Bogoliubov theory for atom scattering into separate regions

We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein Condensate into two well-separated regions. We find the full dynamics of the pair-production process, calculate the first and second order correlation functions and show that the system is ideally number-squeezed. We calculate the Fisher information to show how the entanglement between the atoms from the two regions changes in time. We also provide a simple expression for the lower bound of the useful entanglement in the system in terms of the average number of scattered atoms and the number of modes they occupy. We then apply our theory to a recent "twin-beam" experiment [R. B\"ucker {\it et al.}, Nat. Phys. {\bf 7}, 608 (2011)]. The only numerical step of our semi-analytical description can be easily solved and does not require implementation of any stochastic methods.Comment: 11 pages, 6 figure

Serial Electron Diffraction Data Processing With diffractem and CrystFEL

Serial electron diffraction (SerialED) is an emerging technique, which applies the snapshot data-collection mode of serial X-ray crystallography to three-dimensional electron diffraction (3D Electron Diffraction), forgoing the conventional rotation method. Similarly to serial X-ray crystallography, this approach leads to almost complete absence of radiation damage effects even for the most sensitive samples, and allows for a high level of automation. However, SerialED also necessitates new techniques of data processing, which combine existing pipelines for rotation electron diffraction and serial X-ray crystallography with some more particular solutions for challenges arising in SerialED specifically. Here, we introduce our analysis pipeline for SerialED data, and its implementation using the CrystFEL and diffractem program packages. Detailed examples are provided in extensive supplementary code

Imaging a single atom in a time-of-flight experiment

We perform fluorescence imaging of a single 87Rb atom after its release from an optical dipole trap. The time-of-flight expansion of the atomic spatial density distribution is observed by accumulating many single atom images. The position of the atom is revealed with a spatial resolution close to 1 micrometer by a single photon event, induced by a short resonant probe. The expansion yields a measure of the temperature of a single atom, which is in very good agreement with the value obtained by an independent measurement based on a release-and-recapture method. The analysis presented in this paper provides a way of calibrating an imaging system useful for experimental studies involving a few atoms confined in a dipole trap.Comment: 14 pages, 8 figure

Two-point density correlations of quasicondensates in free expansion

We measure the two-point density correlation function of freely expanding quasicondensates in the weakly interacting quasi-one-dimensional (1D) regime. While initially suppressed in the trap, density fluctuations emerge gradually during expansion as a result of initial phase fluctuations present in the trapped quasicondensate. Asymptotically, they are governed by the thermal coherence length of the system. Our measurements take place in an intermediate regime where density correlations are related to near-field diffraction effects and anomalous correlations play an important role. Comparison with a recent theoretical approach described by Imambekov et al. yields good agreement with our experimental results and shows that density correlations can be used for thermometry of quasicondensates.Comment: 4 pages, 4 figures, minor change

The effect of secondary electrons on radiolysis as observed by in liquid TEM: The role of window material and electrical bias

The effect of window material on electron beam induced phenomena in liquid phase electron microscopy (LPEM) is an interesting yet under-explored subject. We have studied the differences of electron beam induced gold nanoparticle (AuNP) growth subject to three encapsulation materials: Silicon Nitride (Si3N4), carbon and formvar. We find Si3N4 liquid cells (LCs) to result in significantly higher AuNP growth yield as compared to LCs employing the other two materials. In all cases, an electrical bias of the entire LC structures significantly affected particle growth. We demonstrate an inverse correlation of the AuNP growth rate with secondary electron (SE) emission from the windows. We attribute these differences at least in part to variations in SE emission dynamics, which is seen as a combination of material and bias dependent SE escape flux (SEEF) and SE return flux (SERF). Furthermore, our model predictions qualitatively match electrochemistry expectations

Two-point phase correlations of a one-dimensional bosonic Josephson junction

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows to measure the coupling strength and temperature and hence a full characterization of the system

Tomographic reconstruction of the Wigner function on the Bloch sphere

We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern-Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix in that it is insensitive to experimental fluctuations in j, and allows for a natural elimination of high-frequency noise in the Wigner function by taking into account the experimental uncertainties in the determination of j, its projection m, and the quantization axis orientation. No data binning and no arbitrary smoothing parameters are necessary in this reconstruction. Using recently published data [Riedel et al., Nature 464:1170 (2010)] we reconstruct the Wigner function of a spin-squeezed state of a Bose-Einstein condensate of about 1250 atoms, demonstrating that measurements along quantization axes lying in a single plane are sufficient for performing this tomographic reconstruction. Our method does not guarantee positivity of the reconstructed density matrix in the presence of experimental noise, which is a general limitation of backprojection algorithms.Comment: 16 pages, 6 figures; minor modification