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Measurement Based Quantum Heat Engine in a Three-level System

Maron F. Anka, Thiago Rodrigues de Oliveira, Daniel Jonathan

Published Aug 4, 2021• 0 citations
OpenAlex

Abstract

In this work we study the quantum Otto cycle using two different models, a two-bath model and a measurement-based protocol. We study the cycle using two quantum systems, namely one qutrit or a pair of interacting qubits. We find that the qubit efficiency of the Otto cycle can be surpassed by these other systems without invoking entanglement or any other quantum correlation. We also show that the measurement-based protocol can increase the efficiency higher than the two-bath model.

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arXiv:1403.2781•Physical Review E•Sep 2, 2014•101 citations
In this work we study the quantum Otto cycle using two different models, a two-bath model and a measurement-based protocol. We study the cycle using two quantum systems, namely one qutrit or a pair of interacting qubits. We find that the qubit efficiency of the Otto cycle can be surpassed by these other systems without invoking entanglement or any other quantum correlation. We also show that the measurement-based protocol can increase the efficiency higher than the two-bath model.
We compare quantum Otto engines based on two different cycle models: a two-bath model, with a standard heat source and sink, and a measurement-based protocol, where the role of heat source is played by a quantum measurement. We furthermore study these cycles using two different "working substances": a single qutrit (spin-1 particle) or a pair of qubits (spin-1/2 particles) interacting via the XXZ Heisenberg interaction. Although both cycle models have the same efficiency when applied on a single-qubit working substance, we find that both can reach higher efficiencies using these more complex working substances by exploiting the existence of "idle" levels, i.e., levels that do not shift while the spins are subjected to a variable magnetic field. Furthermore, with an appropriate choice of measurement, the measurement-based protocol becomes more efficient than the two-bath model.
We present a quantum-heat engine model utilizing a dual spin-pair architecture, wherein an Otto-like cycle is implemented using a single heat bath. The conventional cold bath is replaced by a measurement protocol, enabling engine operation without the need for a second thermal reservoir. Unlike standard quantum-heat engines, our framework employs an ancillary spin pair in a two-dimensional configuration to regulate performance. Operating in finite time, the engine attains finite power, which is enhanced through quantum correlations, specifically correlation between spin pairs and projective measurements on the ancillary pair. The system consists of dual-qubit pairs, where one pair serves as the working medium and the other as an ancillary system facilitating measurement-induced heat exchange. We demonstrate that the engine efficiency can exceed the standard quantum Otto limit through local control of the ancillary pair while maintaining nonzero power output. Moreover, correlation between spin pairs enables efficiency modulation via the measurement basis, underscoring the role of quantum resources in optimizing quantum thermal machines.
Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.
The quantum heat engines have drawn much attention due to miniaturization of devices recently. We study the dynamics of the quantum Otto heat engine using the driven-dissipative Schrödinger equation. Starting from different initial states, we simulate the time evolutions of the internal energy, power and heat-work conversion efficiency. The initial state impacts on these thermodynamic quantities before the Otto cycle reaches stable. In the transition period, the efficiency and power may be higher or lower than the corresponding values in the cyclostationary state. Remarkably, the efficiency could surpass the Otto limit and even the Carnot limit and the power could be much higher than the rated power. The efficiency anomaly is due to the energy in the initial state. Thus, we suggest that periodically pumping could take the similar role of a hot bath but could be manipulated flexibly. Furthermore, we propose a new quantum engine working in a single reservoir to convert the pump energy into mechanical work. This manipulative engine could potentially be applied to working in the microenvironments without a large temperature difference, such as the biological tissues in vivo. Our protocol is expected to model a new quantum engine with the advantage of applicability and controllability.
Measurement-based quantum heat engines have attracted significant interest as alternatives to conventional thermal engines, as they replace the hot thermal reservoir with quantum measurements, thereby offering greater controllability and simpler implementation. Motivated by these advantages, we investigate a measurement-driven quantum Otto engine with a qubit working substance and study the optimal work extractable from such engines, including whether their performance can surpass that of conventional quantum Otto cycles. We analyze the engine in both the infinite-time (adiabatic) and finite-time (non-adiabatic) regimes, considering two distinct implementations obtained through optimization over all projection-valued measurements (PVMs) and over all two-outcome positive operator-valued measurements (POVMs). We show that measurement-based engines can outperform conventional quantum Otto engines within specific parameter regimes and that POVM-based engines can yield higher optimal work extraction than PVM-based ones. Furthermore, by incorporating the thermodynamic cost associated with resetting the auxiliary system required for POVM implementation, we demonstrate that the resulting net work output can still exceed that of PVM-based engines under suitable conditions on the spectral gaps and cold bath temperature. We also identify regimes in which non-adiabatic implementations can yield higher work output and efficiency than their adiabatic counterparts. Our study provides operational guidelines for designing improved measurement-driven quantum Otto engines.
We propose a four-level quantum heat engine in an Otto cycle with a working substance of two spins subject to an external magnetic field and coupled to each other by a one-axis twisting spin squeezing nonlinear interaction. We calculate the positive work and the efficiency of the engine for different parameter regimes. In particular, we investigate the effects of quantum correlations at the end of the two isochoric processes of the Otto cycle, as measured by the entanglement of formation and quantum discord, on the work extraction and efficiency. The regimes where the quantum correlations could enhance the efficiency and work extraction are characterized.