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Improving quantum thermal transistors through feedback-controlled baths

Uthpala N. Ekanayake, Sarath D. Gunapala, Malin Premaratne

Published Sep 1, 2024• 5 citations

Abstract

In recent years, integrating quantum feedback mechanisms into thermal machines has gained attention due to its benefits in manipulating the system states and energy flows. This is particularly advantageous for quantum thermal transistors in preserving their inherent quantum properties as they lose the purity of the system states due to decoherence and relaxation from interactions with thermal baths, within the subsystems, and monitoring. In the literature, studies have demonstrated that preserving quantum coherence can enhance the performance of quantum thermal machines, improving their efficiency. In our paper, we present a model that proposes engineering baths to be equipped with detectors and a controller to enable feedback in a quantum thermal transistor that emulates a role played by a feedback resistor in an electronic transistor. We use the framework of quantum feedback control via weak monitoring. We modify the system evolution trajectories by using a weak monitoring record from a detector. By taking the ensemble average of these trajectories, we unveil the evolution of the system density matrix that corresponds to the Markovian dynamics of the transistor. This type of feedback introduces minimal perturbation to the system and, once tuned, enhances the system coherence that would otherwise degrade due to bath interactions. Furthermore, there will be no change in the relaxation times. The probabilities of population terms remain unchanged. We treat this an enhancement in the operational characteristics of the quantum thermal transistor as it maintains its quantum features with an added benefit of improved amplification capabilities.

DOI: 10.1063/5.0229630

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thermal baths and Maxwell's demon. The demon performs projective measurements on the engine working substance, the outcome of which is recorded in a classical memory, embedded in its own thermal bath. To perform feedback control, the demon enacts unitary operations on the working substance, conditioned on the recorded outcome. By considering the compound machine-memory as a hybrid (classical-quantum) standard thermal machine interacting with

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thermal baths, our framework puts the working substance and memory on equal footing, thereby enabling a comprehensible resolution to Maxwell's paradox and elucidating the intricate manner in which information impacts the performance of quantum engines. We illustrate the application of our framework with a two-qubit engine. A remarkable observation is that more information does not necessarily result in better thermodynamic performance: sometimes knowing less is better.

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Abstract We investigate the performance of a three-qubits quantum thermal transistor using coarse-graining, global, and local master equations, respectively. Special attention is paid to the validity of the three methods in different internal coupling strengths. The effects of system and bath parameters on the amplification effect are studied. It is found that small middle qubit frequency, weak internal coupling, and symmetric configuration of system-bath coupling lead to large amplification factor. The heat current amplification mechanism is discussed and quantum coherence does not contribute to amplification. Besides, the thermal transistor is realized by tuning the temperature of the middle bath, the temperature of the left bath, or the internal coupling strength.

Introduction In the preceding chapter we introduced quantum trajectories: the evolution of the state of a quantum system conditioned on monitoring its outputs. As discussed in the preface, one of the chief motivations for modelling such evolution is for quantum feedback control. Quantum feedback control can be broadly defined as follows. Consider a detector continuously producing an output, which we will call a current. Feedback is any process whereby a physical mechanism makes the statistics of the present current at a later time depend upon the current at earlier times. Feedback control is feedback that has been engineered for a particular purpose, typically to improve the operation of some device. Quantum feedback control is feedback control that requires some knowledge of quantum mechanics to model. That is, there is some part of the feedback loop that must be treated (at some level of sophistication) as a quantum system. There is no implication that the whole apparatus must be treated quantum mechanically. The structure of this chapter is as follows. The first quantum feedback experiments (or at least the first experiments specifically identified as such) were done in the mid 1980s by two groups [WJ85a, MY86]. They showed that the photon statistics of a beam of light could be altered by feedback. In Section 5.2 we review such phenomena and give a theoretical description using linearized operator equations. Section 5.3 considers the changes that arise when one allows the measurement to involve nonlinear optical processes.

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