Phase Estimation from Atom Position Measurements

We study the measurement of the position of atoms as a means to estimate the relative phase between two Bose-Einstein condensates. First, we consider $N$ atoms released from a double-well trap, forming an interference pattern, and show that a simple least-squares fit to the density gives a shot-noise limited sensitivity. The shot-noise limit can instead be overcome by using correlation functions of order $\sqrt{N}$ or larger. The measurement of the $N\mathrm{th}$-order correlation function allows to estimate the relative phase at the Heisenberg limit. Phase estimation through the measurement of the center-of-mass of the interference pattern can also provide sub-shot-noise sensitivity. Finally, we study the effect of the overlap between the two clouds on the phase estimation, when Mach-Zehnder interferometry is performed in a double-well.Comment: 20 pages, 6 figure

A Study of School Costs in the Bryant Independent School District from 1949-1959

Good business practices have long been recognized for the public schools in South Dakota. It is necessary for efficient operation of school systems. The purpose of this study was to compare a local public school, Bryant Public School, with national, state and city norms as far as total school expenditures are concerned and in percentages with that of other schools. It was also important to determine what percent each character classification reveals itself. It was hoped that this would help for better budgeting procedures and give an overall view of school operations for the preceding ten year school period. The author also attempted to show what the trend of the operational costs are and to compare it with other schools and state norms. People have long been interested in school and where the tax dollar goes. It is with that purpose in mind that this study was made. This study revealed that the Bryant Public School was operating in line with national averages

Direct imaging Raman microscope based on tunable wavelength excitation and narrow band emission detection

A new type of imaging Raman microscope is described. First the advantages and disadvantages of the two possible approaches to Raman microscopy based on signal detection by means of a charge-coupled-device camera (i.e., direct imaging and image reconstruction) are discussed. Arguments are given to show that in most cases direct imaging is to be preferred over image reconstruction, because it provides the desired information in less time. In the direct imaging Raman microscope presented in this communication, detection of scattered light occurs in a narrow interval around a fixed wavelength. Selection of the Raman wavenumber shift at which an image is recorded is established by tuning the wavelength of the exciting laser light in such a way that the wavelength of the Raman scattered light with the desired Raman shift coincides with the detected wavelength. The microscope has been incorporated in a Raman microspectrometer in a way that enables easy switching between the imaging and the multichannel spectroscopy modes of operation. Bright field, fluorescence, and Raman microscopic images can be obtained

A Case of Primary Squamous Cell Carcinoma of the Liver Arising in a Solitary Cyst

A case of primary squamous cell carcinoma in a pre-existing hepatic cyst is presented. A review of the literature suggests that this rare type of liver tumor tends to arise from solitary, nonparasitic cysts, lined with squamous epithelium. Effective therapy is not available, the prognosis is grave

Application of Raman Microspectroscopic and Raman imaging techniques for cell biological studies

Raman spectroscopy is being used to study biological molecules for some three decades now. Thanks to continuing advances in instrumentation more and more applications have become feasible in which molecules are studied in situ, and this has enabled Raman spectroscopy to enter the realms of biomedicine and cell biology [1-5].\ud Here we will describe some of the recent work carried out in our laboratory, concerning studies of human white blood cells and further instrumentational developments

Detection superiority of 7 T MRI protocol in patients with epilepsy and suspected focal cortical dysplasia

In 11 adult patients with suspicion of Focal cortical dysplasia (FCD) on 1.5 T (n = 1) or 3 T (n = 10) magnetic resonance imaging (MRI), 7 T MRI was performed. Visibility, extent, morphological features and delineation were independently rated and subsequently discussed by three observers. Additionally, head-to-head comparisons with corresponding 3 T images were made in the eight patients with a previous 3 T MRI and sustained suspicion of FCD. Comparison with histopathology was done in the five patients that underwent surgery. All lesions, seen at 1.5 and 3 T, were also recognized on 7 T. At 7 T FLAIR highlighted the FCD-like lesions best, whereas T2 and T2* were deemed better suited to review structure and extent of the lesion. Image quality with the used 7 T MRI setup was higher than the quality with the used 3 T MRI setup. In 2 out of 11 patients diagnosis changed, in one after re-evaluation of the images, and in the other based on histopathology. With the used 7 T MRI setup, FCD-like lesions can be detected with more confidence and detail as compared to lower field strength. However, concordance between radiologic diagnosis and final diagnosis seems to be lower than expected

Mesangial function and glomerular sclerosis in rats after unilateral nephrectomy

Mesangial function and glomerular sclerosis in rats after unilateral nephrectomy. To investigate the possible relationship between disturbance of mesangial function and segmental localization of glomerular sclerosis, five uninephrectomized male Wistar rats and five sham-operated controls received colloidal carbon intravenously. At 4 months 8.4 ± 2.5% of the glomeruli of the nephrectomized rats showed focal sclerosis. Glomeruli of nephrectomized rats contained significantly more carbon than glomeruli of controls. Glomeruli with focal sclerosis contained significantly more carbon than normal glomeruli in the same kidneys with a preferential tracer localization within the lesions. In another experiment carbon injections were given before surgery. At 4 months 12.6 ± 4.1% of the glomeruli of the nephrectomized rats showed focal sclerosis, an incidence not significantly different from that of the first experiment. Glomerular carbon content was equal in experimental and control rats and no preferential localization of the tracer within the lesions was found. From these results we conclude that the preferential localization of carbon in the glomerular lesions in rats nephrectomized before injection of carbon is caused by the increased delivery of tracer shortly after injection to those glomerular areas where sclerosis will develop at a later time. The development of focal sclerosis may be related to the local deposition of harmful substances from the circulation.Fonctionnement mésangial et sclérose glomérulaire chez des rats après néphrectomie unilatérale. Afin d'étudier une éventuelle relation entre des anomalies du fonctionnement mésangial et la localisation segmentaire de la sclérose glomérulaire, cinq rats mâles Wistar uninéphrectomisés et cinq contrôles ayant eu un simulacre d'intervention ont reçu du carbone colloïdal par voie intraveineuse. Au bout de 4 mois, 8,4 ± 2,5% des glomérules des rats néphrectomisés avaient une sclérose focale. Les glomérules des rats néphrectomisés contenaient significativement plus de carbone que les glomérules des contrôles. Les glomérules avec une sclérose focale contenaient significativement plus de carbone que les glomérules normaux des mêmes reins, avec une localisation préférentielle du traceur dans les lésions. Dans une autre expérience des injections de carbone ont été faites avant la chirurgie. Au bout de 4 mois, 12,6 ± 4,1% des glomérules des rats néphrectomisés avaient une sclérose focale, cette incidence n'étant pas significativement différente de celle observée au cours de la première expérience. Le contenu en carbone des glomérules était identique chez les rats expérimentaux et contrôles, et il n'a pas été trouvé de localisation préférentielle du traceur dans les lésions. De ces résultats, nous concluons que la localisation préférentielle du carbone dans les lésions glomérulaires de rats néphrectomisés avant une injection de carbone est dûe à une augmentation de l'afflux du traceur peu de temps après l'injection dans les aires glomérulaires où la sclérose se développera ultérieurement. Le développement d'une sclérose focale pourrait être relié au dépôt localisé de substances délétères provenant de la circulation

Atom interferometry with trapped Bose-Einstein condensates: Impact of atom-atom interactions

Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy $\Delta E^{\rm min}$ is on the order of 0.001 times the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary.Comment: 28 pages, 13 figures, extended and correcte

Optimal control of number squeezing in trapped Bose-Einstein condensates

We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.Comment: 17 pages, 21 figures, minor correction