Measurement Based Quantum Heat Engine with Coupled Working Medium

Abstract

We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E 96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and the efficiency of the engine is rather involved. We find that in the higher spin scenario efficiency can sometimes be negative (this means work has to be done to run the engine cycle) for certain range of coupling constants, in contrast to the aforesaid work of Yi, Talkner and Kim, where they showed that the extracted work is always positive in the absence of coupling. We provide arguments for this negative efficiency in higher spin scenarios. Interestingly, this happens only in the asymmetric scenarios, where the two spins are different. Given these facts, for judiciously chosen conditions, an engine with coupled working medium gives advantage for the efficiency over the uncoupled one.

Measurement-based quantum heat engine in a multilevel system

“…However there is no clear connection between any measure of quantum correlation and efficiency increase. Here we will show that the same mechanism of efficiency increase for a qutrit can explain the results obtained for two spins coupled via a Heisenberg Hamiltonian (XXZ model), which were already analyzed for the two bath model [15] and measurement model [52]. Thus in this model correlations are not needed to explain the efficiency increase.…”

“…[15] and for the measurementbased model in Ref. [52]. In these works the authors did find improvements in efficiency, which they attempted to attribute to the presence of quantum correlations between the particles.…”

“…Thus one can have a new kind of engine with one of the thermal baths replaced by a quantum measurement. In this scenario one can furthermore consider using either selective measurements and feedback (a Maxwell demon [45][46][47][48][49][50]) or non-selective measurements and no feedback [25,51,52], [53]. In the latter case, the post-measurement state is taken as the appropriate average over all possible measurement results.…”

“…Das and Ghosh [52] later investigated whether this conclusion still holds in more complex scenarios. They studied the same measurement-based protocol in the cases of two coupled qubits, and of one qubit coupled with a general spin S, interacting via an isotropic Heisenberg Hamiltonian.…”

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

“…A range of quantum working substances has been used to model these QHEs. Amongst these, the study of simple, coupled quantum systems [ 6 , 18 , 29 , 30 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 , 115 , 116 ] can yield important insights into the role of quantum interactions in enhancing the performance of model thermal machines. In particular, an upper bound ( ) for quantum Otto efficiency using two coupled spin- particles has been obtained which is tighter than the Carnot bound ( ) [ 6 , 18 ].…”