Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is investigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Macroscopic quantum tunneling and resonances in coupled Bose-Einstein condensates with oscillating atomic scattering length

We study the macroscopic quantum tunneling, self-trapping phenomena in two weakly coupled Bose-Einstein condensates with periodically time-varying atomic scattering length.The resonances in the oscillations of the atomic populations are investigated. We consider oscillations in the cases of macroscopic quantum tunneling and the self-trapping regimes. The existence of chaotic oscillations in the relative atomic population due to overlaps between nonlinear resonances is showed. We derive the whisker-type map for the problem and obtain the estimate for the critical amplitude of modulations leading to chaos. The diffusion coefficient for motion in the stochastic layer near separatrix is calculated. The analysis of the oscillations in the rapidly varying case shows the possibility of stabilization of the unstable pi-mode regime. (C) 2000 Published by Elsevier B.V. B.V. PACS: 03.75.Fi; 05.30.Jp.

Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length

We investigate dynamical effects of a bright soliton in Bose-Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross-Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.

Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length

Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation, we study the oscillation of the Bose-Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a. When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC.

Dipolar Bose-Einstein condensates with large scattering length

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

A study was conducted on the dynamics of 2D and 3D Bose-Einstein condensates in the case when the scattering length in the Gross-Pitaevskii (GP) equation which contains constant (dc) and time-variable (ac) parts. Using the variational approximation (VA), simulating the GP equation directly, and applying the averaging procedure to the GP equation without the use of the VA, it was demonstrated that the ac component of the nonlinearity makes it possible to maintain the condensate in a stable self-confined state without external traps.

Variational calculation of positronium-helium-atom scattering length

A basis-set calculation scheme for S-waves Ps-He elastic scattering below the lowest inelastic threshold was formulated using a variational expression for the transition matrix. The scheme was illustrated numerically by calculating the scattering length in the electronic doublet state: a=1.0±0.1 a.u.

Microcontroller based double beam modulation system for atomic scattering experiments

Double beam modulation is widely used in atomic collision experiments in the case where the noise arising froth each of the beams exceeds the measured signal. A method for minimizing the statistical uncertainty in a measured signal in a given time period is discussed, and a flexible modulation and counting system based on a low cost PIC microcontroller is described. This device is capable of modifying the acquisition parameters in real time during the course of an experimental run. It is shown that typical savings in data acquisition time of approximately 30% can be achieved using this optimized modulation scheme.

Positronium-positronium interaction: resonance, scattering length, and Bose-Einstein condensation

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin s(T) = 0) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively, and a binding of 0.43 eV of Ps(2). The scattering length for s(T) = 0 is 3.95 Angstrom and for s(T) = 2 is 0.83 Angstrom. The small s(T) = 2 scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Bose-Einstein condensates in 2D with time-periodic scattering length

We discuss two-dimensional Bose-Einstein Condensates (BEC) under time-periodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our results are based on a variational approximation, on direct averaging of the Gross-Pitaevskii equation and on numerical simulations.

Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

Bose-Einstein condensates with inhomogeneous scattering length in one and two dimensions

We report on investigations of the properties of bright solitons in Bose-Einstein condensates in the presence of point-like spatial inhomogeneities, in one and two dimensions. By considering an analytical variational approach and full numerical simulations, we describe such processes due to interactions between the soliton and the inhomogeneity as the trapping, reflection, and transmission of bright matter solitons. We also study the critical number of particles as a function of the magnitude of the impurity.

Measurement of the K + - pi + pi - e + - (-) v e form factors and of the pi pi scattering length a 0 0

The quark condensate is a fundamental free parameter of Chiral Perturbation Theory ($chi PT$), since it determines the relative size of the mass and momentum terms in the power expansion. In order to confirm or contradict the assumption of a large quark condensate, on which $chi PT$ is based, experimental tests are needed. In particular, the $S$-wave $pipi$ scattering lengths $a_0^0$ and $a_0^2$ can be predicted precisely within $chi PT$ as a function of this parameter and can be measured very cleanly in the decay $K^{pm} to pi^{+} pi^{-} e^{pm} stackrel{mbox{tiny(---)}}{nu_e}$ ($K_{e4}$). About one third of the data collected in 2003 and 2004 by the NA48/2 experiment were analysed and 342,859 $K_{e4}$ candidates were selected. The background contamination in the sample could be reduced down to 0.3% and it could be estimated directly from the data, by selecting events with the same signature as $K_{e4}$, but requiring for the electron the opposite charge with respect to the kaon, the so-called ``wrong sign'' events. This is a clean background sample, since the kaon decay with $Delta S=-Delta Q$, that would be the only source of signal, can only take place through two weak decays and is therefore strongly suppressed. The Cabibbo-Maksymowicz variables, used to describe the kinematics of the decay, were computed under the assumption of a fixed kaon momentum of 60 GeV/$c$ along the $z$ axis, so that the neutrino momentum could be obtained without ambiguity. The measurement of the form factors and of the $pipi$ scattering length $a_0^0$ was performed in a single step by comparing the five-dimensional distributions of data and MC in the kinematic variables. The MC distributions were corrected in order to properly take into account the trigger and selection efficiencies of the data and the background contamination. The following parameter values were obtained from a binned maximum likelihood fit, where $a_0^2$ was expressed as a function of $a_0^0$ according to the prediction of chiral perturbation theory: f'_s/f_s = 0.133+- 0.013(stat)+- 0.026(syst) f''_s/f_s = -0.041+- 0.013(stat)+- 0.020(syst) f_e/f_s = 0.221+- 0.051(stat)+- 0.105(syst) f'_e/f_s = -0.459+- 0.170(stat)+- 0.316(syst) tilde{f_p}/f_s = -0.112+- 0.013(stat)+- 0.023(syst) g_p/f_s = 0.892+- 0.012(stat)+- 0.025(syst) g'_p/f_s = 0.114+- 0.015(stat)+- 0.022(syst) h_p/f_s = -0.380+- 0.028(stat)+- 0.050(syst) a_0^0 = 0.246+- 0.009(stat)+- 0.012(syst)}+- 0.002(theor), where the statistical uncertainty only includes the effect of the data statistics and the theoretical uncertainty is due to the width of the allowed band for $a_0^2$.

First πK atom lifetime and πK scattering length measurements

The results of a search for hydrogen-like atoms consisting of π∓K±π∓K± mesons are presented. Evidence for πK atom production by 24 GeV/c protons from CERN PS interacting with a nickel target has been seen in terms of characteristic πK pairs from their breakup in the same target (178±49178±49) as well as in terms of produced πK atoms (653±42653±42). Using these results, the analysis yields a first value for the πK atom lifetime of View the MathML sourceτ=(2.5−1.8+3.0) fs and a first measurement of the S-wave isospin-odd πK scattering length View the MathML source|a0−|=13|a1/2−a3/2|=(0.11−0.04+0.09)Mπ−1 (aIaI for isospin I).

Generation of nonground-state condensates and adiabatic paradox

The problem of resonant generation of nonground-state condensates is addressed aiming at resolving the seeming paradox that arises when one resorts to the adiabatic representation. In this picture, the eigenvalues and eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also functions of time. Since the level energies vary in time, no definite transition frequency can be introduced. Hence no external modulation with a fixed frequency can be made resonant. Thus, the resonant generation of adiabatic coherent modes is impossible. However, this paradox occurs only in the frame of the adiabatic picture. It is shown that no paradox exists in the properly formulated diabatic representation. The resonant generation of diabatic coherent modes is a well defined phenomenon. As an example, the equations are derived, describing the generation of diabatic coherent modes by the combined resonant modulation of the trapping potential and atomic scattering length.