Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

We present a numerical study of the coupled time-dependent Gross-Pitaevskii equation, which describes the Bose-Einstein condensate of several types of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. The same approach is used to study both stationary and time-evolution problems. We consider up to four types of atoms in the study of stationary problems. We consider the time-evolution problems where the frequencies of the traps or the atomic scattering lengths are suddenly changed in a stable preformed condensate. We also study the effect of periodically varying these frequencies or scattering lengths on a preformed condensate. These changes introduce oscillations in the condensate which are studied in detail. Good convergence is obtained in all cases studied.Comment: 9 pages, 10 figures, accepted in Physical Review

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let

Scissors modes in triaxial metal clusters

We study the scissors mode (orbital M1 excitations) in small Na clusters, triaxial metal clusters ${\rm Na}_{12}$ and ${\rm Na}_{16}$ and the close-to-spherical ${{\rm Na}_9}^+$, all described in DFT with detailed ionic background. The scissors modes built on spin-saturated ground and spin-polarized isomeric states are analyzed in virtue of both macroscopic collective and microscopic shell-model treatments. It is shown that the mutual destruction of Coulomb and the exchange-correlation parts of the residual interaction makes the collective shift small and the net effect can depend on details of the actual excited state. The crosstalk with dipole and spin-dipole modes is studied in detail. In particular, a strong crosstalk with spin-dipole negative-parity mode is found in the case of spin-polarized states. Triaxiality and ionic structure considerably complicate the scissors response, mainly at expense of stronger fragmentation of the strength. Nevertheless, even in these complicated cases the scissors mode is mainly determined by the global deformation. The detailed ionic structure destroys the spherical symmetry and can cause finite M1 response (transverse optical mode) even in clusters with zero global deformation. But its strength turns out to be much smaller than for the genuine scissors modes in deformed systems.Comment: 17 pages, 5 figure

Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions

We present a numerical study of the time-dependent and time-independent Gross-Pitaevskii (GP) equation in two space dimensions, which describes the Bose-Einstein condensate of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. Both time-dependent and time-independent GP equations are used to study the stationary problems. In addition the time-dependent approach is used to study some evolution problems of the condensate. Specifically, we study the evolution problem where the trap energy is suddenly changed in a stable preformed condensate. In this case the system oscillates with increasing amplitude and does not remain limited between two stable configurations. Good convergence is obtained in all cases studied.Comment: 9 latex pages, 7 postscript figures, To appear in Phys. Rev.

BEC Collapse and Dynamical Squeezing of Vacuum Fluctuations

We analyze the phenomena of Bose Novae, as described by Donley et al [Nature 412, 295 (2001)], by focusing on the behavior of excitations or fluctuations above the condensate, as driven by the dynamics of the condensate (rather than the dynamics of the condensate alone or the kinetics of the atoms). The dynamics of the condensate squeezes and amplifies the quantum excitations, mixing the positive and negative frequency components of their wave functions thereby creating particles which appear as bursts and jets. By analyzing the changing amplitude and particle content of these excitations, our simple physical picture (based on a test field approximation) explains well the overall features of the Bose Novae phenomena and provide excellent quantitative fits with experimental data on several aspects, such as the scaling behavior of the collapse time and the amount of particles in the jet. The predictions of the bursts at this level of approximation is less than satisfactory but may be improved on by including the backreaction of the excitations on the condensate. The mechanism behind the dominant effect -- parametric amplification of vacuum fluctuations and freezing of modes outside of horizon -- is similar to that of cosmological particle creation and structure formation in a rapid quench (which is fundamentally different from Hawking radiation in black holes). This shows that BEC dynamics is a promising venue for doing `laboratory cosmology'.Comment: Latex 36 pages, 6 figure

The theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with one-dimensional strip-like geometry. This approach is confirmed by numerical simulations which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.Comment: 26 page

The Nuclear Sigma Term in the Skyrme Model: Pion-Nucleus Interaction

The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the NN interaction with respect to the quark mass, $m_q\frac{\partial V_{NN}}{\partial m_q}$. The NN potential is evaluated in the skyrmion-skyrmion picture within the quantized product ansatz. The contribution of the NN potential to the nuclear sigma term provides repulsion to the pion-nucleus interaction. The strength of the s-wave pion-nucleus optical potential is estimated including such contribution. The results are consistent with the analysis of the experimental data.Comment: 16 pages (latex), 3 figures (eps), e-mail: [email protected] and [email protected]

Quark Condensate in the Deuteron

We study the changes produced by the deuteron on the QCD quark condensate by means the Feynman-Hellmann theorem and find that the pion mass dependence of the pion-nucleon coupling could play an important role. We also discuss the relation between the many body effect of the condensate and the meson exchange currents, as seen by photons and pions. For pion probes, the many-body term in the physical amplitude differs significantly from that of soft pions, the one linked to the condensate. Thus no information about the many-body term of the condensate can be extracted from the pion-deuteron scattering length. On the other hand, in the Compton amplitude, the relationship with the condensate is a more direct one.Comment: to appear in Physics Review C (19 pages, 3 figures

Early Universe Quantum Processes in BEC Collapse Experiments

We show that in the collapse of a Bose-Einstein condensate (BEC) {For an excellent introduction to BEC theory, see C. Pethick and H. Smith, Bose-Einstein condensation in dilute gases (Cambridge University Press, Cambridge, England, 2002)} certain processes involved and mechanisms at work share a common origin with corresponding quantum field processes in the early universe such as particle creation, structure formation and spinodal instability. Phenomena associated with the controlled BEC collapse observed in the experiment of Donley et al E. Donley et. al., Nature 412, 295 (2001)(they call it `Bose-Nova', see also J. Chin, J. Vogels and W. Ketterle, Phys. Rev. Lett. 90, 160405 (2003)) such as the appearance of bursts and jets can be explained as a consequence of the squeezing and amplification of quantum fluctuations above the condensate by the dynamics of the condensate. Using the physical insight gained in depicting these cosmological processes, our analysis of the changing amplitude and particle contents of quantum excitations in these BEC dynamics provides excellent quantitative fits with the experimental data on the scaling behavior of the collapse time and the amount of particles emitted in the jets. Because of the coherence properties of BEC and the high degree of control and measurement precision in atomic and optical systems, we see great potential in the design of tabletop experiments for testing out general ideas and specific (quantum field) processes in the early universe, thus opening up the possibility for implementing `laboratory cosmology'.Comment: 7 pages, 3 figures. Invited Talk presented at the Peyresq Meetings of Gravitation and Cosmology, 200