Towards surface quantum optics with Bose–Einstein condensates in evanescent waves

We present a surface trap which enables the study of coherent interactions between ultracold atoms and evanescent waves. The trap combines a magnetic Joffe trap with a repulsive evanescent dipole potential. Exploiting the advantages of both approaches this technique improves recent surfaces traps, which are based either on magnetic or optical traps alone. On the one hand, the position of the magnetic trap can be controlled with high precision which makes it possible to move ultracold atoms to the surface of a glass prism or to withdraw the atoms from the surface in a controlled way. On the other hand, the optical potential of the evanescent wave partially compensates for strong attractive surface forces and generates a potential barrier at only a few hundred nanometers from the surface. This barrier prevents the surface potentials from limiting the trap depth of the magnetic trap. The surface trap is probed with ⁸⁷Rb Bose–Einstein condensates (BECs), which are stably positioned at distances from the surfaces below one micrometer.     

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     

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.     

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     

Soliton breathers in spin-1 Bose–Einstein condensates

We consider a spin-1 Bose-Einstein condensate trapped in a harmonic potential with different nonlinearity coeffi- cients. We illustrate the dynamics of soliton breathers in two-component and three-component states by numerically solv- ing the one-dimensional time-dependent coupled Gross-Pitaecskii equations （GPEs）. We present that two condensates with repulsive interspecies interactions make elastic collision and novel soliton breathers are created in two-component state. We also demonstrate novel soliton breathers in three-component state with attractive coupling constants. Furthermore, possible reasons for creating soliton breathers are discussed.     

Bose–Einstein condensates in 1D- and 2D optical lattices

Bose–Einstein condensates of rubidium atoms are transferred into one- and two-dimensional optical lattice potentials. The phase coherence of the condensate wavefunction in the lattice potential is studied by suddenly releasing the atoms from the trapping potential and observing the multiple matter-wave interference pattern of several thousand expanding quantum gases. We show how arbitrary phase gradients can be mapped onto the periodic wavefunction through the application of a potential gradient. Furthermore, the experimentally measured strength of the momentum components is compared to a theoretical model of the condensate wavefunction in the lattice. Received: 3 July 2001 / Revised version: 26 September 2001 / Published online: 23 November 2001     

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.     

Localized nonlinear vector matter waves in two-component Bose–Einstein condensates with spatially modulated nonlinearities

Exact localized nonlinear vector matter waves in the form of soliton–soliton and vortex–vortex pairs in two-component Bose–Einstein condensates with spatially modulated nonlinearity coefficients and harmonic trapping potentials are reported. It is shown that there exists an infinite number of exact vector pairs sharing the same chemical potential with soliton–soliton ones for odd integer n while vortex–vortex ones for even integer n  . The stability of the vector pairs found is investigated by means of direct numerical simulations and a linear stability analysis; the results show that the stable vortex–vortex pairs (±l,±l)$(\pm l,\pm l)$ with large topological charges can be supported by the spatially modulated interaction when the harmonic trapping potential is presented in this system.     

Characterization and control of phase fluctuations in elongated Bose–Einstein condensates

Quasi-one-dimensional Bose–Einstein condensates (BECs) in elongated traps exhibit significant phase fluctuations even at very low temperatures. We present recent experimental results on the dynamic transformation of phase fluctuations into density modulations during time of flight and show the excellent quantitative agreement with the theoretical prediction. In addition we confirm that, under our experimental conditions, in the magnetic trap density modulations are strongly suppressed even when the phase fluctuates. We also discuss our theoretical results on control of the condensate phase by employing a time-dependent perturbation. Our results set important limitations on future applications of BECs in precision atom interferometry and atom optics, but at the same time suggest pathways to overcome these limitations. Received: 17 August 2002 / Published online: 15 January 2003 RID="*" ID="*"Corresponding author. Fax: +49-511/762-3023, E-mail: Helge.Kreutzmann@ITP.uni-hannover.de     

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.     

3D skyrmion and knot in two-component Bose–Einstein condensates

We present exact solutions to the two-component Bose–Einstein condensates by adopting a method of separating the variables, which exhibit nontrivial topology. These solitonic solutions can form 3D skyrmion and knot in the three-dimensional system.     

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.     

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.     

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.     

Kink-like breathers in Bose–Einstein condensates with helicoidal spin–orbit coupling

We report a kind of kink-like breathers in one-dimensional Bose–Einstein condensates (BECs) with helicoidal spin–orbit coupling (SOC), on whose two sides the background densities manifest obvious difference (called kink amplitude). The kink amplitude and shape of breather can be adjusted by the strength and period of helicoidal SOC, and its atomic number in two components exchanges periodically with time. The SOC has similar influence on the kink amplitude and the exchanged atomic number, especially when the background wave number is fixed. It indicates that the oscillating intensity of breather can be controlled by adjusting initial kink amplitude. Our work showcases the great potential of realizing novel types of breathers through SOC, and deepens our understanding on the formation mechanisms of breathers in BECs.     

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.     

Skyrmion crystals in pseudo-spin-1/2 Bose–Einstein condensates

Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose–Einstein condensates,which are described by the coupled nonlinear Gross–Pitaevskii equations where the intra-and inter-species coupling constants are assumed to be equal.The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions.The stationary solutions form various spin textures which are identified as skyrmion crystals.In a special case,a crystal of skyrmion–anti-skyrmion pairs is formed in the soliton limit.     

Spin–orbit coupled Bose–Einstein condensates with Rydberg-dressing interaction

Interaction between Rydberg atoms can be used to control the properties of interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Here we investigate the effect of the Rydberg-dressing interaction on the ground-state properties of a Bose–Einstein condensate imposed by Raman-induced spin–orbit coupling. We find that,in the case of SU(2)-invariant s-wave interactions, the gas is only in the plane-wave phase and the zero-momentum phase is absent. In particular, we also predict an unexpected magnetic stripe phase composed of two plane-wave components with unequal weight when s-wave interactions are non-symmetric, which originates from the Rydberg-dressing interaction.