Theoretical Study of Calorimetric Measurements in Quantum Integrated Circuits

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http://urn.fi/URN:ISBN:978-951-51-6573-2
Title: Theoretical Study of Calorimetric Measurements in Quantum Integrated Circuits
Author: Donvil, Brecht
Contributor organization: University of Helsinki, Faculty of Science
Doctoral Programme in Mathematics and Statistics
Helsingin yliopisto, matemaattis-luonnontieteellinen tiedekunta
Matematiikan ja tilastotieteen tohtoriohjelma
Helsingfors universitet, matematisk-naturvetenskapliga fakulteten
Doktorandprogrammet i matematik och statistik
Publisher: Helsingin yliopisto
Date: 2020-10-01
Language: eng
URI: http://urn.fi/URN:ISBN:978-951-51-6573-2
http://hdl.handle.net/10138/319285
Thesis level: Doctoral dissertation (article-based)
Abstract: Recent developments in experimental methods allow for the study of thermodynamic properties of quantum systems. In quantum integrated circuits, quantum systems are elements in an electric circuit that can straightforwardly be coupled to other elements. This manipulability allows one to construct quantum heat engines, Maxwell demons etc. Quantum integrated circuits also are one of the main potential settings to realise a working quantum computer. Calorimetric measurements in integrated circuits serve as a promising technique to probe thermodynamic laws of the quantum regime and to study the inner workings of quantum devices. Due to this experimental accessibility, the theoretical study of open quantum systems in the context of quantum integrated circuits is highly relevant. Open quantum systems are typically small systems, e.g. qubits or oscillators, in contact with one or more reservoirs. The research on which this thesis is based can roughly be divided into two parts. The first part is concerned with the thermodynamics of a driven qubit in contact with a thermal bath. This system is the archetype of a quantum out-ofequilibrium system. In one case the qubit is strongly driven by a semiclassical driving field. Building on earlier works, the thermodynamic relations of the system are found by proving the equivalence with an easier to study qubit-oscillator system. In the other, case the qubit is driven by being in contact with two baths with a temperature gradient. The full generating function is derived in a proper approximative scheme and a fluctuation-dissipation relation is found. The second part focusses on a specific experimental scheme to perform calorimetric measurements. The scheme relies on coupling a quantum system to a finite reservoir and performing fast temperature measurements on the reservoir. Doing so allows one to infer energy changes in the reservoir and therefore to obtain the heat exchanged with the system. The dynamics of this system are modelled for weak system-reservoir coupling and concrete experimental predictions are made. In new work, the dynamics for a toy model of a system interacting with a finite reservoir are derived from first principles for a specific model. The first principle derivation matches with the earlier modelled dynamics in the weak coupling and allows to consider strong system-reservoir coupling as well.We are currently on the verge of a second quantum revolution which promises devices and applications based on genuine quantum effects. The hope is that these devices, such as quantum computers, will result in large leaps in computing power and efficiency. One of the factors preventing the realization of such applications is the fact that the interaction between a quantum mechanical system and its environment leads to the destruction of the quantum effects on which the devices are based. Therefore, it is important to have a good understanding of these quantum system-environment interactions. Recent experimental progress has made it possible to study these effects by measuring small changes in the temperature of the environment. In the articles on which this dissertation is based, the interactions between a quantum bit and its environment are studied in a general context as well as focused specifically on the aforementioned experimental setup. In the general context, thermodynamic relations are derived and they describe the heat exchange between the system and environment. The other studies lead to concrete predictions for the behavior of the environment temperature in possible experiments. Finally, the thesis presents original work to extend the theoretical description of the experiment to new parametric regimes.Olemme tällä hetkellä toisen kvanttivallankumouksen partaalla, joka lupaa laitteita ja sovelluksia perustuen aitoihin kvantti-ilmiöihin. Toiveena on, että nämä laitteet, kuten kvanttitietokoneet, johtavat suuriin harppauksiin laskentatehossa ja tehokkuudessa. Yksi tällaisten sovellusten toteutumisen esteistä, on se, että kvanttimekaanisen systeemin ja sen ympäristön välinen vuorovaikutus johtaa laitteiden perustana olevien kvantti-ilmiöiden tuhoutumiseen. Siksi on tärkeää ymmärtää nämä kvanttisysteemien ja ympäristön vuorovaikutukset. Viimeaikainen kokeellinen kehitys on mahdollistanut näiden ilmiöiden tutkimisen mittaamalla pieniä muutoksia ympäristön lämpötilassa. Tämän väitöskirjan artikkeleissa kvanttibitin ja sen ympäristön välisiä vuorovaikutuksia tutkitaan sekä yleisesti että keskittyen erityisesti edellä mainittuun kokeelliseen asetelmaan. Yleisestä yhteydestä johdetaan termodynaamiset suhteet, jotka kuvaavat systeemin ja ympäristön välistä lämmönvaihtoa. Muiden artikkelien tutkimukset johtavat konkreettisiin ennusteisiin ympäristön lämpötilan käyttäytymisestä mahdollisissa kokeissa. Lopuksi väitöskirjassa esitetään uusia tuloksia kokeen teoreettisen kuvauksen laajentamiseksi uusille parametrialueille.
Subject: mathematics
Rights: Julkaisu on tekijänoikeussäännösten alainen. Teosta voi lukea ja tulostaa henkilökohtaista käyttöä varten. Käyttö kaupallisiin tarkoituksiin on kielletty.


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