Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Radiative and Topological Properties of One-Dimensional Atomic Chains(01. Izmir Institute of Technology, 2024) İyican, Arda Deniz; Çakır, ÖzgürBu tezde, bir boyutlu, her birim hücresinde iki özdeş iki seviyeli atom bulunan bir diatomik zincirin topolojik ve vakum aracılı kolektif özellikleri incelenmiştir. Zincir üzerinde sabit sayıda uyarılmanın olduğu altuzayda, sistem, dissipatif etkileri dikkate alan non-Hermityen bir efektif Hamiltonyen ile tanımlanmaktadır. Zincirde tek bir uyarım varlığında, sonsuz bir zincir için kolektif radyatif davranış, öz durumları Bloch tipi durumlar olan etkin Hamiltoniyene karşılık gelen karmaşık enerji bantlarından ortaya çıkarılmıştır.Tek bir uyarıma sahip sonlu bir zincir için radyatif özellikler, sistemin etkin Hamiltonyeninin tam diyagonalizasyonuyla ortaya çıkarılmıştır. Altışınımlı durumların varlık koşulları belirlenmiştir. Ele alınan model, uzun menzilli etkileşimler ve dissipasyon nedeniyle genişletilmiş, non-Hermityen bir SSH modelidir. Bu sistem için topolojik özellikleri ortaya çıkarmak amacıyla kompleks Berry fazı hesaplanmış ve ardından topolojik olarak trivial olmayan durumlar için kenar durumları belirlenmiştir. Ayrıca, ışınımlı, altışınımlı ve topolojik kenar durumlarından gelen radyasyon desenleri, radyasyon bölgesindeki Poynting vektörünün hesaplanmasıyla gösterilmiştir.Master Thesis Electronic Transport in a Boundary-Driven One-Dimensional Chain With Bulk Dephasing(01. Izmir Institute of Technology, 2024) Yeler, Hakan; Çakır, ÖzgürBu tezde, etkileşimli ve etkilemşimsiz fermiyonların bir boyutlu zincir üzerinde denge dışı durağan durumdaki taşınım özellikleri, çevre etkilerini de hesaba katarak incelenmiştir. Sistem dinamiği Lindblad master denklemi kullanılarak hesaplanmıştır. Taşınımı karakterize eden akım operatörü tanımlanmıştır. Hilbert uzayının eksponansiyel artış göstermesi sebebiyle, çok parçacıklı sistemlerin çözümünü hesaplamak zordur. Bu sebeple farklı çözüm metodları incelenmiştir. Hesaplama avantajlarından dolayı, etkileşimsiz sistemlerin çözümü için kovaryans matris methodu tanıtılmıştır. Etkileşimli sistemler için ortalama alan ve korelasyon fonksiyonların hiyerarşisi gibi yaklaşık metodlar tanıtılıp, birbirleriyle kıyaslanmıştır. Taşınımın davranışı kesin çözüm yöntemi yardımıyla incelenmiştir. Lindblad denklemi vektörize edilerek doğrusal denklem sistemi elde edilmiştir. Elde edilen doğrusal denklem sistemi, Python programlama dili kullanılarak çözülmüştür. Denge dışı durağan durum yoğunluk matrisi ve akım, farklı çevre parametrelerine göre hesaplanmıştır.Master Thesis Electronic Properties of Correlated Impurities in Two Dimensional Materials(01. Izmir Institute of Technology, 2023) Dolu, Volkan; Çakır, ÖzgürThis Master's thesis investigates the effects of single and dual impurity potentials on the electronic properties of both pristine and gapped graphene, being examples of two-dimensional materials. The behavior of 2D materials at the atomic levels, particularly graphene, has been of interest due to their particular electronic properties, such as high electron mobility at certain conditions. The presence of impurities may significantly influence these properties, providing a modifiable platform for rearranging electronic characteristics for diverse applications. Our research focuses on how the impurity states that emerge, especially around energies at low DOS, affect the electronic structure and the interaction between the impurities. We study these effects in the presence of both single and dual impurity potentials of varied strength using computational models based on tight-binding approach. We begin by looking at how the single impurity potentials affect the electronic properties of pristine graphene and gapped graphene. We analyze the change in DOS and energy of the system, along with the identification of the impurity states, utilizing participation ratio for localization. Then, we extend our study to dual impurity potentials and their impacts to provide a knowledge of multi-impurity scenarios. We explore the interaction of the impurities mediated by the Fermi sea. In particular, we studied the hybridization of impurity states and corresponding impurity energies. Next, we determine the force arising between impurities for various Fermi energies, impurity-impurity distances and impurity potential strengths for graphene and gapped graphene.Master Thesis Entanglement and Topological Phenomena in Quantum Walks(01. Izmir Institute of Technology, 2023) Gökalp, Harun; Çakır, ÖzgürQuantum walk, a counterpart of classical random walk, is widely used in the development of quantum algorithms and the modelling of physical systems. Since it has a simple and powerful mathematical structure, its implementation in physical systems serves to solve complex problems. In one-dimensional space, we investigated the topological properties of the simple quantum walk, and under which conditions the simple quantum walk possesses winding numbers. Then, we introduced the split-step quantum walk in a twodimensional space and numerically obtained Chern number phase diagram of each band as a function of rotation parameters. Subsequently, we introduced and studied the quantum walk protocols governed by two coins in a two-dimensional space. We first explored the entanglement and topological properties of a quantum walk protocol governed by a single non-local two-coin operator followed by translations along two spatial directions each governed by a different coin. We deduced that the motion reduces to one-dimensional motion in two spatial directions in decoupled coin subspaces. Then, we studied the split-step quantum walk protocols, where each step is comprised of local coin operations, followed by translations, non-local coin operations, and translations again. In these protocols, each step involves two translations along two spatial directions, and translations along a given spatial direction were either governed by the same coin or alternating coins. We also explored three different non-local coin operations, where a collective rotation takes place in a coin space conditioned on the state of the other coin's state along the same direction or perpendicular direction. We identified the effective Hamiltonian of the system and determined its eigenstates which are comprised of four bands in the Brillouin zone. For all the protocols we have introduced, we studied the coin-coin entanglement and topological properties as a function of coin rotation parameters.Master Thesis Emission Characteristics of Two and Three Level Systems(Izmir Institute of Technology, 2022) Yılmaz, Teyfik; Çakır, Özgür; Çakır, ÖzgürIn this thesis, we mainly focus on the two subjects. Firstly, we investigate the spontaneous emission from a V-type three-level atom. We mainly study the influence of quantum interference between the decay processes from the two upper levels to a lower level to which the upper levels are coupled by the same vacuum modes. The effects of quantum interference on the spontaneous emission spectrum are studied. These effects are shown to induce spectral narrowing and a dark line in the spectrum. The influence of the interference on the upper level populations is also examined. It is seen that the upper level populations are not simple exponential decays. In the second part of this study, the fluorescence spectrum of a driven two-level atom is evaluated. Both the resonance and the off-resonance cases, and the weak and the strong coupling regimes are investigated.Master Thesis Electron Optics in Graphene(01. Izmir Institute of Technology, 2022) Coşgel, Gürcan; Çakır, ÖzgürNegative refraction, also known as Veselago lensing, was first predicted by Victor Veselago in 1968 (Veselago (1968)). Its unique effect has a great potential for both scientific and technological applications such as superlenses. Unlike the conventional positive refractive index, focusing effect can be observed by negative refraction. In this thesis, the focusing effect was investigated theoretically through on n-p junction in graphene. The opposite chirality of electrons and holes enable the negative refraction where electrons( holes) have their momentum parallel(anti-parallel) to the group velocity. The case when potential barrier is directed perpendicular to KK direction, where K and K are the Dirac points were considered. The Green’s functions were calculated analytically and derived the susceptibility using the Green’s functions for various positions of the sources and the receiver at various Fermi energies. The spatial Green’s functions were calculated analytically and derived the static susceptibility (response function).Master Thesis B92 Based Quantum Key Distribution With Faint Pulsed Laser(01. Izmir Institute of Technology, 2021) Mutlu, Görkem; Ateş, Serkan; Çakır, ÖzgürIn quantum key distribution (QKD), photons are used to share the key between the transmitter and receiver, and in principle, single photon sources should be used to create a secure communication channel. Nowadays, attenuated laser sources are used in many studies. While it is practical to use attenuated laser pulses for QKD system, it poses many safety issues due to the possibility of multiple photons in the laser pulses. In addition, the key rate is waived to increase the level of security. However, the use of single photon sources is not as easy and practical as using attenuated laser sources. Today, studies of single photon sources to be used for QKD continue. In order for these single photon sources to be used actively, a photon source that operates at room temperature, operates in a wide band-gap range for different areas of use (underwater, optical fiber-based and free space) and can be excited at high speed is required. Since hBN defect centers are a material that can produce single photons at room temperature and have a wide band gap, it seems very ideal for these studies. In this thesis, studies have been carried out on the realization of the protocol, which is a part of QKD, with solid-state materials that produce single photons. In the studies, a key was produced with a faint pulsed laser. Also, data is encrypted using the key of the transmitter. Then the data is successfully decrypted with the key measured by the receiver.Master Thesis Quantum Walks: Entanglement Between Spatial Degrees of Freedom and Interference in Multi-Photon Walks(Izmir Institute of Technology, 2020) Karlı, Yusuf; Çakır, ÖzgürQuantum walks can be described as quantum analogues of classical random walks. In quantum walks, the direction of the walker is dictated by the quantum state of a coin in a coherent fashion. Unlike classical random walk with a fair coin, quantum walk has non-Markovian property. First, we studied 2-D quantum walk analytically and numerically with one-walker and two entangled coins to investigate the transfer of the entanglement in initial coins state to spatial degrees of freedom. The coins are Hadamard Coin, Fourier Coin, among which the Fourier coin generates entanglement, thus increase entanglement between spatial degrees of freedom. Here we calculated the amount of entanglement using negativity. In the second part we studied average photon number correlations for 1-D quantum walk with many body bosonic walkers, like different light sources, to investigate quantum interference effects and we showed the second-order intensity correlations function in terms of the probability amplitudes of the 1-D quantum walk with Hadamard coin. We compared the resulting correlations for various initial many photon states.Master Thesis Rkky Interaction and Its Control in Graphene and Related Materials(Izmir Institute of Technology, 2019) Canbolat, Ahmet Utku; Çakır, ÖzgürGraphene got dramatic attention and lead the two-dimensional material physics after its first successful synthesis in 2004. Its unique electronic properties contain great potential for both scientific and technological applications. RKKY (Ruderman-Kittel-Kasuya Yosida) is an indirect exchange interaction mediated by conduction electrons. In graphene, the interaction strength decay as 1/R³ where R is the distance between the magnetic moments. In the first part of this work, we calculated that applying circular potential on a graphene sheet forms quasi-bound states in the potential region. Via these states, the RKKY interaction is enhanced between magnetic moments on the edge of the potential well. This can be thought of an electronic analog of the Purcell effect. We showed that the interaction strength is even more enhanced if the Fermi level is in resonance with the energies of the quasi-bound states. In the second part, we considered zigzag edged hexagonal nanoflakes. It is known that zigzag edged flakes have zero-energy edge-states. It is also known that the states with closer energies contribute more to RKKY interaction. Thus, we calculated that there is an enhancement between these edge-states. In the third part, we investigated the behavior of RKKY interaction for two dimensional materials with quartic dispersion. An energy dispersion is said to be quartic if it is of the form E = α(k² - kc² )². Here, α and kc are material dependent constants. There are many materials exhibiting the quartic dispersion such as nitrogene, phosphorene, and arsenene. These materials are also sharing two-dimensional hexagonal lattice structure with graphene. What makes quartic dispersion special is that it has van-Hove singularity in its density of states near the band-edge. RKKY interaction is sensitive to the density of states because it depends on the number of electrons contributing spin exchange. Thus, the larger the number of electrons, the stronger the coupling. In this part, we tuned the Fermi level so that it lies on the DOS singularity and then we calculated the interaction strength as a function of R. We found a slowly decaying RKKY interaction for quartic dispersion. If the energy dispersion is pure quartic (i.e. E = ak4), we found the interaction strength depends on 1/(kf R) instead of 1/R which makes the RKKY interaction long range for arbitrarily small Fermi level.Master Thesis Three-Photon Electromagnetically Induced Transparency in Rydberg Atoms(Izmir Institute of Technology, 2019) Oyun, Yağız; Sevinçli, Sevilay; Çakır, ÖzgürElectromagnetically Induced Transparency (EIT) is a quantum coherence phe- nomenon, in which an atomic medium is rendered transperent via destructive interference of excitation pathways. EIT was first observed in a three-level lambda scheme where a modified optical response is achieved by the interference of light field induced atomic state coherences at the resonance of transition. An EIT system also produces important optical effects including giant Kerr non-linearity and slow light. Rydberg-EIT media have been used to study optical properties of atomic media, non-linear optical effects and to gain better understanding on interacting many-body systems due to the controllable in- teractions of Rydberg atoms. Recently EIT in a four-level ladder scheme was realized experimentally in a dressed-state manner with Cs atomic vapor, in which a strong dress- ing field allows for a transparency window to be opened for probe field. Rydberg EIT has potential applications in terahertz regime, electrometry, metrology and quantum in- formation science, but extensive studies on four-level Rydberg EIT schemes are scarce. In this thesis; three-photon EIT in a cold atomic ensemble that has a ladder type excita- tion scheme, in which the highest energy state is a Rydberg state is investigated. Atom- light interactions of a four-level ladder system is developed for non-interacting case, then extended to many-body case. Starting with the steady-state solutions without atomic in- teractions, Rydberg EIT system is analyzed using mean-field and rate equation methods, though due to inadequate computing power and lack of time we could not finalize the rate equation method. To understand effects of Rydberg-Rydberg interactions on these systems in detail, two-body case is investigated with mean-field method. Afterwards, to achieve more realistic results, a self-consistent mean-field method for larger systems is developed. It is observed that as the van der Waals interaction energy increases, Rydberg blockade becomes more prominent. Therefore induced transparency weakens, broadens and shifts away from the resonance as expected. This means that, controllable interac- tions in a Rydberg EIT medium enables to control and modify the optical response of the atomic medium.