Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.

Weakly bound atomic trimers in ultracold traps

The scaling dependence of the recombination parameter as a function of the ratio between the energies of the atomic dimer and the most excited trimer states was derived. The scaling function tends to a unversal function in the limit of zero-range interaction or infinite scattering length. This paper reports on how one can obtain the trimer binding energy of a trapped atomic system, from the three-body recombination rate and the corresponding two-body scattering length.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

Mean-field model of jet formation in a collapsing Bose-Einstein condensate

We perform a systematic numerical study, based on the time-dependent Gross-Pitaevskii equation, of jet formation in collapsing and exploding Bose-Einstein condensates as in the experiment by Donley et al (2001 Nature 412 295). In the actual experiment, via a Feshbach resonance, the scattering length of atomic interaction was suddenly changed from positive to negative on a pre-formed condensate. Consequently, the condensate collapsed and ejected atoms via explosion. On disruption of the collapse by suddenly changing the scattering length to zero, a radial jet of atoms was formed in the experiment. We present a satisfactory account of jet formation under the experimental conditions and also make predictions beyond experimental conditions which can be verified in future experiments.

Three-body recombination in ultracold systems: Prediction of weakly-bound atomic trimer energies

The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E 3 of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein condensates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, E3 (N+1) and E3 (N), can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r0/a (r0 is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited E3 (N+1) state disappears in the 2 + 1 threshold, is given by √E2/E3 (N) ≈ 0.38+0.12(r0/a). © 2012 Springer-Verlag.

Dipolar droplet bound in a trapped Bose-Einstein condensate

We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164Dy droplet bound in a trapped nondipolar 87Rb BEC with a variable number of 164Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a 164Dy droplet by relaxing the trap on the 164Dy BEC in a trapped binary 87Rb-164Dy mixture. © 2013 American Physical Society.

Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures

The generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are considered: a variation of the fermion-boson scattering length and the boson-boson scattering length. We predict the properties of the generated Faraday patterns and study the parameter regions where they can be excited. © 2013 American Physical Society.

Universalidade em sistemas de 3 e 4 bósons

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Oscilações não-lineares em condensados de Bose-Einstein

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

Self-trapping of a dipolar Bose-Einstein condensate in a double well

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

Solitons in atomic condensates, with optical lattices and field-induced dipole moments

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

Theoretical prevision for the low-energy 3S1-3D1 mixing parameters

Using a recent shape-independent approximation for the 3S1-3D1 mixing parameter, theoretical prevision for the low-energy mixing parameters is made. The present prevision is consistent with the deuteron binding energy, its asymptotic D-state to S-state ratio, ηd, the triplet-scattering length, and the meson exchange tail of the tensor nucleon-nucleon potential. The theoretical prevision up to an incident laboratory energy of 25 MeV is consistent with the recent multi-energy determination of mixing parameters, but is much higher than many single-energy determinations of the same. The low single-energy values of the mixing parameter could be reproduced by meson-theoretical potentials only with a substantially reduced ηd. © 1994 The American Physical Society.

Coupling collective modes in a trapped superfluid

We consider a superfluid cloud composed of a Bose-Einstein condensate oscillating within a magnetic trap (dipole mode) where, due to the existence of a Feshbach resonance, an effective periodic time-dependent modulation in the scattering length is introduced. Under this condition, collective excitations such as the quadrupole mode can take place. We approach this problem by employing both the Gaussian and the Thomas-Fermi variational Ansatze. The resulting dynamic equations are analyzed by considering both linear approximations and numerical solutions, where we observe coupling between dipole and quadrupole modes. Aspects of this coupling related to the variation of the dipole oscillation amplitude are analyzed. This may be a relevant effect in situations where oscillation in a magnetic field in the presence of a bias field B takes place, and should be considered in the interpretation of experimental results.