We study a quantum Otto cycle that uses a 2-qubit working substance whose Hamiltonian does not commute with itself at different times during unitary strokes. We investigate how the cycle responds to the loss of quantum adiabaticity when these strokes are operated with a finite duration. We find that qualitative features such as the possibility of counter-rotating cycles operating as heat engines, or a cycle efficiency that can increase with a decrease in the temperature difference between the baths, are resilient even to highly nonadiabatic strokes. However, cycle efficiency rapidly decreases, although it can still remain above the standard Otto value for small degrees of quantum nonadiabaticity.
We study a quantum Otto cycle that uses a 2-qubit working substance whose Hamiltonian does not commute with itself at different times during unitary strokes. We investigate how the cycle responds to the loss of quantum adiabaticity when these strokes are operated with a finite duration. We find that qualitative features such as the possibility of counter-rotating cycles operating as heat engines, or a cycle efficiency that can increase with a decrease in the temperature difference between the baths, are resilient even to highly nonadiabatic strokes. However, cycle efficiency rapidly decreases, although it can still remain above the standard Otto value for small degrees of quantum nonadiabaticity.
Abstract The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.
Algebraic methods for solving time-dependent Hamiltonians are used to investigate the performance of quantum thermal machines. We investigate the thermodynamic properties of an engine formed by two coupled qubits, performing an Otto cycle. The thermal interaction occurs with two baths at different temperatures, while work is associated with the interaction with an arbitrary time-dependent magnetic field that varies in intensity and direction. For the coupling, we consider the 1D isotropic Heisenberg model, which allows us to describe the system by means of the irreducible representation of the su(2) Lie algebra within the triplet subspace. We also inspect different settings of the temperatures and frequencies of the cycle, and investigate the corresponding operation regimes. We describe how these regimes can change with the speed of the protocol. Finally, we compare the weak and strong coupling regimes, and conclude that for the weak case the efficiency is optimal and can surpass the value of the classical Otto cycle. For low temperatures of the heat baths, we show that losses due to quantum friction are reduced in the strong coupling limit.
In this work we investigate a finite-time quantum Otto-like heat engine with a single-qubit working substance, distinguished from the standard Otto cycle by introducing a unitary operation before the cold isochore. This operation suppresses the slowest decaying mode of the open-system dynamics and broadens the spectral gap, thereby inducing an exponential to accelerate the subsequent thermalization process toward stationarity. We derive analytic expressions for the work, heat, and efficiency, and perform numerical simulations comparing the standard Otto engine, the shortcut to adiabatic engine, and our proposed Otto-like engine. Our analysis demonstrates that with an appropriate parameter selection, the additional unitary operation can significantly boost the system's power and efficiency. Finally, using the unified optimization criterion Φ, we further show that the modified cycle consistently outperforms both the conventional cycle and the shortcut to adiabatic protocol.
We demonstrate that under specific conditions, a finite-time quantum Otto engine, employing a spin-1/2 particle as the working substance, despite undergoing incomplete Otto cycles, can achieve higher efficiency than an ideal quantum Otto engine. A finite-time quantum Otto engine refers to an Otto engine where the two isochoric strokes are prematurely terminated before reaching thermal equilibrium with their respective hot and cold baths. We observe that the enhancement of efficiency of a finite-time quantum Otto engine over the ideal one can be realized by adjusting the initial temperature of the working substance within the temperature range of the hot and cold baths. We also find that incorporating an auxiliary qubit, and activating specific interactions between the single-qubit working substance and the auxiliary one, can enhance the efficiency of a finite-time as well as an ideal quantum Otto engine. Furthermore, we analyze the impact of glassy disorder within the system-bath coupling during the two isochoric strokes on the efficiency of a finite-time quantum Otto engine. We find that as strength of disorder increases, efficiency of a finite-time quantum Otto engine tends to decrease, albeit with relatively modest reduction even for strong disorder. However, the advantage in efficiency of the finite-time quantum Otto engine over the ideal one, obtained by tuning the initial state temperature, and the efficiency enhancement obtained by incorporating an auxiliary over the without-auxiliary scenario, persists even in presence of substantial disorder. Additionally, we show that while this disorder does not affect the ideal efficiency, it does influence the duration of isochoric strokes needed for an Otto engine to reach ideal efficiency. This stroke duration remains nearly constant until a specific disorder strength, beyond which it increases rapidly.
Devising and constructing quantum many-body heat engines is a key challenge of quantum thermodynamics. Most of the research in this field assumes the strokes to be ideal transformations. Here, the authors study the performance of realistic Otto engines with finite-time duration, whose working substance is made of free-fermion systems. They provide analytic expressions for the work and the power delivered through imperfect adiabatic and isochoric strokes. These findings are applied to the case study of an Ising-like quantum Otto cycle.
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.