Browsing by Subject "Quantum theory."

Now showing 1 - 9 of 9

Open Access
Entanglement : quantification via uncertainties and search among ultracold bosons in optical lattices
(2009) Öztop, Barış
In the first part of the Thesis, the known measures of entanglement for finite dimensional systems are reviewed. Both the simplest case of pure states that belong to bipartite systems and more general case of mixed states are discussed. The multipartite extensions are also mentioned. In addition to the already existing ones, we propose a new measure of entanglement for pure states of bipartite systems. It is based on the dynamical symmetry group approach to quantum systems. The new measure is given in terms of the total uncertainty of basic observables for the corresponding state. Unlike conventional measures concurrence and 3-tangle, which measure the amount of entanglement of different groups of correlated parties, our measure gives the total amount of multipartite entanglement in a specific state. In the second part of the Thesis, the trapping of bosonic atoms in optical lattices is reviewed. The band structure together with Bloch functions and Wannier basis are discussed for this system. In relation with that, the corresponding Bose-Hubbard model and by the use of this model, the resulting superfluid to Mott-insulator quantum phase transition is summarized. In this regard, the Bose-Hubbard Hamiltonian of a specific system, namely ultracold spin-1 atoms with coupled ground states in an optical lattice is considered. For this system we examine particle entanglement, that is characterized by pseudo-spin squeezing both for the superfluid and Mott-insulator phases in the case of ferromagnetic and antiferromagnetic interactions. The role of a small but nonzero angle between the polarization vectors of counterpropagating lasers forming the optical lattice on quantum correlations is investigated as well.
Open Access
Entanglement in atom-photon systems
(2004) Can, Muhammet Ali
In this work we propose a new principle from the point of view of quantum fluctuations of observables. This new principle can be considered as an operational definition of ME states. Moreover, we show the existence of perfect entangled states of a single “spin-1” particle. We give physical examples related to the photons, and particle physics. We show that a system of 2n identical two-level atoms interacting with n cavity photons manifests entanglement and that the set of entangled states coincides with the so-called SU(2) phase states. In particular, violation of classical realism in terms of Greenberger-Horne-Zeilinger (GHZ) and Clauser-Horne-Shimoni-Holt (GHSH) conditions is proved. We also show that generation of entangled states in the atom-photon systems under consideration strongly depends on the choice of initial conditions In order to obtain maximally robust entangled states we have combined maximum principle with minimum of energy requirement for stabilization, called Mini-max principle. We discuss the generation and monitoring of durable atomic entangled state via Raman-type process, which can be used in the quantum information processing. It is shown that the system of two three-level atoms in Λ configuration in a cavity can evolve to a long-lived maximum entangled state if the Stokes photons vanish from the cavity by means of either leakage or damping. We presented some results based on the application of spherical wave representation to description of quantum properties of multipole radiation generated by atomic transitions. In particular, the angular momentum of photons including the angular momentum entanglement, the quantum phase of photons, and the spatial properties of polarization are discussed.
Open Access
Entanglement in local systems
(2008) Binicioğlu Çetiner, Sinem
In this study, we first discuss entanglement measures and we introduce a way to construct generic entangled states of an n-level quantum system. Then we discuss entanglement as a local object. Particularly we use a spin qutrit, and investigate whether an entangled spin qutrit obeys entanglement criteria or not. While doing this, we also discuss, which criteria of entanglement are essential and which of them are not. We show the relation between quantum fluctuations and entanglement. Lastly, we discuss Bell type inequalities and we show violation of a Bell type condition by a single particle entangled state.
Open Access
Experimental study of critical casimir forces on microparticles in critical binary liquid mixtures
(2014) Tuna, Yazgan
Long-ranged forces between mesoscopic objects emerge when a fluctuating field is confined. Analogously to the well known quantum-electro-dynamical (QED) Casimir forces, emerging between conducting objects due to the confinement of the vacuum electromagnetic fluctuations, critical Casimir forces emerge between objects due to confinement of the fluid density fluctuations. Here, we studied experimentally several novel aspects and applications of critical Casimir fluctuations in a critical mixture of walter-2,6-lutidine, which are a promising candidate to harness forces and interactions at mesoscopic and nanoscopic lengthscales and promise to deliver results of both fundamental and applied interest. In particular, we studied the critical Casimir forces between multiple objects and multiple-body effects. We first extended the experimental study of critical Casimir forces in configurations different from the particle-wall system[1]. The forces acting between two particles in far from any surface and the third particle effect were explored. Then we employed multiple reconfigurable holographic optical tweezers (HOTs) which permit to optically trap several colloids and used a technique known as ”digital video microscopy” (DVM) to track the particles’ trajectories and the forces acting on the particles. We studied the critical Casimir force arising between two particles as a function of their distance and investigated how this is affected by the presence of a third neighboring particle.
Open Access
Hyperdeterminants, entangled states, and invariant theory
(2013) Şen, Emre
In [1] and [2], A. Klyachko connects quantum entanglement and invariant theory so that entangled state of a quantum system can be explained by invariants of the system. After representing states in multidimensional matrices, this relation turns into finding multidimensional matrix invariants so called hyperdeterminants. Here we provide a necessary and sufficient condition for existence of a hyperdeterminant of a multidimensional matrix of an arbitrary format. The answer is given in terms of the so called castling transform that relates hyperdeterminants of different formats. Among castling equivalent formats there is a unique castling reduced one, that has minimal number of entries. We prove the following theorem: “Multidimensional matrices of a given format admit a non-constant hyperdeterminant if and only if logarithm of dimensions of the castling reduced format satisfy polygonal inequalities.”
Open Access
Low-temperature thermodynamics of finite and discrete quartic quantum oscillator in one dimension
(1999) Sıddıki, Afif
I.' this work we examined a quartic Hamiltonian using two different approaches. We first introduced a mean-field Gaussian approximation in order to handle this Hamiltonian analytically and observed that this approximation is insufficient for all coupling strengths. Hence we applied second and third order non-degenerate time-independent perturbation and obtained third or- ■ ler correcHo
Open Access
Quantum entanglement and light propagation through Bose-Einstein condensate (BEC)
(2009) Taşgın, Mehmet Emre
We investigate the optical response of coherent media, a Bose-Einstein condensate (BEC), to intense laser pump stimulations and weak probe pulse propagation. First, we adopt the coherence in sequential superradiance (SR) as a tool for continuous-variable (CV) quantum entanglement of two counter-propagating pulses from the two end-fire modes. In the first-sequence the end-fire and side mode are CV entangled. In the second sequence of SR, this entanglement is swapped in between the two opposite end-fire modes. Second, we investigate the photonic bands of an atomic BEC with a triangular vortex lattice. Index contrast between the vortex cores and the bulk of the condensate is achieved through the enhancement of the index via atomic coherence. Frequency dependent dielectric function is used in the calculations of the bands. We adopt a Poynting vector method to distinguish the photonic band gaps from absorption/gain regimes.
Open Access
Quantum polarization properties of radiation
(1999) Ünsal, Mithat
New bosonic operators, describing the polarization properties of photons at any point with respect to a source, are introduced. It is shown that, unlike the classical picture, the local quantum description of polarization needs nine independent local Stokes operators, forming a representation of the SU(3) subalgebra in the Weyl-Heisenberg algebra of photons. The Cartan algebra of this SU(3) determines the cosine and sine of radiation phase operators. It is shown that the use of plane wave photons can lead to wrong results for quantum fluctuation of polarization even in the far zone. Dual representation of multipole photons is proposed. The exponential operator is diagonal in this representation, hence dual number states describe radiation phase states.. The discrete spectrum of exponential operator is found for dipole and quadrupole photons and a natural behaviour in the classical limit. Application of the results to the near-field optics is discussed.
Open Access
Spatial properties of quantum multipole radiation
(2000) Can, Muhammet Ali
Complete quantum mechanical treatment of multipole radiation is constructed. Vacuum noise of polarization for transversally and longitudirudly polcirized fields is discussed for different total angular momentum values due to the presence of quantum localized sources. It is shown that the spatial properties of the multipole vacuum noise are independent of the type of the radiation, either electric or magnetic. New definition of polarization matrix constructed from the field-strength tensor, Ricci Tensor, is introduced. Using Jaynes-Cummings model Hamiltonian for electrical dipole atom, some statistical properties of the rcidiation are considered. A new method for polarization measurement at short and intermediate distances from the source, based on the use of optical Aharonov-Bohm effect is proposed which is classified as a quantum nondemolition measurement. This proposed experiment leads to measure the longitudinal pohirization and spcicetirne correlation of polarizations of multipole radiation.