Ansatz from Non-Linear Optics Applied to Trapped Bose-Einstein Condensates

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime.Comment: 4 pages, 3 figures, published versio

Pseudo Hermitian formulation of Black-Scholes equation

We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system

Variational study of a dilute Bose condensate in a harmonic trap

A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for $N_0$ condensed bosons in an isotropic harmonic trap with oscillator length $d_0$ and interacting through a repulsive two-body scattering length $a>0$. The dimensionless parameter ${\cal N}_0 \equiv N_0a/d_0$ characterizes the effect of the interparticle interactions, with ${\cal N}_0 \ll 1$ for an ideal gas and ${\cal N}_0 \gg 1$ for a strongly interacting system (the Thomas-Fermi limit). The trial function interpolates smoothly between these two limits, and the three separate contributions (kinetic energy, trap potential energy, and two-body interaction energy) to the variational condensate energy and the condensate chemical potential are determined parametrically for any value of ${\cal N}_0$, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly.Comment: 14 pages, RevTeX, submitted to Journal of Low Temperature Physic

Undulator A diagnostics at the Advanced Photon Source

Diagnostics of Undulator A{number_sign}2 (UA2) radiation was performed during the October 1997 mn at the Advanced Photon Source (APS). The UA2 undulator is a standard 3.3-cm-period APS Undulator A, which was positioned downstream from the center of the straight section at Sector 8. The diagnostics included the angular-spectral measurements of the undulator radiation to determine the undulator radiation absolute spectral flux and the particle beam divergence. The results of the absolute spectral flux measurements are compared to the undulator spectrum calculated from measured undulator magnetic field. The particle`s energy spread was determined from spectra comparison. Previously, the authors reported the first measurements made on Undulator A at the APS. The purpose of the present report is to summarize the results of the diagnostics performed on the Sector 8 undulator at the request of the IMM-CAT staff, and to present a more general discussion of undulator radiation sources at the APS and details of their diagnostics

NSLS-II X-Ray Diagnostics Development

NSLS-II x-ray diagnostics will provide continuous online data of electron beam dimensions, which will be used to derive electron beam emittance and energy spread. It will also provide information of electron beam tilt for coupling evaluation. X-ray diagnostics will be based on imaging of bending magnet and three-pole wiggler synchrotron radiation sources. Diagnostics from three-pole wiggler source will be used to derive particles energy spread. Beta and dispersion functions will have to be evaluated for emittance and particles energy spread calculations. Due to small vertical source sizes imaging need to be performed in x-ray energy range. X-ray optics with high numerical aperture, such as compound refractive lens, will be used to achieve required spatial resolution. Optical setups with different magnifications in horizontal and vertical directions fill be employed to deal with large aspect ratio of the source. X-ray diagnostics setup will include x-ray imaging optics, monochromatization, x-ray imaging and recording components

Observation of a red-blue detuning asymmetry in matter-wave superradiance

We report the first experimental observations of strong suppression of matter-wave superradiance using blue-detuned pump light and demonstrate a pump-laser detuning asymmetry in the collective atomic recoil motion. In contrast to all previous theoretical frameworks, which predict that the process should be symmetric with respect to the sign of the pump-laser detuning, we find that for condensates the symmetry is broken. With high condensate densities and red-detuned light, the familiar distinctive multi-order, matter-wave scattering pattern is clearly visible, whereas with blue-detuned light superradiance is strongly suppressed. In the limit of a dilute atomic gas, however, symmetry is restored.Comment: Accepted by Phys. Rev. Let

An Imaging System for Focusing Tests of Li Multiprism X‐ray Refractive Lenses

For rapid and efficient tests of novel X‐rays optics, such as lithium‐based compound refractive lenses, we have built a fast X‐ray sensitive CCD imaging system. We report on the linearity, response and resolution of the microscope‐based imaging system. For the low magnifications used here (X2‐X10), we find that a thinly doped YAG screen has a poorer resolution than a thick YAG screen. We provide an example of its use in testing a new 2D focusing multiprism X‐ray lens. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87661/2/780_1.pd

X-ray microdiffraction studies of an integrated laser-modulator system

The authors report the use of a spatially resolved x-ray microdiffraction technique for the structural study of an integrated laser-modulator system. The monochromatic (11 keV) x-ray beam microfocused to less than 1 {micro}m in the vertical direction was obtained using a phase zone plate. The photon flux at the focal spot exceeded 3 {times} 10{sup 10} photons/s/0.01% bw/{micro}m{sup 2}. The intense flux density and high spatial resolution of the focused beam was used to study the structure of a laser-modulator system, which is a 1-{micro}m-wide and 1-mm-long multi-quantum well structure on an InP substrate. The superlattice d-spacing and the strain field in the direction normal to the diffracting planes were mapped as a function of position along the length of the device

Some practical aspects of undulator radiation properties

It is important to be able to accurately predict the spectral and angular distribution of undulator radiation properties when designing beamlines; at new synchrotron radiation facilities or when performing radiation experiments at already existing beamlines. In practice, the particle beam emittance and beam energy spread must be taken into account in modeling these properties. The undulators fabricated today are made with small RMS phase errors, making them perform almost as, ideal devices. Calculation tools for numerical modeling of undulator radiation sources (ideal and nonideal) will be discussed, and the excellent agreement with experimentally obtained absolute spectral flux measurements of undulator A at the Advanced Photon Source verifies the high accuracy of the computer codes and the high quality of the undulators being built today. Our focus here is on flux properties useful in practical beamline designs, and the chosen examples demonstrate the versatility of computer programs available to beamline designers and experimentalists