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

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

Algorithms for Spectral Analysis of Irregularly Sampled Time Series

In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

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

Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates

We theoretically analyze a Mach-Zehnder interferometer with trapped condensates, and find that it is surprisingly stable against the nonlinearity induced by inter-particle interactions. The phase sensitivity, which we study for number squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or Maximum-Likelihood phase estimation strategy is used. We finally demonstrate robustness of the Mach-Zehnder interferometer in presence of interactions against condensate oscillations and a realistic atom counting error.Comment: 4 pages, 5 figures, minor revision

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

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

Increased Expression of Cell-Cell Signaling Genes by Stimulated Mononuclear Leukocytes in Patients with Previous Atherothrombotic Stroke A Whole Genome Expression Profile Study

Background/Aims: Inflammation plays an important role in atherosclerosis and stroke. Acute infections are recognized as trigger factors for ischemic stroke. Methods: In this whole genome expression profile study of 15 patients and 15 control subjects, we tested the hypothesis that patients with a history of atherothrombotic stroke show enhanced transcription of inflammatory genes in circulating leukocytes. RNA from unstimulated or lipopolysaccharide (LPS)-stimulated peripheral blood mononuclear cells (PBMCs) was analyzed with Affymetrix U133A GeneChips using a pooling design. Expression of single genes and functional groups of genes was analyzed by global statistical tests. Results: A total of 10,197 probe sets showed positive calls. After correction for multiple testing no single probe set revealed significant differences either without or with LPS stimulation. However, significant global expression differences were found upon LPS stimulation for the group of genes that are involved in cell-cell signaling. Conclusion: LPS stimulation of PBMCs, a condition mimicking bacterial infection, induces differential expression of a group of cell-cell signaling genes in patients with previous atherothrombotic stroke. This finding can be caused by genetic differences between both groups, but acquired risk factors, medication and technical factors may also have contributed to the result. Copyright (C) 2009 S. Karger AG, Base

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