Mean-field model of interaction between bright vortex solitons in Bose-Einstein condensates

Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation we study the dynamics of interaction among vortex solitons in a rotating matter-wave bright soliton train in a radially trapped and axially free Bose-Einstein condensate to understand certain features of the experiment by Strecker et al (2002 Nature 417 150). In a soliton train, solitons of opposite phase (phase δ = π) repel and stay apart without changing shape; solitons with δ = 0 attract, interact and coalesce, but eventually come out; solitons with a general δ usually repel but interact inelastically by exchanging matter. We study this and suggest future experiments with vortex solitons.

Oscilações não-lineares em condensados de Bose-Einstein

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

Dynamics of the corotating vortices in dipolar Bose-Einstein condensates in the presence of dissipation

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

Dynamics of dissipative Bose-Einstein condensation

We resolve the real-time dynamics of a purely dissipative s=1/2 quantum spin or, equivalently, hard-core boson model on a hypercubic d-dimensional lattice. The considered quantum dissipative process drives the system to a totally symmetric macroscopic superposition in each of the S3 sectors. Different characteristic time scales are identified for the dynamics and we determine their finite-size scaling. We introduce the concept of cumulative entanglement distribution to quantify multiparticle entanglement and show that the considered protocol serves as an efficient method to prepare a macroscopically entangled Bose-Einstein condensate.

Excitations in Bose-Einstein condensates: collective modes, quantum turbulence and matter wave statistics

In this thesis, we present the generation and studies of a 87Rb Bose-Einstein condensate (BEC) perturbed by an oscillatory excitation. The atoms are trapped in a harmonic magnetic trap where, after an evaporative cooling process, we produce the BEC. In order to study the effect caused by oscillatory excitations, a quadrupole magnetic field time oscillatory is superimposed to the trapping potential. Through this perturbation, collective modes were observed. The dipole mode is excited even for low excitation amplitudes. However, a minimum excitation energy is needed to excite the condensate quadrupole mode. Observing the excited cloud in TOF expansion, we note that for excitation amplitude in which the quadrupole mode is excited, the cloud expands without invert its aspect ratio. By looking these clouds, after long time-of-flight, it was possible to see vortices and, sometimes, a turbulent state in the condensed cloud. We calculated the momentum distribution of the perturbed BECs and a power law behavior, like the law to Kolmogorov turbulence, was observed. Furthermore, we show that using the method that we have developed to calculate the momentum distribution, the distribution curve (including the power law exponent) exhibits a dependence on the quadrupole mode oscillation of the cloud. The randomness distribution of peaks and depletions in density distribution image of an expanded turbulent BEC, remind us to the intensity profile of a speckle light beam. The analogy between matter-wave speckle and light speckle is justified by showing the similarities in the spatial propagation (or time expansion) of the waves. In addition, the second order correlation function is evaluated and the same dependence with distance was observed for the both waves. This creates the possibility to understand the properties of quantum matter in a disordered state. The propagation of a three-dimensional speckle field (as the matter-wave speckle described here) creates an opportunity to investigate the speckle phenomenon existing in dimensions higher than 2D (the case of light speckle).

Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

Experiments with Bose-Einstein condensates on an atom chip

We describe the production of BECs on a new type of atom chip based on silver foil. Our atom chip is fabricated with thick wires capable of carrying currents of several amperes without overheating. The silver surface is highly reflective to light resonant with optical transitions used for Rb. The pattern on the chip consists of two parallel Z-trap wires, capable of producing two-wire guide, and two additional endcap wires for varying the axial confinement. Condensates are produced in magnetic microtraps formed within 1 mm of surface of the chip. We have observed the fragmentation of cold atom clouds when brought close to the chip surface. This results from a perturbed trapping potential caused by nanometer deviations of the current path through the wires on the chip. We present results of fragmentation of cold clouds at distances below 100 µm from the wires and investigate the origin of the deviating current. The fragmentation has different characteristics to those seen with copper conductors. The dynamics of atoms in these microtraps is also investigated. ©2005 COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.

Colliding and Moving Bose-Einstein Condensates: Studies of superfluidity and optical tweezers for condensate transport

In this thesis, two different sets of experiments are described. The first is an exploration of the microscopic superfluidity of dilute gaseous Bose- Einstein condensates. The second set of experiments were performed using transported condensates in a new BEC apparatus. Superfluidity was probed by moving impurities through a trapped condensate. The impurities were created using an optical Raman transition, which transferred a small fraction of the atoms into an untrapped hyperfine state. A dramatic reduction in the collisions between the moving impurities and the condensate was observed when the velocity of the impurities was close to the speed of sound of the condensate. This reduction was attributed to the superfluid properties of a BEC. In addition, we observed an increase in the collisional density as the number of impurity atoms increased. This enhancement is an indication of bosonic stimulation by the occupied final states. This stimulation was observed both at small and large velocities relative to the speed of sound. A theoretical calculation of the effect of finite temperature indicated that collision rate should be enhanced at small velocities due to thermal excitations. However, in the current experiments we were insensitive to this effect. Finally, the factor of two between the collisional rate between indistinguishable and distinguishable atoms was confirmed. A new BEC apparatus that can transport condensates using optical tweezers was constructed. Condensates containing 10-15 million sodium atoms were produced in 20 s using conventional BEC production techniques. These condensates were then transferred into an optical trap that was translated from the ‘production chamber’ into a separate vacuum chamber: the ‘science chamber’. Typically, we transferred 2-3 million condensed atoms in less than 2 s. This transport technique avoids optical and mechanical constrainsts of conventional condensate experiments and allows for the possibility of novel experiments. In the first experiments using transported BEC, we loaded condensed atoms from the optical tweezers into both macroscopic and miniaturized magnetic traps. Using microfabricated wires on a silicon chip, we observed excitation-less propagation of a BEC in a magnetic waveguide. The condensates fragmented when brought very close to the wire surface indicating that imperfections in the fabrication process might limit future experiments. Finally, we generated a continuous BEC source by periodically replenishing a condensate held in an optical reservoir trap using fresh condensates delivered using optical tweezers. More than a million condensed atoms were always present in the continuous source, raising the possibility of realizing a truly continuous atom lase.

Vortex entanglement in Bose-Einstein condensates coupled to Laguerre-Gauss beams

We study the establishment of vortex entanglement in remote Bose-Einstein condensates (BECs). We consider a two-mode photonic resource entangled in its orbital angular momentum (OAM) degree of freedom and, by exploiting the process of light-to-BEC OAM transfer, demonstrate that such entanglement can be efficiently passed to the matterlike systems. Our proposal thus represents a building block for novel dissipation-free and long-memory communication channels based on OAM. We discuss issues of practical realizability, stressing the feasibility of our scheme, and present an operative technique for the indirect inference of the set vortex entanglement.

Modulational instability criteria for two-component Bose-Einstein condensates

The stability of colliding Bose-Einstein condensates is investigated. A set of coupled Gross-Pitaevskii equations is thus considered, and analyzed via a perturbative approach. No assumption is made on the signs ( or magnitudes) of the relevant parameters like the scattering lengths and the coupling coefficients. The formalism is therefore valid for asymmetric as well as symmetric coupled condensate wave states. A new set of explicit criteria is derived and analyzed. An extended instability region, in addition to an enhanced instability growth rate, is predicted for unstable two component bosons, as compared to the individual ( uncoupled) state.

Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrodinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type. (c) 2005 Elsevier B.V. All rights reserved.

Solitons in Bose-Einstein condensates trapped in a double-well potential

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves (radiation). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system. (C) 2003 Elsevier B.V. All rights reserved.

Energy level statistics for models of coupled single-mode Bose-Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.