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Strategies for Discriminating and Comparing Unknown Unitary Transformations
Year of Dissertation:
How to discriminate or compare two unitary transformations that are completely unknown? We first examine the unambiguous discrimination of two unknown unitary transformations; we show that the results are the same as those found for the programmable discrimination of two unknown quantum states. Next we consider the minimum-error comparison of two unknown unitary transformations; the results are obtained in the general case where the prior probabilities are different. Last we study the unambiguous discrimination of two unknown unitary transformations in the case where multiple copies of data are available.
Colloidal Quantum Dot Based Photonic Circuits and Devices
Year of Dissertation:
Colloidal quantum dots have desirable optical properties which can be exploited to realize a variety of photonic devices and functionalities. However, colloidal dots have not had a pervasive utility in photonic devices because of the absence of patterning methods. The electronic chip industry is highly successful due to the well-established lithographic procedures. In this thesis we borrow ideas from the semiconductor industry to develop lithographic techniques that can be used to pattern colloidal quantum dots while ensuring that the optical properties of the quantum dots are not affected by the process. In this thesis we have developed colloidal quantum dot based waveguide structures for amplification and switching applications for all-optical signal processing. We have also developed colloidal quantum dot based light emitting diodes. We successfully introduced CdSe/ZnS quantum dots into a UV curable photo-resist, which was then patterned to realize active devices. In addition, "passive" devices (devices without quantum dots) were integrated to "active" devices via waveguide couplers. Use of photo-resist devices offers two distinct advantages. First, they have low scattering loss and secondly, they allow good fiber to waveguide coupling efficiency due to the low refractive index which allows for large waveguide cross-sections while supporting single mode operation. Practical planar photonic devices and circuits incorporating both active and passive structures can now be realized, now that we have patterning capabilities of quantum dots while maintaining the original optical attributes of the system. In addition to the photo-resist host, we also explored the incorporation of colloidal quantum dots into a dielectric silicon dioxide and silicon nitride one-dimensional microcavity structures using low temperature plasma enhanced chemical vapor deposition. This material system can be used to realize microcavity light emitting diodes that can be realized on any substrate. As a proof of concept demonstration we show a 1550 nm emitting all-dielectric vertical cavity structure embedded with PbS quantum dots. Enhancement in spontaneous emission from the dots embedded in the microcavity is also demonstrated.
Wave Scattering in Random Layered Media
Year of Dissertation:
The scaling and statistics of the transport of waves in random media depend strongly on the dimensionality of the medium. The statistic of transmission in one dimension (1D) and quasi-1D (Q1D) have been calculated and tested. However, the statistic for other dimensions has not been established. Exploring transport in a layered system of stacks of glass cover slips with transverse nonuniformity has allowed us to study a dimensional crossover in transport from 1D towards 3D. The crossover occurs when the lateral spread of the wave become larger than the transverse coherence length in the transmitted speckle pattern as the number of layers increases. In thin samples, in which light does not spread beyond a single coherence area of the field on the output surface, the statistics of normalized intensity follow 1D statistics associated with a segment of a log-normal distribution with a sharp drop below the log-normal distribution for low values of intensity. Once the lateral spread is larger than the transverse coherence length, the probability density of intensity becomes a mixture of a mesoscopic distribution and an intensity distribution of a Gaussian field. This distribution was originally found for Q1D. Beyond 1D, the intensity statistics have a same form as Q1D statistics which is a function of a single localization parameter, the “statistical conductance” g’. This transition from 1D to Q1D statistics reflects a topological change in the transmitted field. In 1D, the transmitted intensity never vanishes, while beyond 1D, a speckle pattern built upon a network of phase singularities forms.
Initial conditions in high-energy collisions
Year of Dissertation:
This thesis is focused on the initial stages of high-energy collisions in the saturation regime. We start by extending the McLerran-Venugopalan distribution of color sources in the initial wave-function of nuclei in heavy-ion collisions. We derive a fourth-order operator in the action and discuss its relevance for the description of color charge distributions in protons in high-energy experiments. We calculate the dipole scattering amplitude in proton-proton collisions with the quartic action and find an agreement with experimental data. We also obtain a modification to the fluctuation parameter of the negative binomial distribution of particle multiplicities in proton-proton experiments. The result implies an advancement of the fourth-order action towards Gaussian when the energy is increased. Finally, we calculate perturbatively the expectation value of the magnetic Wilson loop operator in the first moments of heavy-ion collisions. For the magnetic flux we obtain a first non-trivial term that is proportional to the square of the area of the loop. The result is close to numerical calculations for small area loops.
Ordering and topological defects in solids with quenched randomness
Year of Dissertation:
We explore multiple different examples of quenched randomness in systems with a continuous order parameter. In all these systems, it is shown that understanding the effects of topology is critical to the understanding of the effects of quenched randomness. We consider n-component fixed-length order parameter interacting with a weak random field in d=1,2,3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions have been studied on lattices containing hundreds of millions sites. At n-1d, when topological objects are absent, the final, lowest-energy, state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument. In the borderline case of n-1=d, when topological structures are non-singular, the system possesses a weak metastability with the Imry-Ma state likely to be the global energy minimum. We study random-field xy spin model at T=0 numerically on lattices of up to 1000x1000x1000 spins with the accent on the weak random field. Our numerical method is physically equivalent to slow cooling in which the system is gradually losing the energy and relaxing to an energy minimum. The system shows glass properties, the resulting spin states depending strongly on the initial conditions. Random initial condition for the spins leads to the vortex glass (VG) state with short-range spin-spin correlations defined by the average distance between vortex lines. Collinear and some other vortex-free initial conditions result in the vortex-free ferromagnetic (F) states that have a lower energy. The energy difference between the F and VG states correlates with vorticity of the VG state. Correlation functions in the F states agree with the Larkin-Imry-Ma theory at short distances. Hysteresis curves for weak random field are dominated by topologically stable spin walls raptured by vortex loops. We find no relaxation paths from the F, VG, or any other states to the hypothetical vortex-free state with zero magnetization. XY and Heisenberg spins, subjected to strong random fields acting at few points in space with concentration c_r << 1, are studied numerically on 3d lattices containing over four million sites. Glassy behavior with strong dependence on initial conditions is found. Beginning with a random initial orientation of spins, the system evolves into ferromagnetic domains inversely proportional to c_r in size. The area of the hysteresis loop, m(H), scales as c_r^2. These findings are explained by mapping the effect of strong dilute random field onto the effect of weak continuous random field. Our theory applies directly to ferromagnets with magnetic impurities, and is conceptually relevant to strongly pinned vortex lattices in superconductors and pinned charge density waves. The random-anisotropy Heisenberg model is numerically studied on lattices containing over ten million spins. The study is focused on hysteresis and metastability due to topological defects, and is relevant to magnetic properties of amorphous and sintered magnets. We are interested in the limit when ferromagnetic correlations extend beyond the size of the grain inside which the magnetic anisotropy axes are correlated. In that limit the coercive field computed numerically roughly scales as the fourth power of the random anisotropy strength and as the sixth power of the grain size. Theoretical arguments are presented that provide an explanation of numerical results. Our findings should be helpful for designing amorphous and nanosintered materials with desired magnetic properties.
PHASE SPACE EXPLORATIONS IN TIME DEPENDENT DENSITY FUNCTIONAL THEORY
Year of Dissertation:
Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated functional of the co-ordinate density, non-local in space and time. Adiabatic approximations (such as ALDA), which are local in time, are most commonly used in the increasing applications of the field. Going beyond ALDA, has been proved difficult leading to mathematical inconsistencies. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from two electron model systems. In this thesis work we propose a phase-space extension of the TDDFT. We want to answer the challenges the theory is facing currently by exploring the one-body phase-space. We give a general introduction to this theory iv and its mathematical background in the first chapter. In second chapter, we carryout a detailed study of instantaneous phase-space densities and argue that the functionals of distributions can be a better alternative to the nonlocality issue of the exchange-correlation potentials. For this we study in detail the interacting and the non-interacting phase-space distributions for Hookes atom model. The applicability of ALDA-based TDDFT for the dynamics in strongfields can become severely problematic due to the failure of single-Slater determinant picture.. In the third chapter, we analyze how the phase-space distributions can shine some light into this problem. We do a comparative study of Kohn-Sham and interacting phase-space and momentum distributions for single ionization and double ionization systems. Using a simple model of two-electron systems, we have showed that the momentum distribution computed directly from the exact KS system contains spurious oscillations: a non-classical description of the essentially classical two-electron dynamics. In Time dependent density matrix functional theory (TDDMFT), the evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be expressed in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. In v our fourth chapter, we show that by applying the quasi-classical and semiclassical approximations one can capture the natural occupations of the excited systems.We study a time-dependent Moshinsky atom model for this. The fifth chapter contains a comparative work on the existing non-local exchange-correlation kernels that are based on current density response frame work and the co-moving frame work. We show that the two approaches though coinciding with each other in linear response regime, actually turn out to be different in non-linear regime.
Non-linear response of 2D electron systems at low temperatures to electric and magnetic fields
Natalia Romero Kalmanovitz
Year of Dissertation:
The nonlinear behavior of low-dimensional electron systems has attracted a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. This work focuses on experimental results related to the nonlinear behavior of two dimensional electron systems. We first observed the non-linear zero-differential resistance state (ZDRS) that occurs for highly mobile two dimensional electron systems in response to a dc bias in the presence of a strong magnetic field applied perpendicular to the electron plane is suppressed. We found that it disappears gradually as the magnetic field is tilted away from the perpendicular at fixed filling factor. Good agreement is found with a model that considers the effect of the Zeeman splitting of Landau levels enhanced by the in-plane component of the magnetic field. Furthermore, we observed that when an electric field is applied to conductors, it heats electric charge carriers. It is demonstrated that an electric field applied to a conductor with a discrete electron spectrum produces a non-equilibrium electron distribution, which cannot be described by temperature. Such electron distribution changes significantly the conductivity of the electrons in a magnetic field, and forces them into a state with a zero differential resistance. Most importantly, the results demonstrate that in general, the effective overheating in the systems with discrete spectrum is significantly stronger than the one in systems with continuous and homogeneous distribution of the energy levels at the same input power. In the last part we observed non-linear behavior in a silicon MOSFET. Measurements of the rectification of microwave radiation at the boundary between two-dimensional electron systems separated by a narrow gap on a silicon surface for different temperatures, electron densities and microwave power, were performed. A theory is proposed that attributes the rectification to the thermoelectric response due to strong local overheating by the microwave radiation at the boundary between two dissimilar 2D metals.
Optical and Magneto-Optical Properties of type-II Excitons in ZnTe/ZnSe Stacked Submonolayer Quantum Dots
Year of Dissertation:
In this thesis we plan to develop understanding of the fundamental physical and material properties of type-II excitons in stacked ZnTe/ZnSe submonolayer quantum dots (QDs). The samples, grown via combination of molecular beam epitaxy (MBE) and migration enhanced epitaxy (MEE) are studied using photoluminescence (PL), time-resolved PL (TRPL) and PL in external magnetic field (Magneto-PL) as well as Magneto-TRPL. This thesis aims to discuss the key realizations keeping in mind the fundamental and advanced interests for such and related systems. In the first part of the thesis, effects of varying two crucial MBE growth parameters on the size and composition of the QDs are studied via detailed optical characterization with the goal of attaining better control over intentional growth. The second part of the thesis is focused on the magneto-optical studies, wherein observation of the optical excitonic Aharonov-Bohm (AB) effect in these type-II QD system has been discussed in details. The AB phase is revealed via the optical emission in magnetic field, observed as oscillation (AB `peak') in PL intensity. Presence of built-in electric field in the system is indicated from the narrow and robust AB oscillations. Detailed spectral analysis of the AB peak enabled us to determine lateral excitonic size with sub-nanometer precision as well as distinguish the presence of different QD stacks of the submonolayer QDs in the ensemble system. Magneto-time resolved PL measurements were performed to understand the influence of AB effect on the lifetime of magneto excitons due to transitions of angular momentum between optically "bright" and "dark" excitonic states. Our understandings have been discussed to the extent of the achieved results.
Variable Pressure Nuclear Magnetic Resonance Studies of Ionic Liquids and Electrophoretic Probe Design
Year of Dissertation:
Energy storage materials play a key role in, efficient, clean, and versatile use of energy, and are crucial for the exploitation of renewable energy. The improve efficiency of energy use stimulates the development of energy storage such as batteries or super capacitors, toward higher power and energy density, which significantly depends upon the advancement of new materials used in these devices. The new materials need better understanding and description in the electrochemical properties. Nuclear Magnetic Resonance (NMR) has been an important tool in the characterization of ionic liquids and solids. The measurements of the relaxation times and the diffusion coefficient are of great importance in understanding the dynamics at micro and macro scale and are performed as a function of temperature and pressure to obtain parameters such as activation energies and activation volumes respectively. In this work, studies of ionic liquids and polycarbonates are presented and the design and fabrication of cells used in the study of NMR under an electric field.
OPTOMECHANICS OF CAVITY DRIVEN NANOPARTICLES
Year of Dissertation:
The subject of this thesis is the opto-mechanical interaction of a spherical high-Q microresonator and a subwavelength particle, which, at optical wavelengths, corresponds to a size on the order of nanometers. After a review of the basic theory of spherical resonators and multi-sphere scattering, the full self-consistent electromagnetic field of the coupled resonator-particle system is derived. The particle-induced frequency shift and broadening is calculated by examining the poles of the scattering coefficients of the resonator. The force exerted on the particle by the field is determined via the Maxwell stress tensor, and is found to be in general non-conservative. From the force, the trajectories of the particle positioned outside the resonator are investigated. The relationship between frequency shift and the conservative and non-conservative components of the force is found to differ from the well-known formulas for the "gradient" and "scattering" force, which are commonly derived by neglecting the modification of the resonator field by the particle. The key aspects of this difference are investigated by re-deriving the results of the exact field calculations from a modified gradient/scattering framework, which explicitly takes into account the modification of the resonator field due to the particle.