Quantum fluctuations of a vortex in an optical lattice

Using a variational ansatz for the wave function of the Bose-Einstein condensate, we develop a quantum theory of vortices and quadrupole modes in a one-dimensional optical lattice. We study the coupling between the quadrupole modes and Kelvin modes, which turns out to be formally analogous to the theory of parametric processes in quantum optics. This leads to the possibility of squeezing vortices. We solve the quantum multimode problem for the Kelvin modes and quadrupole modes numerically and find properties that cannot be explained with a simple linear-response theory.Comment: final version, minor change

Quantum theory of a vortex line in an optical lattice

We investigate the quantum theory of a vortex line in a stack of weakly-coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin modes and the quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.Comment: Minor changes in response to a referee repor

Socioeconomic Inequalities in Mortality Rates in Old Age in the World Health Organization Europe Region

Socioeconomic adversity is among the foremost fundamental causes of human suffering, and this is no less true in old age. Recent reports on socioeconomic inequalities in mortality rate in old age suggest that a low socioeconomic position continues to increase the risk of death even among the oldest old. We aimed to examine the evidence for socioeconomic mortality rate inequalities in old age, including information about associations with various indicators of socioeconomic position and for various geographic locations within the World Health Organization Region for Europe. The articles included in this review leave no doubt that inequalities in mortality rate by socioeconomic position persist into the oldest ages for both men and women in all countries for which information is available, although the relative risk measures observed were rarely higher than 2.00. Still, the available evidence base is heavily biased geographically, inasmuch as it is based largely on national studies from Nordic and Western European countries and local studies from urban areas in Southern Europe. This bias will hamper the design of European-wide policies to reduce inequalities in mortality rate. We call for a continuous update of the empiric evidence on socioeconomic inequalities in mortality rate

Health of singletons born after frozen embryo transfer until early adulthood : a Finnish register study

STUDY QUESTION Is the health of singletons born after frozen embryo transfer (FET) comparable to that of singletons born after fresh embryo transfer (ET) until early adulthood? SUMMARY ANSWER The health of singletons born after FET does not differ from that of singletons born after fresh ET. WHAT IS KNOWN ALREADY The differences in perinatal outcomes of children born after FET and fresh ET are well known. FET is associated with an increased risk of large-for-gestational-age but diminished risks of preterm birth (PTB), small-for-gestational-age and decreased perinatal mortality compared to fresh ET. However, knowledge on the long-term health after FET is scarce. STUDY DESIGN, SIZE, DURATION This retrospective register-based cohort study compares singletons born after FET (n = 1825) between the years 1995 and 2006 to those born after fresh ET (n = 2933) and natural conception (NC, n = 31 136) with a mean follow-up time of 18-20 years. PARTICIPANTS/MATERIALS, SETTING, METHODS Singletons born after FET were compared to those born after fresh ET and NC regarding the frequencies of diagnoses in the main ICD-10 chapters (International Statistical Classification of Diseases and Related Health Problems, 10th revision), the number of outpatient visits and hospital admissions, and mortality. Adjustments were made for PTB, maternal age, parity, socioeconomic status based on mother's occupation and offspring sex. The study combines data from the Finnish Medical Birth Register, the Finnish Care Register for Health Care (CRHC) and the Cause-of-Death Register at Statistics Finland. The Student's T-test was used for continuous variables, and the Chi-square test was used for categorical variables. Cox regression was used to estimate crude and adjusted hazard ratios (HRs and aHRs, respectively). A general linear model was used to compare the means of outpatient visits, hospital admissions and lengths of hospital stays per person. MAIN RESULTS AND THE ROLE OF CHANCE No significant differences between the FET and fresh ET groups were found in the frequency of diagnoses in any of the ICD-10 chapters or in the parameters describing the need for hospital care. However, compared to the NC group, higher proportions in the FET group had outpatient visits in the hospital (93.5% vs 92.2%, aHR 1.23, 95% CI 1.17, 1.30) or hospital admissions (48% vs 46.5%, aHR 1.28, 95% CI 1.19, 1.37). Compared to the NC group, the FET group had elevated adjusted risks of diagnoses of infectious and parasitic diseases (aHR 1.24; 95% CI 1.11, 1.38), neoplasms (aHR 1.68; 95% CI 1.48, 1.91), diseases of the eye and adnexa, the ear or mastoid process (aHR 1.11; 95% CI 1.01, 1.21), the respiratory system (aHR 1.15; 95% CI 1.06, 1.23), the digestive system (aHR 1.17; 95% CI 1.05, 1.32), the skin or subcutaneous tissue (aHR 1.28; 95% CI 1.14, 1.43) and the genitourinary system (aHR 1.27; 95% CI 1.11, 1.45), as well as congenital malformations or chromosomal abnormalities (aHR 1.31; 95% CI 1.14, 1.50) and symptoms, signs or abnormal clinical or laboratory findings (aHR 1.25, 95% CI 1.16, 1.34). LIMITATIONS, REASONS FOR CAUTION Only hospital-based inpatient and outpatient care is covered by the CRHC register, excluding milder cases diagnosed elsewhere. We were not able to study the effect of ART treatments and subfertility separately in our setting. In addition, although our cohort is reasonably sized, even larger cohorts would be needed to reliably study rare outcomes, such as cancer. WIDER IMPLICATIONS OF THE FINDINGS For many ICD-10 chapters, we present the first published data on the long-term outcome of singletons born after FET. The results on FET versus fresh ET are reassuring, whereas the results on FET versus NC warrant further investigation. STUDY FUNDING/COMPETING INTEREST(S) Finnish government research funding was obtained for this study. Funding was also obtained from the Finnish Medical Society Duodecim, the Paivikki and Sakari Sohlberg Foundation, Orion Research Foundation, Finnish Society of Obstetrics and Gynaecology (research grants to A.M.T.) and Finnish government research funding. The funding sources were not involved in the planning or execution of the study. The authors have no competing interests to declare.Peer reviewe

Bose-Einstein condensation in shallow traps

In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure

Theory of spin-2 Bose-Einstein condensates: spin-correlations, magnetic response, and excitation spectra

The ground states of Bose-Einstein condensates of spin-2 bosons are classified into three distinct (ferromagnetic, ^^ ^^ antiferromagnetic", and cyclic) phases depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the hermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied agnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ^^ ^^ pairs" undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ^^ ^^ trios" condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.Comment: 28 pages, 4 figure

Topological defects in spinor condensates

We investigate the structure of topological defects in the ground states of spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.Comment: 10 pages, 1 figure. Published versio

Flow and critical velocity of an imbalanced Fermi gas through an optical potential

Optical lattices offer the possibility to investigate the superfluid properties of both Bose condensates and Fermionic superfluid gases. When a population imbalance is present in a Fermi mixture, this leads to frustration of the pairing, and the superfluid properties will be affected. In this contribution, the influence of imbalance on the flow of a Fermi superfluid through an optical lattice is investigated. The flow through the lattice is analysed by taking into account coupling between neighbouring layers of the optical lattice up to second order in the interlayer tunneling amplitude for single atoms. The critical velocity of flow through the lattice is shown to decrease monotonically to zero as the imbalance is increased to 100%. Closed-form analytical expressions are given for the tunneling contribution to the action and for the critical velocity as a function of the binding energy of pairs in the (quasi) two-dimensional Fermi superfluid and as a function of the imbalance.Comment: 8 pages, 1 figure, contribution for the QFS 2007 conferenc