A space-dependent atomic superfluid current in Bose–Einstein condensates

A space-dependent atomic superfluid current with an explicit analytical expression and its role in Bose–Einstein condensates are studied. The factors determining the intensity and oscillating amplitude of the space-dependent atomic superfluid current are explored in detail. Research findings reveal that the intensity of the current can be regulated by setting an appropriate configuration of the trap and its oscillating amplitude can be adjusted via Feshbach resonance. It is numerically demonstrated that the space-dependent atomic superfluid current can exert great influence on the spatial distribution of condensed atoms, and even force condensed atoms into very complex distributional states with spatial chaos.     

Spinor Bose–Einstein condensates

An overview of the physics of spinor and dipolar Bose–Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor–dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed.     

Solitons in Bose–Einstein condensates

The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density profile. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.     

Phase fluctuations in Bose–Einstein condensates

We demonstrate the existence of phase fluctuations in elongated Bose–Einstein condensates (BECs) and study the dependence of these fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase-coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed. Received: 13 July 2001 / Revised version: 28 September 2001 / Published online: 23 November 2001     

Bose–Einstein condensates in magnetic waveguides

In this article, we describe an experimental system for generating Bose–Einstein condensates and controlling the shape and motion of a condensate by using miniaturised magnetic potentials. In particular, we describe the magnetic trap setup, the vacuum system, the use of dispenser sources for loading a high number of atoms into the magneto-optical trap, the magnetic transfer of atoms into the microtrap, and the experimental cycle for generating Bose–Einstein condensates. We present first results on outcoupling of condensates into a magnetic waveguide and discuss influences of the trap surface on the ultra-cold ensembles. Received: 21 August 2002 / Revised version: 10 December 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-7071/295-829, E-mail: fortagh@pit.uni-tuebingen.de     

Wave functions,relative phase and interference for atomic Bose–Einstein condensates

In this article, we present a tutorial discussion of the coherence properties of Bose–Einstein condensates. We use a formalism which is similar to the one used in quantum optics. We describe within the variational approximation the question of the relative phase of two condensates. To evaluate the structure factors of a condensate, we briefly review the Bogolubov approach and describe light scattering off a condensate using the linear response formalism. Finally, we study the effect of atomic interactions on the condensate's dynamics.     

Bose–Einstein condensation of atomic hydrogen

The recent creation of a Bose–Einstein condensate of atomic hydrogen has added a new system to this exciting field. The differences between hydrogen and the alkali metal atoms require other techniques for the initial trapping and cooling of the atoms and the subsequent detection of the condensate. The use of a cryogenic loading technique results in a larger number of trapped atoms. Spectroscopic detection is well suited to measuring the temperature and density of the sample in situ. The transition was observed at a temperature of 50 μK and a density of 2×10¹⁴ cm^-3. The number of condensed atoms is about 10⁹ at a condensate fraction of a few percent. A peak condensate density of 4.8×10¹⁵ cm^-3 has been observed. Received: 22 June 1999 / Published online: 3 November 1999     

Time-domain Ramsey interferometry with Bose–Einstein condensates

We report on the observation of time-domain interference with Bose–Einstein condensates, by means of a double separated oscillator technique. We discuss the decay of the Ramsey oscillations amplitude, that in our system occurs on a time scale of tens of microseconds. To elucidate the origin of this fast decay, we compare the behaviour of a condensate with that of a thermal cloud.     

Three-dimensional solitons in two-component Bose–Einstein condensates

We investigate a kind of solitons in the two-component Bose–Einstein condensates with axisymmetric configurations in the R2×S1space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional(3D) skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross–Pitaevskii equations in imaginary time.     

Effects of spatially inhomogeneous atomic interactions on Bose–Einstein condensates in optical lattices

An interplay of optical lattices and nonlinear impurities in controlling the dynamics of Bose–Einstein condensate bright solitons is investigated using an effective potential approach. The ability of pushing the solitons into or away from the impurity region by changing both lattice and impurity parameters is suggested. A possibility for the existence of stable fundamental gap solitons, which appear to satisfy an inverted Vakhitov–Kolokolov criterion, is examined.     

Beliaev theory of spinor Bose–Einstein condensates

By generalizing the Green’s function approach developed by Beliaev [S.T. Beliaev, Sov. Phys. JETP 7 (1958) 299; S.T. Beliaev, Sov. Phys. JETP 7 (1958) 289], we study effects of quantum fluctuations on the energy spectra of spin-1 spinor Bose–Einstein condensates, in particular, of a ⁸⁷Rb condensate in the presence of an external magnetic field. We find that due to quantum fluctuations, the effective mass of magnons, which characterizes the quadratic dispersion relation of spin-wave excitations, increases compared with its mean-field value. The enhancement factor turns out to be the same for two distinct quantum phases: the ferromagnetic and polar phases, and it is a function of only the gas parameter. The lifetime of magnons in a spin-1 ⁸⁷Rb spinor condensate is shown to be much longer than that of phonons due to the difference in their dispersion relations. We propose a scheme to measure the effective mass of magnons in a spinor Bose gas by utilizing the effect of magnons’ nonlinear dispersion relation on the time evolution of the distribution of transverse magnetization. This type of measurement can be applied, for example, to precision magnetometry.     

Generating periodic interference in Bose–Einstein condensates

The interference between two condensates with repulsive interaction is investigated numerically by solving the onedimensional time-dependent Gross–Pitaevskii equation.The periodic interference pattern forms in two condensates,which are prepared in a double-well potential consisting of two truncated harmonic wells centered at different positions.Dark solitons are observed when two condensates overlap.Due to the existence of atom–atom interactions,atoms are transferred among the ground state and the excited states,which coincides with the condensate energy change.     

Collective enhancement and suppression in Bose–Einstein condensates

The coherent and collective nature of a Bose–Einstein condensate can enhance or suppress physical processes. Bosonic stimulation enhances scattering in already occupied states which leads to matter wave amplification, and the suppression of dissipation leads to superfluidity. In this article we present several experiments where enhancement and suppression have been observed and discuss the common roots of and differences between these phenomena.     

Trapped Bose–Einstein condensates with quadrupole–quadrupole interactions

We numerically investigate the ground-state properties of a trapped Bose–Einstein condensate with quadrupole–quadrupole interaction.We quantitatively characterize the deformations of the condensate induced by the quadrupolar interaction.We also map out the stability diagram of the condensates and explore the trap geometry dependence of the stability.     

Spinor molecule in atomic Bose–Einstein condensate

We have performed two-photon photoassociation experiments in atomic Bose–Einstein condensate (BEC) of ⁸⁷Rb with spin degree of freedom which is created by all-optical method with CO₂ lasers. The spinor character of the molecules has been revealed by the photoassociation spectrum with a new structure. The hyperfine structure of the molecules near the dissociation limit is identified by observations of the Zeeman and AC-Stark effects of the molecules. The molecules have been spin-selectively probed by the use of the light shift. This result would open the new possibility of research on novel spinor molecular BEC.     

The physics of trapped dilute-gas Bose–Einstein condensates

The experimental realisation of Bose–Einstein condensates of dilute atomic vapours has generated immense interest and activity in this field. Here, we present a review of recent theoretical research into the properties of trapped dilute-gas Bose–Einstein condensates. Topics covered include ground-state properties of trapped condensates, elementary excitations, light scattering properties, tests of broken gauge symmetry, and the atom laser.     

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.