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Theory of Computing Systems

The Study of Modeled Atomtronic Barrier Potentials Through the Impedance Method

Ava Ashby

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

The general impedance method developed by Khondker et.al [1] is applied to multiple barrier potentials to study the transmission behaviors of a single Gaussian barrier potential, double rectangular barrier potential, and a double Gaussian barrier potential. Using the impedance method we will find quantum mechanical transmission behaviors like resonant tunneling for the quasi bound-states of the double barrier potentials. The single Gaussian barrier potential is an approximation for the atomtronic battery and the double Gaussian barrier potential is an approximation for the atomtronic transistor. Thus far, the atomtronic work presented in reference [2] was done in the classical regime where thermal currents dominate. The work presented in this thesis analyzes the quantum mechanical characteristics, such as tunneling, to be incorporated and perhaps used to explore coherent transistor action.

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•Jan 1, 2016•0 citations
The general impedance method developed by Khondker et.al [1] is applied to multiple barrier potentials to study the transmission behaviors of a single Gaussian barrier potential, double rectangular barrier potential, and a double Gaussian barrier potential. Using the impedance method we will find quantum mechanical transmission behaviors like resonant tunneling for the quasi bound-states of the double barrier potentials. The single Gaussian barrier potential is an approximation for the atomtronic battery and the double Gaussian barrier potential is an approximation for the atomtronic transistor. Thus far, the atomtronic work presented in reference [2] was done in the classical regime where thermal currents dominate. The work presented in this thesis analyzes the quantum mechanical characteristics, such as tunneling, to be incorporated and perhaps used to explore coherent transistor action.
A method for determining the quantum wave impedance function for a quantum-mechanical system with an arbitrary piecewise constant potential has been developed.Using this method, both the well-known iterative formula [A.N. Khondker, M. R. Khan, A. F. M. Anwar, J. Appl.Phys.63, 5191 (1988)] and an alternative approach for calculating quantum wave impedance were derived.This approach was applied to both scattering and bound state cases.The general form of the wave functions for bound states, as well as the transmission and reection coecients in the scattering case, were obtained for systems with a potential consisting of an arbitrary number of rectangular barriers and wells.The application of the developed method was demonstrated by describing symmetric rectangular double-well and double-barrier quantum-mechanical systems.
An application of the quantum wave impedance method for the analytical study of quantum-mechanical systems containing a set of delta-wells and delta-barriers is considered in this study.The algorithm for determining both transmission and reflection coefficients for a set of delta-barriers was proposed.Similarly, the scheme for analytically deriving the expressions for energy levels and wave functions of bound states for a set of delta-wells was developed.In both cases, the solution for the quantum wave impedance function in the region with a constant potential [1] and the matching conditions at the origins of deltafunctions were used.As an illustration of the application of the proposed approach, the quantum-mechanical systems with symmetric double-barrier potential and double-well potential were investigated.In the case of a single delta-well, the eigenenergy value as well as the expression for the eigenfunction were obtained directly using the non-linear differential equation for the quantum wave impedance function.The results demonstrate the effectiveness of the quantum wave impedance method in handling quantum-mechanical systems with deltalike potentials, offering a robust framework for further studies in this area.
Abstract Quantum tunneling through potential barriers plays a central role in diverse physical phenomena ranging from nuclear fusion and radioactive decay to semiconductor devices and superconducting technologies. In this work, we calculate tunneling probabilities and wave functions for an arbitrary number of potential barriers with diverse functional forms, including square, Gaussian, parabolic, and Lorentzian profiles, using a general numerical framework. The numerical results are first validated by comparison with exact analytical solutions for double, triple and quadruple-square barrier systems, demonstrating excellent agreement. The results reveal that for a system with N barriers, a single resonance peak splits into ( N − 1 ) distinct peaks, which eventually merge into an energy band as N becomes large, in a manner fully consistent with the existing literature. A key additional result is the incorporation of absorption effects through an imaginary component of the potential, providing a realistic description of particle trapping and leading to a progressive suppression of resonant transmission. For sufficiently strong absorption, the resonant structures are completely washed out. Further, if the barriers become non-uniform or disordered, the regular resonance pattern is also observed to be completely washed out. These findings demonstrate the broad applicability of the approach to complex potential landscapes and offer insights relevant to both fundamental quantum mechanics and the design of next-generation quantum devices.
Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems. In this work, based on the transfer matrix method, we study the quantum effects of proton transfer in a series of one-dimensional (1D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers (wells). In the case of single barriers, when the incident energies of protons are above the barrier height, the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers. It is found that atomic resonant tunneling (ART) not only presents in the rectangular single well and rectangular double barriers as expected, but also exists in the other types of potential wells and double barriers. For hetero-structured double barriers, there is no resonant tunneling in the classical forbidden zone, i.e., in the case when the incident energy (E i) is lower than the barrier height (E b). Furthermore, we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers.
Research in the field of atomtronics aims to develop a new paradigm for the use of ultracold atomic systems in a manner that mimics the functionality of electronic circuits and devices. Given the ubiquity of the electronic transistor and its application to a vast array of signal processing tasks, the development of its atomtronic counterpart is of significant interest. This dissertation presents the experimental studies of two atomtronic circuit elements: a battery and transistor. Experiments are conducted in an atom-chip-based apparatus utilizing hybrid magnetic and optical trapping techniques that enable one to "pattern" atomtronic circuit elements. An atomtronic battery is realized in a double-well trapping potential in which a finite-temperature Bose-Einstein condensate is prepared in a non-equilibrium state to generate thermodynamic gradients that drive atom current flow. Powered by the atomtronic battery, a triple-well atomtronic transistor is demonstrated, and quasi-steady-state behavior of the device is characterized. Results are found to be in agreement with a semiclassical model of the transistor that is also used to study the active properties of the device, including current gain. Based on these results, future directions regarding signal processing operations are proposed.