Quantum phase engineering is demonstrated with two techniques that allow the spatial phase distribution of a Bose-Einstein condensate (BEC) to be written and read out. A quantum state was designed and produced by optically imprinting a phase pattern onto a BEC of sodium atoms, and matter-wave interferometry with spatially resolved imaging was used to analyze the resultant phase distribution. An appropriate phase imprint created solitons, the first experimental realization of this nonlinear phenomenon in a BEC. The subsequent evolution of these excitations was investigated both experimentally and theoretically.

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.

We present accurate time-dependent ab initio calculations on fully differential and total integrated (generalized) cross sections for the nonsequential two-photon double ionization of helium at photon energies from 40 to 54 eV. Our computational method is based on the solution of the time-dependent Schroedinger equation and subsequent projection of the wave function onto Coulomb waves. We compare our results with other recent calculations and discuss the emerging similarities and differences. We investigate the role of electronic correlation in the representation of the two-electron continuum states, which are used to extract the ionization yields from the fully correlated final wave function. In addition, we study the influence of the pulse length and shape on the cross sections in time-dependent calculations and address convergence issues.Comment: 14 pages, 10 figures; final version (acknowledgements and reference added, typos fixed

Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time. 03.75.Fi, 05.45.Yv,

We study the density modulation that appears in a Bose-Einstein condensate flowing with supersonic velocity against an obstacle. The experimental density profiles observed at JILA are reproduced by a numerical integration of the Gross-Pitaevskii equation and then interpreted in terms ofCerenkov emission of Bogoliubov excitations by the defect. The phonon and the single-particle regions of the Bogoliubov spectrum are respectively responsible for a conical wavefront and a fan-shaped series of precursors.PACS numbers: 03.75. Kk, 41.60.Bq TheCerenkov effect was first discovered in the electromagnetic radiation emitted by charged particles traveling through a dielectric medium at a speed larger than the medium's phase velocity [1]. A charge moving at the speed v is in fact able to resonantly excite those modes of the electromagnetic field which satisfy the kinematicCerenkov resonance condition ω em (k) = v · k: part of the kinetic energy of the particle is then emitted asCerenkov radiation, with a peculiar frequency and angular spectrum [2]. Electromagnetic waves in a nondispersive medium of refractive index n have a linear dispersion law relation ω em (k) = ck/n: theCerenkov condition is then satisfied on a conical surface in k-space of aperture cos φ = c/(nv), which corresponds to a conical wavefront of aperture θ = π/2 − φ behind the particle. Thanks to the interplay of interference and propagation, much richer features appear in the spatial and k-space pattern ofCerenkov radiation in dispersive media [3,4] and photonic crystals [5].The concept ofCerenkov radiation can be generalized to any system where a source is uniformly moving through a homogeneous medium at a speed larger than the phase velocity of some elementary excitation to which the source couples. Many systems have been investigated in this perspective, ranging from e.m. waves emitted by the localized nonlinear polarization induced by a strong light pulse travelling in a nonlinear medium [6,7], to the sonic waves generated by an airplane moving at supersonic velocities, to phonons in a polaritonic superfluid [8], and in a broader sense, to the surface waves emitted by a boat moving on the quiet surface of a lake [9]. In this Letter we compare our theoretical results of the density perturbation induced in a Bose-Einstein condensate (BEC) which flows against a localized obstacle at rest with the experimental images taken by the JILA group [10]. Modulo a Galilean transformation, the physics of a moving source in a stationary medium is in fact equivalent to the one of a uniformly moving medium interacting with a stationary defect. The experiment has been performed by letting a BEC expand at hypersonic speed against the lo- The experiment. The experimental results analyzed in this paper have been obtained by the JILA group [10] with a gas of N = 3 × 10 6 Bose-Einstein condensed 87 Rb atoms confined in a cylindrically symmetric harmonic trap of frequencies {ω r , ω z } = 2π{8.3, 5.3} Hz. The BEC is slightly cigar shaped, with the long axis pointing in the...

We have performed molecular dynamics simulations to obtain the internal energy and pressure of shockcompressed fluid deuterium at 24 separate ͑density temperature͒ points. Our calculations were performed using the generalized gradient approximation ͑GGA͒ in density-functional theory. We obtained a good fit to this simulation data with a thermodynamically consistent virial expansion. The single-shock Hugoniot derived from this equation of state is compared to previous theoretical and experimental results. We discuss several types of error inherent in the GGA, as they relate to the quality of our results.

We present the first large-scale simulations of an ultracold, neutral plasma, produced by photoionization of laser-cooled xenon atoms, from creation to initial expansion, using classical molecular dynamics methods with open boundary conditions. We reproduce many of the experimental findings such as the trapping efficiency of electrons with increased ion number, a minimum electron temperature achieved on approach to the photoionization threshold, and recombination into Rydberg states of anomalously-low principal quantum number. In addition, many of these effects establish themselves very early in the plasma evolution (∼ ns) before present experimental observations begin.That a common characteristic connects such diverse environments as the surface of a neutron star, the initial compression stage of an inertial confinement fusion capsule, the interaction region of a high-intensity laser with atomic clusters, and a very cold, dilute, and partiallyionized gas within an atomic trap, seems at first rather remarkable. Yet all these cases embrace a regime known as a strongly-coupled plasma. For such a plasma, the interactions among the various constituents dominate the thermal motions. The plasma coupling constant Γ α , the ratio of the average electrostatic potential energy Z α /a α [ Z α , the charge; a α , the ion-sphere radius = 3/(4πn α 1/3 ); and n α , the number density for a given component α] to the kinetic energy k B T α , provides an intrinsic measure of this effect [1]. When Γ α exceeds unity, various strong-coupling effects commence such as collective modes and phase transitions. For multi-component plasmas, the coupling constants need not be equal or even comparable, leading to a medium that may contain both strongly-and weakly-coupled constituents.Since temperatures usually start around a few hundred Kelvin, most plasmas found in nature or engineered in the laboratory attain strongly-coupled status from high densities, as in the case of a planetary interior or a shockcompressed fluid [2,3], or from highly-charged states, as in colloidal or "dusty" plasmas [4]. In both situations, the particle density usually rises well above 10 18 /cm 3 . On the other hand, ion trapping and cooling methods have produced dilute, strongly-coupled plasmas by radically lowering the temperature. At first, these efforts were limited to nonneutral plasmas confined by a magnetic field [5]. However, recently, new techniques [6-9] have generated neutral, ultracold plasmas, free of any external fields at densities of the order of 10 8 -10 10 /cm 3 and temperatures at microkelvins (µK).Two methods, one direct and one indirect, but both employing laser excitation of a highly-cooled sample of neutral atoms, have successfully created such neutral plasmas. The direct approach employs the photoionization of laser-cooled xenon atoms [6][7][8], while the indirect generates a cold Rydberg gas in which a few collisions with room-temperature atoms produces the ionization [9,10]. In both cases, the electron and ion temperatures start very far a...

Complete two-photon break-up of He near threshold has been investigated by solving the time-dependent closing-coupling equations on a numerical lattice. We have obtained good agreement for the total double ionization cross-section with previous theoretical results. The triple-differential cross-sections exhibit interesting features as the two-photon energy approaches the threshold of double ionization. We found that two-electron ejection with equal energy sharing is most probable near the two-photon threshold, in contrast to the case away from threshold, where ejection with large unequal energy sharings is most probable.