Stability, effective dimensions, and interactions for bosons in deformed fields

The hyperspherical adiabatic method is used to derive stability criteria for Bose-Einstein condensates in deformed external fields. An analytical approximation is obtained. For constant volume the highest stability is found for spherical traps. Analytical approximations to the stability criterion with and without zero point motion are derived. Extreme geometries of the field effectively confine the system to dimensions lower than three. As a function of deformation we compute the dimension to vary continuously between one and three. We derive a dimension-dependent effective radial Hamiltonian and investigate one choice of an effective interaction in the deformed case.Comment: 7 pages, 5 figures, submitted to Phys. Rev. A. In version 2 figures 2 and 5 are added along with more discussions and explanations. Version 3 contains added comments and reference

Condensates and correlated boson systems

We study two-body correlations in a many-boson system with a hyperspherical approach, where we can use arbitrary scattering length and include two-body bound states. As a special application we look on Bose-Einstein condensation and calculate the stability criterium in a comparison with the experimental criterium and the theoretical criterium from the Gross-Pitaevskii equation.Comment: 6 pages, 4 figures. Contribution to Workshop on Critical Stability III in Trento. Submitted to Few-Body System

Stability and structure of two coupled boson systems in an external field

The lowest adiabatic potential expressed in hyperspherical coordinates is estimated for two boson systems in an external harmonic trap. Corresponding conditions for stability are investigated and the related structures are extracted for zero-range interactions. Strong repulsion between non-identical particles leads to two new features, respectively when identical particles attract or repel each other. For repulsion new stable structures arise with displaced center of masses. For attraction the mean-field stability region is restricted due to motion of the center of masses

Effective Hamiltonian Theory and Its Applications in Quantum Information

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.Comment: 5 pages, 3 figures, to be published in Canadian Journal of Physic

The primordial deuterium abundance at z = 2.504 from a high signal-to-noise spectrum of Q1009+2956

The spectrum of the $z_{\rm em} = 2.63$ quasar Q1009+2956 has been observed extensively on the Keck telescope. The Lyman limit absorption system $z_{\rm abs} = 2.504$ was previously used to measure D/H by Burles & Tytler using a spectrum with signal to noise approximately 60 per pixel in the continuum near Ly {\alpha} at $z_{\rm abs} = 2.504$. The larger dataset now available combines to form an exceptionally high signal to noise spectrum, around 147 per pixel. Several heavy element absorption lines are detected in this LLS, providing strong constraints on the kinematic structure. We explore a suite of absorption system models and find that the deuterium feature is likely to be contaminated by weak interloping Ly {\alpha} absorption from a low column density H I cloud, reducing the expected D/H precision. We find D/H = $2.48^{+0.41}_{-0.35}\times10^{-5}$ for this system. Combining this new measurement with others from the literature and applying the method of Least Trimmed Squares to a statistical sample of 15 D/H measurements results in a "reliable" sample of 13 values. This sample yields a primordial deuterium abundance of (D/H)$_{\rm p} = (2.545 \pm 0.025)\times10^{-5}$. The corresponding mean baryonic density of the Universe is $\Omega_{\rm b}h^2 = 0.02174\pm0.00025$. The quasar absorption data is of the same precision as, and marginally inconsistent with, the 2015 CMB Planck (TT+lowP+lensing) measurement, $\Omega_{\rm b}h^2 = 0.02226\pm0.00023$. Further quasar and more precise nuclear data are required to establish whether this is a random fluctuation.Comment: accepted by MNRAS, 18 pages, 12 figures, 6 table