Observation of faraday waves in a Bose-Einstein condensate

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.     

Ramsey fringes in a Bose-Einstein condensate between atoms and molecules

In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a 85Rb Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules.     

Controllable soliton emission from a Bose-Einstein condensate

We demonstrate, through numerical simulations, the controllable emission of matter-wave bursts from a Bose-Einstein condensate in a shallow optical dipole trap. The process is triggered by spatial variations of the scattering length along the trapping axis. In our approach, the outcoupling mechanisms are atom-atom interactions and thus, the trap remains unaltered. Once emitted, the matter wave forms a robust soliton. We calculate analytically the parameters for the experimental implementation of these matter-wave bursts of solitons.     

Observation of Bose-Einstein condensation of molecules

We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic 6Li atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into 6Li2 molecules. Below 600 nK, a Bose-Einstein condensate of up to 900 000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.     

Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap

We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit variant Planck's over 2pi of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply connected, and was observed with a Bose-Einstein condensate fraction as small as 20%. We also created flow with two units of angular momentum and observed its splitting into two singly charged vortices when the trap geometry was changed from multiply to simply connected.     

Observation of spontaneous coherence in Bose-Einstein condensate of magnons

The room-temperature dynamics of a magnon gas driven by short microwave pumping pulses is studied. An overpopulation of the lowest energy level of the system following the pumping is observed. Using the sensitivity of the Brillouin light scattering technique to the coherence degree of the scattering magnons we demonstrate the spontaneous emergence of coherence of the magnons at the lowest level, if their density exceeds a critical value. This finding is clear proof of the quantum nature of the observed phenomenon and direct evidence of Bose-Einstein condensation of magnons at room temperature.     

Radiation from accelerated impurities in a Bose-Einstein condensate

We investigate radiation spectra arising from accelerated point-like impurities in the homogeneous Bose-Einstein condensate. A general formula for the radiation spectrum is obtained in the integral form as a function of given impurity trajectory within the Bogoliubov approximation. The Planckian spectrum is obtained for a special accelerated motion, which is shown to be unphysical. Non-Planckian spectrum is found in the case of a uniformly accelerated impurity. We compare our result with similar settings discussed in other quantum systems.     

Levinson-like theorem for scattering from a Bose-Einstein condensate

A relation between the number of bound elementary excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalizes Levinson's theorem. Specific features of the Bogoliubov model such as complex energy and continuum bound states are discussed and a numerical example is given.     

Chaos in a Bose-Einstein condensate

It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.     

Semiclassical theory of superradiant scattering from a Bose-Einstein condensate

A semiclassical theory of superradiant scattering of light from a Bose-Einstein condensate of a dilute atomic gas is proposed. Choosing atomic states with definite values of the momenta as a basis, we derive a nonlinear Schrödinger equation. Its solutions describe the evolution of the scattered light intensity and of the populations of the coherent atomic states with different recoil momenta.     

Explosion of a collapsing Bose-Einstein condensate

We show that elastic collisions between atoms in a Bose-Einstein condensate with attractive interactions can lead to an explosion that ejects a large fraction of the collapsing condensate. We study variationally the dynamics of this explosion and find excellent agreement with recent experiments on magnetically trapped 85Rb. We also determine the energy and angular distribution of the ejected atoms during the collapse.     

Excitation spectrum of a Bose-Einstein condensate

We report a measurement of the excitation spectrum omega(k) and the static structure factor S(k) of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the superfluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spectrum in the local density approximation, even close to the long-wavelength limit of the region of applicability. Feynman's relation between omega(k) and S(k) is verified, within an overall constant.     

Controlled collapse of a Bose-Einstein condensate

The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable 85Rb BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be N(absolute value of a) / a(ho) = 0.459+/-0.012+/-0.054, slightly lower than the predicted value of 0.574.     

Fast rotation of a Bose-Einstein condensate

We study the rotation of a 87Rb Bose-Einstein condensate confined in a quadratic plus quartic potential. This trap configuration allows one to increase the rotation frequency of the gas above the trap frequency. In such a fast rotation regime we observe a dramatic change in the appearance of the quantum gas. The vortices which were easily detectable for a slower rotation become much less visible, and their surface density is well below the value expected for this rotation frequency domain. We discuss some possible tracks to account for this effect.     

Vortex-antivortex pair in a Bose-Einstein condensate

Presented is a type-II quantum algorithm for superfluid dynamics, used to numerically predict solutions of the GP equation for a complex scalar field (spinless bosons) in φ⁴ theory. The GP equation is a long wavelength effective field theory of a microscopic quantum lattice gas with nonlinear state reduction. The quantum lattice gas algorithm for modeling the dynamics of the one-body BEC state in 3+1 dimensions is presented. To demonstrate the method's strength as a computational physics tool, a difficult situation of filamentary singularities is simulated, the dynamics of solitary vortex-antivortex pairs, which are a basic building block of morphologies of quantum turbulence.     

Bose-Einstein condensate in a random potential

An optical speckle potential is used to investigate the static and dynamic properties of a Bose-Einstein condensate in the presence of disorder. With small levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. Uncorrelated frequency shifts of the two modes are measured and are explained using a sum-rules approach and by the numerical solution of the Gross-Pitaevskii equation.     

Knots in a spinor Bose-Einstein condensate

We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.     

Dynamical transition from a quasi-one-dimensional Bose-Einstein condensate to a Tonks-Girardeau gas

We analyze in detail the expansion of a 1D Bose gas after removing the axial confinement. We show that during its one-dimensional expansion the density of the Bose gas does not follow a self-similar solution. Our analysis is based on a nonlinear Schr?dinger equation with variable nonlinearity whose validity is discussed for the expansion problem, by comparing with an exact Bose-Fermi mapping for the case of an initial Tonks-Girardeau gas. For this case, the gas is shown to expand self-similarly, with a different scaling law compared to the one-dimensional Thomas-Fermi condensate.     

Overcritical rotation of a trapped Bose-Einstein condensate

The rotational motion of an interacting Bose-Einstein condensate confined by a harmonic trap is investigated by solving the hydrodynamic equations of superfluids, with the irrotationality constraint for the velocity field. We point out the occurrence of an overcritical branch where the system can rotate with angular velocity larger than the oscillator frequencies. We show that in the case of isotropic trapping the system exhibits a bifurcation from an axisymmetric to a triaxial configuration, as a consequence of the interatomic forces. The dynamical stability of the rotational motion with respect to the dipole and quadrupole oscillations is explicitly discussed.