Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations

In this paper we study the phase of self-similar solutions to general Nonlinear Schr\"odinger equations. From this analysis we gain insight on the dynamics of nontrivial solutions and a deeper understanding of the way collective coordinate methods work. We also find general evolution equations for the most relevant dynamical parameter $w(t)$ corresponding to the width of the solution. These equations are exact for self-similar solutions and provide a shortcut to find approximate evolution equations for the width of non-self-similar solutions similar to those of collective coordinate methods

Coupling single molecule magnets to quantum circuits

In this work we study theoretically the coupling of single molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main results of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (of the order of microseconds), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy gaps and the simplicity with which they can be tuned and oriented. Finally, we also discuss practical advantages of SMMs, such as the possibility to fabricate the SMMs ensembles on the chip through the deposition of small droplets.Comment: 23 pages, 12 figure

Structural instability of vortices in Bose-Einstein condensates

In this paper we study a gaseous Bose-Einstein condensate (BEC) and show that: (i) A minimum value of the interaction is needed for the existence of stable persistent currents. (ii) Vorticity is not a fundamental invariant of the system, as there exists a conservative mechanism which can destroy a vortex and change its sign. (iii) This mechanism is suppressed by strong interactions.Comment: 4 pages with 3 figures. Submitted to Phys. Rev. Let

Construction of exact solutions by spatial traslations in inhomogeneous Nonlinear Schrodinger equations. Applications to Bose-Einstein condensation

In this paper we study a general nonlinear Schr\"odinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many others which are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave-packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave-packet, but also the shape of the solution is independent of the behaviour of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic trapsComment: Submitted to Phys. Re

A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions

To show a mechanism leading to the breakdown of a particle picture for the multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high dimensions, we investigate the corresponding 2-$d$ nonlinear Schr{\"o}dinger equation (Gross-Pitaevskii equation) with use of a modified variational principle. A molecule of two identical Gaussian wavepackets has two degrees of freedom(DFs), the separation of center-of-masses and the wavepacket width. Without the inter-component interaction(ICI) these DFs show independent regular oscillations with the degenerate eigen-frequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks a particle picture, which however can be recovered by introducing a time-periodic ICI with zero average. In case of the molecule of three wavepackets for a three-component BEC, the increase of amplitude of ICI yields a transition from regular to chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure

Split vortices in optically coupled Bose-Einstein condensates

We study a rotating two-component Bose-Einstein condensate in which an optically induced Josephson coupling allows for population transfer between the two species. In a regime where separation of species is favored, the ground state of the rotating system displays domain walls with velocity fields normal to them. Such a configuration looks like a vortex split into two halves, with atoms circulating around the vortex and changing their internal state in a continuous way.Comment: 4 EPS pictures, 4 pages; Some errata have been corrected and thep resentation has been slightly revise

Soliton molecules in trapped vector Nonlinear Schrodinger systems

We study a new class of vector solitons in trapped Nonlinear Schrodinger systems modelling the dynamics of coupled light beams in GRIN Kerr media and atomic mixtures in Bose-Einstein condensates. These solitons exist for different spatial dimensions, their existence is studied by means of a systematic mathematical technique and the analysis is made for inhomogeneous media

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde

Extended parametric resonances in nonlinear Schrodinger systems

We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the same way. The results have applicability in recent experiments in Bose-Einstein condensation and to classical problems in Nonlinear Optics.Comment: 1 figur

Dipole-Mode Vector Solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. These solitons, which appear as a consequence of the vector nature of the two component system, are more stable than the previously found optical vortex-mode solitons and represent a new type of extremely robust nonlinear vector structure.Comment: Four pages with five eps figure