Formation of dark-state polaritons and two-polariton bound states in arrays of atoms and optical cavities
Формирање тамних поларитона и дво-поларитонских везаних стања у низовима атома и оптичких микрорезонатора.
Author
Maggitti, AngeloMentor
Radonjić, MilanCommittee members
Jelenković, BranislavKuraica, Milorad
Konjević, Nikola
Damnjanović, Milan
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This thesis covers a theoretical analysis of non-interacting and interacting quasi
particles, called polaritons. Polaritons are composites, based on photonic and atomic
excitations in a tunable and controlled manner. Dark-state polaritons, as a subclass
of polaritons, are very curious objects, as they can act as a quantum memory of
photons within an ensemble of alkali-metal atoms in -type conguration which
admit electromagnetically induced transparency (EIT). This thesis focus on the
formation of dark-state polaritons in degenerate two-level systems, where two light
elds, a quantum probe and a classical driving eld, couple the same transition
between the ground state and excited state manifold. An algorithm is going to
be derived in order to determine the dispersion relation and inherent composition
of the dark-state polaritons in the degenerate two-level system. The algorithm is
based on a microscopic equation of motion technique and provides an extension of
the non-degenerate case. D...epending on the polarization of the light elds, it will be
shown that either one or two dark-state polaritons can exist. Further, the calculated
dark-state polaritons can be used in order to perform a frequency conversion and
even a conversion of linear light polarization.
In the second part of the thesis, interacting polaritons in arrays of coupled QED
cavities will be discussed. In rst place, the standard Jaynes-Cummings model is
discussed in order to provide a better insight to polaritons in QED cavities. Then,
a modied Jaynes-Cummings model is introduced and derived in order to study
dark-polaritons and their interaction. It will be shown that dark-polaritons directly
depend on the common single photon detuning of the two coupling elds, quantum
probe and classical driving eld. The interaction between dark-polaritons will be
discussed where the emergence of dark-polariton bound pairs will be shown. By
tuning the Stark-shift due to the classical control eld, the number and the composition
of dark-polariton bound pairs can be controlled. It will be demonstrated
that there exists a dark-polariton bound pair which diers from the aforementioned
ones, because it represents a ground state of the system. Using that kind of a darkpolariton
bound pair, storage and retrieval of a single photon can be performed,
even though that the photons are in a two-photon bound state.
In the last part of the thesis, disorder between QED cavities will be introduced
in a controlled manner through staggered inter-cavity photon hopping strengths J1
and J2. Further, the appearance of a dark-polariton bound pair of a completely
dierent type will be presented.
Ova teza predstav a teorijsku analizu neinteragujuih i interagujuih
kvazi-qestica, tzv. polaritona. Polaritoni su kombinacije fotonskih i atom-
skih ekscitacija u kontrolisano promen ivom odnosu. Vrsta polaritona,
tamni polaritoni, su veoma neobiqni objekti budui da mogu da slue kao
kvantna memorija za fotone unutar ansambla atoma alkalnih metala u -
konfiguraciji, a u vezi sa efektom elektromagnetno indukovane transparen-
cije (EIT). Teza se fokusira na prouqavae formiraa tamnih polaritona u
sistemima sa dva nivoa, osnovnim i pobuenim, koji poseduju mnogostrukosti
degenerisanih podnivoa i spregnuti su kvantnim probnim i klasiqnim kon-
trolnim laserskim po em. Bie izveden algoritam za dobijae disperzione
relacije i odgovarajueg sastava tamnih polaritona u sistemima sa dva-nivoa
i degeneracijom. Algoritam je zasnovan na tehnici mikroskopskih jednaqina
kretaa i predstav a proxiree sluqaja bez degeneracije. Bie pokazano da
u zavisnosti od polarizacije po a mogu postojati jedan ili dva tam...na polari-
tona. Tako dobijeni tamni polaritoni mogu biti korixeni za konverziju
frekvencije i linearne polarizacije svetlosti.
U drugom delu teze razmatraemo interagujue polaritone u nizovima spreg-
nutih kvantno-elektrodinamiqkih optiqkih mikrorezonatora. Kao prvo, pri-
kazan je standardni ejns-Kamingsov model da bi se obezbedio bo i uvid u
polaritone unutar optiqkih mikrorezonatora. Zatim je uveden modifikovani
ejns-Kamingsov model radi prouqavaa tamnih polaritona i interakcije
meu ima. Bie pokazano da tamni polaritoni direktno zavise od zajed-
niqke jednofotonske razdexenosti (detjuninga) korixenih po a, kvantnog
probnog i klasiqnog kontrolnog. Interakcija izmeu tamnih polaritona e
biti prodiskutovana, pri qemu e biti pokazana pojava vezanog para tamnih
polaritona. Podexavaem Xtarkovog pomeraja usled kontrolnog po a moe
se uticati na broj i osobine tih vezanih parova. Bie pokazano da postoji
vezani par tamnih polaritona koji se razlikuje od pomenutih poxto pred-
stav a osnovno stae sistema. Takav vezani par tamnih polaritona omoguava
zarob avae i ixqitavae jednog od dva vezana fotona. U posledem delu
teze bie uvedeno kontrolisano neureee u obliku naizmeniqnih parametara
sprezaa meu mikrorezonatorima, J1 i J2, i bie pokazana pojava potpuno
novog tipa vezanog para tamnih polaritona.