Search results for "Formula"
showing 10 items of 755 documents
AC-Stark shift and photoionization of Rydberg atoms in an optical dipole trap
2010
We have measured the AC-Stark shift of the $14D_{5/2}$ Rydberg state of rubidium 87 in an optical dipole trap formed by a focussed CO$_2$-laser. We find good quantitative agreement with the model of a free electron experiencing a ponderomotive potential in the light field. In order to reproduce the observed spectra we take into account the broadening of the Rydberg state due to photoionization. The extracted cross-section is compatible with previous measurements on neighboring Rydberg states.
Unsteady turbulence in plane channel flow
2011
Abstract Direct numerical simulations were conducted for oscillating flow with zero time mean (reciprocating flow) in a plane channel subject to a harmonic forcing term of varying amplitude and frequency. The results confirmed the existence of four flow regimes (laminar, “disturbed laminar”, intermittently turbulent, and fully turbulent) depending on the above parameters. The flow behaviour was found to depend on the complex interplay of mean and turbulence quantities, as described by the closed loop formed by the streamwise Reynolds-averaged momentum equation in conjunction with the exact transport equations for the turbulent (Reynolds) stresses. A crucial role in this loop appeared to be …
Regularized Euler-alpha motion of an infinite array of vortex sheets
2016
We consider the Euler- $$\alpha $$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.
Rydberg Series Excitation of a Single Trapped Ca+40 Ion for Precision Measurements and Principal Quantum Number Scalings
2021
A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $n{S}_{1/2}$ states with $38\ensuremath{\le}n\ensuremath{\le}65$ and for $n{D}_{5/2}$ states with $37\ensuremath{\le}n\ensuremath{\le}50$ on a single trapped $^{40}{\mathrm{Ca}}^{+}$ ion. We determined the ionization energy of 2 870 575.582(15) GHz, 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of ${\ensuremath{\delta}}_{{S}_{1/2}}=1.802\text{ }995(5)$ and ${\ensuremath{\delta}}_{{D}_{5/2}}=0.626\text{ }888(9)$ for $n{S}_…
Improved test of time dilation in special relativity.
2003
An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in 7 Li + ions at v = 0.064c have been measured in the forward and backward direction to an accuracy of Δν/ν = 1 × 10 - 9 using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of 2.2 × 10 - 7 for deviations from the time dilation factor γ S R = (1 - ν 2 /c 2 ) - 1 / 2 .
A semiconductor laser system for the production of antihydrogen
2012
Laser-controlled charge exchange is a promising method for producing cold antihydrogen. Caesium atoms in Rydberg states collide with positrons and create positronium. These positronium atoms then interact with antiprotons, forming antihydrogen. Las er excitation of the caesium atoms is essential to increase the cross section of the charge-exchange collisions. This method was demonstrated in 2004 by the ATRAP collaboration by using an available copper vapour laser. For a second generation of charge-e xchange experiments we have designed a new semiconductor laser system that features several improvements compared to the copper vapour laser. We describe this new laser system and show the resul…
Simplicial Wheeler-DeWitt equation in 2+1 spacetime dimensions.
1993
We introduce an equation which rue suggest to be a simplicial counterpart to the Wheeler-DeWitt equation in 2 + 1 spacetime dimensions. Our approach is based on the use of the Ashtekar variables
A simple microsuperspace model in 2 + 1 spacetime dimensions
1992
Abstract We quantize the closed Friedmann model in 2 + 1 spacetime dimensions using euclidean path-integral approach and a simple microsuperspace model. A relationship between integration measure and operator ordering in the Wheeler-DeWitt equation is found within our model. Solutions to the Wheeler-DeWitt equation are exactly reproduced from the path integral using suitable integration contours in the complex plane.
New methods for approximating general relativity in numerical simulations of stellar core collapse
2006
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented. Such an effective relativistic potential can be used in an otherwise standard Newtonian hydrodynamic code. An alternative approximation of general relativity is the assumption of conformal flatness for the three-metric, and its extension by adding second post-Newtonian order terms. Using a code which evolves the coupled system of metric and fluid equations, we apply the various approximation methods to numerically simulate axisymmetric models for the col…
CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations
2004
Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity have been done using approximations of the Einstein field equations. As recently shown by Dimmelmeier et al (2002a,b), one of the most interesting such approximation is the so-called conformal flatness condition (CFC) of Isenberg, Wilson and Mathews. Building on this previous work we present here new results from numerical simulations of relativistic rotational core collapse in axisymmetry, aiming at improving the dynamics and the gravitational waveforms. The computer code used for these simulations evolves th…