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Author:Huhtamäki, Jukka
Title:Quantum Dynamics of Markovian and non-Markovian Atom-Cavity Systems
Kvattidynaaminen Markovinen ja ei-Markovinen atomi-kaviteetti systeemi
Publication type:Master's thesis
Publication year:2004
Pages:64      Language:   eng
Department/School:Teknillisen fysiikan ja matematiikan osasto
Main subject:Materiaalifysiikka   (Tfy-44)
Supervisor:Salomaa, Martti M.
Instructor:Salo, Janne
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark TF80     | Archive
Keywords:quantum optics
two-level atom
optical cavity
QED
Markovian time-evolution
kvanttioptiikka
kaksi-taso atomi
optinen kaviteetti
QED
Markovinen aikakehitys
Abstract (eng): Quantum optics has been a rapidly developing field of theoretical physics in the past few decades, especially after the experimental demonstration of non-classical light in the 1970's.
Applications of quantum optics are numerous, including lasers, semiconductors, fiber optics, possible realizations of quantum computers and much more.

In this thesis we concentrate on a specific quantum-optical system consisting of an atom trapped inside a leaking cavity.
First the cavity is eliminated adiabatically from the system, yielding a time-evolution equation for the atom alone.
This is fairly easy to do in the Markovian approximation, but in this case the memory effects are lost: the future evolution of the atom depends merely on its current state.
In order to include memory effects in our description, we try to work through the calculations with less strict assumptions which we refer to as the non-Markovian case.
This scheme yields a coupled system of integrodifferential equations which we solve iteratively, using the Markovian results as the initial guess.

The time-evolution equations resulting from both the Markovian and non-Markovian cases are solved using tailored Fortran 90 programs.
The approximate solutions are then compared with the exact time-evolution of the system obtained using the MATLAB quantum optics toolbox.
Abstract (fin): Kvanttioptiikka on ollut nopeasti kehittyvä teoreettisen fysiikan haara viime vuosikymmenillä, etenkin lähtien epäklassisen valon kokeellisesta todentamisesta 1970-luvulla.
Teorian sovellusalueita on lukuisia, muun muassa laserit, puolijohteet, optiset kuidut ja kvanttitietokoneen mahdolliset realisaatiot.

Työssä keskitymme yhteen tiettyyn kvanttioptiseen systeemiin, joka koostuu vuotavaan kaviteettiin vangitusta atomista.
Aluksi eliminoimme adiabaattisesti kaviteetin systeemistä, josta saamme aikakehitysyhtälön ainoastaan atomille.
Tämä on kohtalaisen helppoa tehdä Markovin approksimaatiossa, mutta tässä tapauksessa muisti-ilmiöt katoavat: atomin tulevaisuus riippuu ainoastaan sen tämänhetkisestä tilasta.
Jotta saisimme myös muisti-ilmiöt mukaan systeemin kuvailuun, yritämme laskea laskut läpi väljemmillä oletuksilla, johon viittaamme ei-Markovisella tapauksella.
Tämä lähestymistapa johtaa kytkettyyn integrodifferentiaaliyhtälösysteemiin, jonka ratkaisemme iteratiivisesti käyttämällä Markovin approksimaatiosta saatua tulosta alkuarvauksena.

Sekä Markovisen että ei-Markovisen tapauksen aikakehitysyhtälöt ratkaistaan käyttämällä Fortran 90:llä kirjoitettuja ohjelmia.
Approximatiivisia ratkaisuja verrataan systeemin tarkkaan aikakehitykseen, joka voidaan laskea MATLAB:in quantum optics toolbox:lla.
ED:2004-07-14
INSSI record number: 25438
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