two unified, compromise-based figures of merit. Their optimization shows that only a limited set of heat transfer laws in the Carnot-like model are compatible with the results stemming from the low-dissipation approximation, even though there is an agreement of the related physical spaces of variables. A comparison between two operation regimes and relations among entropy generation, efficiency, cooling power. and power input are obtained, with emphasis on the role of dissipation symmetries. The results extend previous findings for heat engines at maximum power conditions.

Quantum Otto engine with exchange coupling in the presence of level degeneracy

We consider a quasistatic quantum Otto cycle using two effectively two-level systems with degeneracy in the excited state. The systems are coupled through isotropic exchange interaction of strength J>0, in the presence of an external magnetic field B which is varied during the cycle. We prove the positive work condition and show that level degeneracy can act as a thermodynamic resource, so that a larger amount of work can be extracted than in the nondegenerate case, both with and without coupling. We also derive an upper bound for the efficiency of the cycle. This bound is the same as derived for a system of coupled spin-1/2 particles [G. Thomas and R. S. Johal, Phys. Rev. E 83, 031135 (2011)PLEEE81539-375510.1103/PhysRevE.83.031135], i.e., without degeneracy, and depends only on the control parameters of the Hamiltonian, being independent of the level degeneracy and the reservoir temperatures.

Measurement-induced operation of two-ion quantum heat machines

We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, which undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths is never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.

Efficiency and its bounds of minimally nonlinear irreversible heat engines at arbitrary power

The efficiency for minimally nonlinear irreversible heat engines at any arbitrary power has been systematically evaluated, and general lower and upper efficiency bounds under the tight coupling condition for different operating regions have been proposed, which can be seen as the generalization of the bounds [η_{C}/2<η_{maxP}<η_{C}/(2-η_{C})] on efficiency at maximum power (η_{maxP}), where η_{C} means the Carnot efficiency. We have also calculated the universal bounds of the maximum gain in efficiency in different operating regions to give further insight into the efficiency gain with the power away from the maximum power. In the region of higher loads (higher than the load which corresponds to the maximum power), a small power loss away from the maximum power induces a much larger gain in efficiency. As actual heat engines may not work at the maximum power condition, this paper may contribute to operating actual heat engines more efficiently.

Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles

We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is, environments described by the generalized or Gibbs canonical ensemble. We demonstrate that small systems weakly coupled to such reservoirs exchange both heat and work by verifying a local detailed balance relation for the induced stochastic dynamics. Based on this analysis, we help to rationalize the observation that nonthermal reservoirs can increase the efficiency of thermodynamic heat engines.

Entropy production and thermodynamic power of the squeezed thermal reservoir

We analyze the entropy production and the maximal extractable work from a squeezed thermal reservoir. The nonequilibrium quantum nature of the reservoir induces an entropy transfer with a coherent contribution while modifying its thermal part, allowing work extraction from a single reservoir, as well as great improvements in power and efficiency for quantum heat engines. Introducing a modified quantum Otto cycle, our approach fully characterizes operational regimes forbidden in the standard case, such as refrigeration and work extraction at the same time, accompanied by efficiencies equal to unity.

Non-hermitian quantum thermodynamics

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.