Quantum heat machines with trapped ions

Abstract

Since the last two centuries, thermal machines have been studied extensively. Thermal mechanics have a major in uence on the development of the modern society that started with the invention of a steam engine during the industrial revolution. With the recent improvement in manufacturing techniques, we are now able to manufacture a smaller device, and we are going to the nanoscale domain. Now, the quantum e ect cannot be overlooked in the nanoscale domain, and we have to consider this e ect when we manufacture any device. This brings with it the idea of building a quantum heat machine (QHM) and has an active research topic in the last sixty years. But the quantum heat machine still has no proper experimental implementation. The purpose of this thesis is to propose an experimentally realizable model of a QHM and study a di erent aspect of quantum thermodynamics. There are several proposals to implement a QHM using di erent quantum systems as the working substance. Modelling two di erent baths, e.g. a hot bath and a cold bath, is the most crucial part in modelling such an engine. We have two adiabatic steps in a quantum Otto machine (QOM), where we have to switch o the system's interaction with the bath. People generally assume that the bath can be switched o or on in a controlled manner. But as the heat bath is always on in the quantum level, it may not be possible experimentally to turn it on or o during a particular cycle. We show the working of a QOM with the always-on bath condition. Here we have taken advantage of the trapped ion setup. We have identi ed the importance of the two degrees of freedom of the ions. The ion's electronic state acts as a working substance, while the vibrational mode is modelled as the e ective cold bath and the thermal environment act as a thermal bath. The instantaneous post-selective projective measurement on the electronic states mimics the heat exchange with the cold bath. Thus, the trapped ion setup poses as a promising platform for studying the experimentally feasible QHM model using current tapped-ion technology. The present thesis focusses on how the reciprocating heat cycle of a QHM can be implemented using trapped ions and an always-on thermal environment. We have shown how a single trapped ion can be used to implement all the heat strokes of a QHM. We have also looked for a correlation e ect in QHM. We have shown how a quantum heat machine can be implemented using two interacting trapped ions in the presence of a thermal bath where measurement a suitable basis can result in either a Quantum Heat Engine or a Refrigerator. We have looked for how the QHM will behave near or across the quantum phase transition point. We have shown that long-range interaction can substantially enhance the e ciency of a heat engine. The work was demonstrated in a system of two trapped ions, which plays the role of quantum fuel for a heat engine that works only above a critical value of the applied magnetic eld, pertaining to a quantum critical point. We analyse QHM's endoreversible behavior and compare maximum power e ciency with Curzon-Ahlborn e ciency. We have also shown how the nite time thermodynamical cycle e ect QHM e ciency. The detailed analytical and numerical study supports all the results presented in this thesis.