Exploiting soliton decay and phase fluctuations in atom chip interferometry of Bose-Einstein condensates

We show that the decay of a soliton into vortices provides a mechanism for measuring the initial phase difference between two merging Bose-Einstein condensates. At very low temperatures, the mechanism is resonant, operating only when the clouds start in anti-phase. But at higher temperatures, phase fluctuations trigger vortex production over a wide range of initial relative phase, as observed in recent experiments at MIT. Choosing the merge time to maximize the number of vortices created makes the interferometer highly sensitive to spatially varying phase patterns and hence atomic movement.Comment: 5 pages, 5 figure

Implications of non-feasible transformations among icosahedral hh orbitals

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5) \supset S_6 \supset S_5 \supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ that rotates the weight space of SO(5) by $\pi/2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figur

Quantifying Finite Temperature Effects in Atom Chip Interferometry of Bose-Einstein Condensates

We quantify the effect of phase fluctuations on atom chip interferometry of Bose-Einstein condensates. At very low temperatures, we observe small phase fluctuations, created by mean-field depletion, and a resonant production of vortices when the two clouds are initially in anti-phase. At higher temperatures, we show that the thermal occupation of Bogoliubov modes makes vortex production vary smoothly with the initial relative phase difference between the two atom clouds. We also propose a technique to observe vortex formation directly by creating a weak link between the two clouds. The position and direction of circulation of the vortices is subsequently revealed by kinks in the interference fringes produced when the two clouds expand into one another. This procedure may be exploited for precise force measurement or motion detection.Comment: 7 pages, 5 figure

Quantum reflection of ultracold atoms from thin films, graphene, and semiconductor heterostructures

We show that thin dielectric films can be used to enhance the performance of passive atomic mirrors by enabling quantum reflection probabilities of over 90% for atoms incident at velocities ~1 mm/s, achieved in recent experiments. This enhancement is brought about by weakening the Casimir-Polder attraction between the atom and the surface, which induces the quantum reflection. We show that suspended graphene membranes also produce higher quantum reflection probabilities than bulk matter. Temporal changes in the electrical resistance of such membranes, produced as atoms stick to the surface, can be used to monitor the reflection process, non-invasively and in real time. The resistance change allows the reflection probability to be determined purely from electrical measurements without needing to image the reflected atom cloud optically. Finally, we show how perfect atom mirrors may be manufactured from semiconductor heterostructures, which employ an embedded two-dimensional electron gas to tailor the atom-surface interaction and so enhance the reflection by classical means.Comment: 8 pages, 4 figure

An efficient approach for spin-angular integrations in atomic structure calculations

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to calculate graphically the irreducible tensorial products of the second quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to find graphically the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second quantization operators. As a result, it allows us to use standard quantities uniformly for both diagona and off-diagonal matrix elements

Dietary patterns are associated with cognitive function in the REasons for Geographic And Racial Differences in Stroke (REGARDS) cohort.

Identifying factors that contribute to the preservation of cognitive function is imperative to maintaining quality of life in advanced years. Of modifiable risk factors, diet quality has emerged as a promising candidate to make an impact on cognition. The objective of this study was to evaluate associations between empirically derived dietary patterns and cognitive function. This study included 18 080 black and white participants aged 45 years and older from the REasons for Geographic And Racial Differences in Stroke (REGARDS) cohort. Principal component analysis on data from the Block98 FFQ yielded five dietary patterns: convenience, plant-based, sweets/fats, Southern, and alcohol/salads. Incident cognitive impairment was defined as shifting from intact cognitive status (score >4) at first assessment to impaired cognitive status (score ≤4) at latest assessment, measured by the Six-Item Screener. Learning, memory and executive function were evaluated with the Word List Learning, Word List Delayed Recall, and animal fluency assessments. In fully adjusted models, greater consumption of the alcohol/salads pattern was associated with lower odds of incident cognitive impairment (highest quintile (Q5) v. lowest quintile (Q1): OR 0·68; 95 % CI 0·56, 0·84; P for trend 0·0005). Greater consumption of the alcohol/salads pattern was associated with higher scores on all domain-specific assessments and greater consumption of the plant-based pattern was associated with higher scores in learning and memory. Greater consumption of the Southern pattern was associated with lower scores on each domain-specific assessment (all P < 0·05). In conclusion, dietary patterns including plant-based foods and alcohol intake were associated with higher cognitive scores, and a pattern including fried food and processed meat typical of a Southern diet was associated with lower scores

Characterization of anomalous Zeeman patterns in complex atomic spectra

The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the sigma and pi profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Land\'{e} factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past. Finally, a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed. It relies on our recently published recursive technique for the numbering of LS-terms of an arbitrary configuration.Comment: submitted to Physical Review

Two-Center Integrals for r_{ij}^{n} Polynomial Correlated Wave Functions

All integrals needed to evaluate the correlated wave functions with polynomial terms of inter-electronic distance are included. For this form of the wave function, the integrals needed can be expressed as a product of integrals involving at most four electrons

Zone-plate focusing of Bose-Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components

We show that Fresnel zone plates, fabricated in a solid surface, can sharply focus atomic Bose-Einstein condensates that quantum reflect from the surface or pass through the etched holes. The focusing process compresses the condensate by orders of magnitude despite inter-atomic repulsion. Crucially, the focusing dynamics are insensitive to quantum fluctuations of the atom cloud and largely preserve the condensates' coherence, suggesting applications in passive atom-optical elements, for example zone plate lenses that focus atomic matter waves and light at the same point to strengthen their interaction. We explore transmission zone-plate focusing of alkali atoms as a route to erasable and scalable lithography of quantum electronic components in two-dimensional electron gases embedded in semiconductor nanostructures. To do this, we calculate the density profile of a two-dimensional electron gas immediately below a patch of alkali atoms deposited on the surface of the nanostructure by zone-plate focusing. Our results reveal that surface-induced polarization of only a few thousand adsorbed atoms can locally deplete the electron gas. We show that, as a result, the focused deposition of alkali atoms by existing zone plates can create quantum electronic components on the 50 nm scale, comparable to that attainable by ion beam implantation but with minimal damage to either the nanostructure or electron gas.Comment: 13 pages, 7 figure

Sickle cell trait and risk of cognitive impairment in African-Americans: The REGARDS cohort

Background: Sickle cell anemia may be associated with cognitive dysfunction, and some complications of sickle cell anemia might affect those with sickle cell trait (SCT), so we hypothesized that SCT is a risk factor for cognitive impairment. Methods: The Reasons for Geographic and Racial Differences in Stroke (REGARDS) study enrolled a national cohort of 30,239 white and black Americans from 2003 to 7, who are followed every 6 months. Baseline and annual global cognitive function testing used the Six-Item Screener (SIS), a validated instrument (scores range 0-6; ≤ 4 indicates cognitive impairment). Participants with baseline cognitive impairment and whites were excluded. Logistic regression was used to calculate the association of SCT with incident cognitive impairment, adjusted for risk factors. Linear mixed models assessed multivariable-adjusted change in test scores on a biennially administered 3-test battery measuring learning, memory, and semantic and phonemic fluency. Findings: Among 7743 participants followed for a median of 7·1 years, 85 of 583 participants with SCT (14·6%) developed incident cognitive impairment compared to 902 of 7160 (12·6%) without SCT. In univariate analysis, the odds ratio (OR) of incident cognitive impairment was 1·18 (95% CI: 0·93, 1·51) for those with SCT vs. those without. Adjustment did not impact the OR. There was no difference in change on 3-test battery scores by SCT status (all p > 0·11). Interpretation: In this prospective cohort study of black Americans, SCT was not associated with incident cognitive impairment or decline in test scores of learning, memory and executive function. Funding: National Institutes of Health, American Society of Hematology