Physics Commons^™

Casimir Force In Schwarzschild Metric: Progress Report, Munawar Karim

Physics Faculty/Staff Publications

In this paper I report progress on both theoretical and experimental aspects. I describe two approaches to calculating putative effects of gravitational curvature on the Casimir force. The work I describe continues the quest to answer the question: do virtual field excitations follow geodesics?

New Experiments In Gravitational Physics, Munawar Karim, Ashfaque H. Bokhari

Physics Faculty/Staff Publications

We propose experiments to examine and extend interpretations of the Einstein field equations. Experiments encompass the fields of astrophysics, quantum properties of the gravity field, gravitational effects on quantum electrodynamic phenomena and coupling of spinors to gravity. As an outcome of this work we were able to derive the temperature of the solar corona.

Optical Properties And Growth Dynamics Of Oxides On Single Crystal Ain, Jacob Bugno, Sujit Biswas

The Review: A Journal of Undergraduate Student Research

Aluminum nitride (AIN) is a novel wide bandgap semiconductor. This research focused on optical properties of AIN as well as native oxide properties of single crystal AIN. Refractive index, absorption coefficient, and oxide film thickness were measured using absorption spectrophotometer and ellipsometer. Additionally, we were also interested in characterizing the oxide and studying its growth dynamics. To achieve this, we used successive ellipsometric measurements. Transmission measurements from the spectrophotometer were analyzed, and absorption spectra between 200 and 2500 nm was numerically extracted. To analyze ellipsometric data, a two parameter analytical algorithm was used. This calculated the best fit parameters for …

Wave Equation On Spherically Symmetric Lorentzian Metrics, Ashfaque H. Bokhari, Ahmad Y. Al-Dweik, A. H. Kara, Munawar Karim

Physics Faculty/Staff Publications

Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of θ and ϕ are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.

Characterizing Planetary Orbits And The Trajectories Of Light In The Schwarzschild Metric, Foek T. Hioe, David Kuebel

Physics Faculty/Staff Publications

Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can be associated with different characteristics of the orbits. The boundaries for these regions are clearly defined. Observational data can be directly associated with points in the regions. A possible extension of these considerations with an additional parameter for the case of Kerr geometry is briefly discussed.

Adiabatic Shape Preservation And Solitary Waves In A Five-Level Atomic Medium, Foek T. Hioe

Physics Faculty/Staff Publications

Adiabatically shape-preserving-wave and solitary-wave solutions for five-level atomic systems are presented. They give the idealized situations for the shape preserving propagation of optical waves through a five-level atomic medium, and provide some useful comparisons with the electromagnetically induced transparency experiments performed by Harris and his collaborators on atoms with hyperfine structure.

N Coupled Nonlinear Schrödinger Equations: Special Set And Applications To N=3, Foek T. Hioe

Physics Faculty/Staff Publications

Analytic solutions for a special set of N coupled nonlinear Schrödinger equations characterized by 2^N interaction types are presented for N = 1–3. They provide an overview of the important role played by nonlinear couplings

Solitary Waves For Two And Three Coupled Nonlinear Schrödinger Equations, Foek T. Hioe

Physics Faculty/Staff Publications

We present solitary-wave solutions of two and three coupled nonlinear Schrödinger equations when the waves propagate in the normal and anomalous group-velocity dispersion regions. A wave of the form sech² £-2/3 is found, which, together with two known waves of the forms tanh £ sech £ and sech² £, are shown to form a new generation of complementary waves. The implication of this wave set and its applications to coupled solitary-wave propagation is discussed.

Solitary Waves And Atomic Population Transfer Via The Continuum, Foek T. Hioe, C. E. Carroll

Physics Faculty/Staff Publications

Exact analytic results are presented that represent a pair of solitary waves that can propagate through an atomic medium with their shapes invariant while producing transfer of atoms or molecules from one bound state to another via a continuum. The speed of the waves and the amount of population transfer are given in terms of the wave amplitudes. A general ~not solitary wave! solution for the case of a single wave is presented, together with a nonlinear Beer’s law of absorption.

Selective Excitation And Structure In The Continuum, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

We show that efficient transfer of molecules or atoms from one bound state to another is possible via the continuum in some cases, using two overlapping laser pulses. The structure of the continuum determines the pulse delay, laser frequencies, and laser intensities that should be used. We present simple formulas that relate the optimum values of pulse intensities, pulse separation, and detuning; these estimates can be used as a guide. More detailed calculations give quantitative results for two specific potentials.

Radio-Frequency Superconducting Parametric Transducer For Gravitational-Wave Antennae, M. A. Fisher, Mark F. Bocko, Linda E. Marchese, Guizhen Zhang, Munawar Karim

Physics Faculty/Staff Publications

We report on the design and testing of an ultrasensitive, electromechanical transducer for use on resonant mass gravitational wave antennae. The transducer is a superconducting, radio frequency resonant bridge circuit operating near 200 MHz. We have minimized several important sources of noise in this transducer system. The Johnson noise of the transducer circuit is reduced through using a superconducting niobium stripline circuit and low‐loss insulating materials. At a temperature of 4.2 K we have achieved unloaded electrical quality factors of 200 000. The bridge circuit is balanced by piezoelectric actuators which control the spacing between the proof mass and capacitive …

Formation Of Shape-Preserving Pulses In A Nonlinear Adiabatically Integrable System, R. Grobe, Foek T. Hioe, J. H. Eberly

Physics Faculty/Staff Publications

No abstract provided.

Matched Optical Solitary Waves For 3-Level And 5-Level Systems, Foek T. Hioe, R. Grobe

Physics Faculty/Staff Publications

Exact analytic results are presented that give a general solution for a pair of solitary waves which can propagate through a three- and a five-level system with their shapes invariant. These solitary waves vary widely in shape and form: from ones for which the pulses have similar shape to ones which have very different but ''complementary'' shapes. A general type of solitary-wave pair which is insensitive to small perturbations is identified.

Performance Of An Inertially Coupled, 3-Mode Gravitational-Wave Antenna Prototype, Linda E. Marchese, Mark F. Bocko, Guizhen Zhang, Munawar Karim

Physics Faculty/Staff Publications

A prototype three‐mode gravitational wave antenna which employs a two‐mode torsional transducer has been constructed and tested. For the torsional transducer the coupling from one stage to the next is via inertial forces, whereas in a conventional transducer the stage‐to‐stage coupling is proportional to the relative displacements via the springs. Experiments with our antenna‐torsional transducer prototype demonstrate a maximum antenna bandwidth of 260 Hz (29% of the antenna resonant frequency of 900 Hz) and a mechanical amplification factor of 40. A mathematical model for the three‐mode antenna has been developed and predictions of the system transfer functions and transient response …

Selective Excitation Via The Continuum And Suppression Of Ionization, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

Two laser pulses that overlap in time have been successfully used for coherent excitation of a molecule or atom to a desired state. An intermediate state that is at or near resonance with the laser frequencies has been used in past experiments and calculations. Here we replace this intermediate state by a continuum of intermediate states. An analytic solution of a simple model suggests that the continuum can be used in such an excitation scheme, provided that the laser pulses are arranged in the so-called counter intuitive order. %'e use a special case of this solution to relate this work …

Coherent Population Transfer Via The Continuum, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

We present a remarkable analytic result which suggests that a continuum can be used as an intermediary for a significant transfer of population from one discrete state to another discrete state in a stimulated Raman transition. the population transfer is accomplished by employing two laser pulses that overlap in time, arranged in the so-called counterintuitive order. That a continuum can be used for population transfer is shown here for the first time. It promises to open up more channels for selective coherent excitation of atoms or molecules.

Analytic Solutions For Three-State Systems With Overlapping Pulses, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

Two classes of analytic solutions for three-state systems involving two overlapping laser pulses of different shapes, or of similar shapes but with their centers displaced, are presented. We find a remarkable connection between the order of arrival of the two overlapping pulses and the effectiveness of transfer from the ground state to the third state, and we find remarkable results for the maximum occupation probability of the intermediate state. The approach of these analytic solutions to the adiabatic-following process is also demonstrated.

Analytic Solution Of The Two-State Problem, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

An exact solution of the time-dependent Schrodinger equation is obtained for a simple model with only two quantum states. The calculated transition probability involves only exponential and hyperbolic functions.

Adiabatic Population Transfer In A Three-Level System Driven By Delayed Laser Pulses, J. R. Kuklinski, U. Gaubatz, Foek T. Hioe, K Bergmann

Physics Faculty/Staff Publications

We give a simple analytic solution that describes a novel method for population transfer in a three-level system driven by delayed pulses and which accounts for recent experimental results. This solution describes a procedure that is counter intuitive, and yet it is shown to be, in fact, one of the simplest solutions for multilevel systems arising from the adiabatic theorem. Its possible application to many-level systems is suggested.

Lossless Propagation Of Optical Pulses Through N-Level Systems With Gell-Mann Symmetry, Foek T. Hioe

Physics Faculty/Staff Publications

Propagation of optical pulses through atomic media consisting of atoms with N transition levels and possessing the so-called Gell-Mann symmetry is studied. An analytic solution of the appropriate Maxwell-Bloch equations having the form of simultaneous different wavelength optical solutions is presented. The special case of N = 3 was known previously.

Certain Stability Type And Integrable Two-Dimensional Hamiltonian Systems, Foek T. Hioe

Physics Faculty/Staff Publications

We present the results of applying an analytical method, using a new concept involving a periodic stability around a line of initial values, to two Hamiltonian systems with two degrees of freedom each with several parameters. By requiring the systems to have this type of stability, we have been led to known integrable cases for the systems. For one of the systems, our analysis gives six other cases, two of which turn out to be nonintegrable. The status of the remaining four cases has not been established.

Lossless Propagation Of Optical Pulses Through N-Level Systems With Su(2) Symmetry, Foek T. Hioe

Physics Faculty/Staff Publications

Propagation of optical pulses through atomic media consisting of atoms with N transition levels and possessing the so-called SU(2) symmetry is studied. It is shown that there are generally N - 1 sets of conditions, each of which, when satisfied, would permit the appropriate Maxwell-Bloch equations to have a solution having the form of simultaneous different-wavelength optical solutions, so-called simulations. The first two sets of solutions were known previously, but the remaining sets are new.

Erratum: Micellar-Shape Anisometry Near Isotropic–Liquid-Crystal Phase Transitions, Foek T. Hioe

Physics Faculty/Staff Publications

In lieu of an abstract, below is the first paragraph:

In our paper the binary sodium dodecyl (lauryl) sulfate (SLS)–water system was investigated by small-angle x-ray scattering in the isotropic (I) phase up to the I-hexagonal (H_a) transition and the ternary system (with decanol added to a binary system containing 26 wt% of SLS in water) up to what was considered to be an I-nematic cylindrical (N_c) phase transition. Our paper did not focus on the phase diagram of the studied system but rather on the detailed modeling of the …

Three-State Systems Driven By Resonant Optical Pulses Of Different Shapes, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

New analytic solutions to the problem of a three-state system driven simultaneously by resonant optical pulses of different shapes are presented. The solutions are useful for prescribing the conditions for complete population transfer from one state to another or for complete population return.

Coherent Population Trapping In N-Level Quantum Systems, Foek T. Hioe, C. E. Carroll

Physics Faculty/Staff Publications

A multilevel quantum system interacting with an intense laser Seld is shown to exhibit many invariants, or constants of evolution, under various conditions. Our results also apply to other similar physical problems.

N-Level Quantum Systems With Gell-Mann Dynamic Symmetry, Foek T. Hioe

Physics Faculty/Staff Publications

A set of conditions is presented for an N-level quantum system to possess the Gell-Mann-type dynamic symmetry, which was introduced in an earlier paper. The characteristic set of constants of motion that the system has when it possesses the symmetry and also the equivalent two-level system, which the system can be reduced to, are also presented.

Driven 3-State Model And Its Analytic Solutions, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

For an atom or molecule in which two transitions are driven by laser beams, a three‐state model is used. Transitions among the three states are caused only by the oscillating electric fields of the laser beams. The amplitudes and detunings of the two laser beams, which are various functions of the time, appear in the Schrödinger equation for the atom or molecule. In certain cases, the Schrödinger equation can be solved analytically, to find transition probabilities and the probability of no transition. This is done by using Clausen’s special function, or by assuming that the sum of the two detunings …

N-Level Quantum Systems With Su(2) Dynamic Symmetry, Foek T. Hioe

Physics Faculty/Staff Publications

We present an analytic solution of the coherent evolution of a laser-driven N-level quantum system that possesses an SU(2) dynamic symmetry.

Three-State Model Driven By Two Laser Beams, C. E. Carroll, Foek T. Hioe

Physics Faculty/Staff Publications

We use a three-state model for an atom or molecule in which two transitions are simultaneously driven by the oscillating electric fields of two laser beams. The amplitudes and detunings of the applied oscillating fields vary during the optical pulse, which can cause transitions from one state to another. For some special cases not previously known, the transition probabilities and probabilities of no transition are obtained analytically. We give conditions for complete transfer of the atomic population from one state to another, and for complete return to the initial state.

Stability-Instability Transitions In Hamiltonian Systems Of N Dimensions, Foek T. Hioe, Z Deng

Physics Faculty/Staff Publications

We show analytically that for a class of simple periodic motions in a general Hamiltonian system of n dimensions, if C is a parameter of the system and Cz one of its generally many critical values at which the motion undergoes a stability-instability transition, the behavior of the largest Lyapunov exponent p as C approaches Ce from the unstable region is given by µ, =constX |~ C—C_p |^β where β= 1/2, independent of the transition point, type of transitions, or the dimensionality of the system. We present numerical results for a three-dimensional Harniltonian system which exhibits three types …