The objective of this PhD thesis was the examination of the dynamical behaviour of coherent wave packets realised by Bose-Einstein condensates (BEC) out of 87Rubidium atoms. Their dynamics is mainly affected by linear dispersion due to momentum uncertainty and by nonlinear atomic interaction due to s-wave scattering. The primary objective was the realisation of bright atomic solitons, which represent density distributions with time-independent shape. They only exist if the effects of dispersion and nonlinearity cancel out each other. For 87Rb atoms with repulsive interaction this requires the dispersion of the ensemble to be anomalous. The dispersion of the wave packet can be influenced in sign and in magnitude by superimposing a periodic potential and by changing the quasi-momentum of the atoms. For that purpose an apparatus to produce Bose-Einstein condesates as source of coherent matter waves was build up and characterised. The phase transition was observed as well in magnetic as in optical dipole traps. Experiments related to the dynamic of wave packets were conducted in a twodimensional optical trap retaining the atoms against gravity and allowing them to propagate along the axis of the trap. The periodic potential to influence the dispersion results from two counterpropagating interfering laser beams superimposed to the dipole trap. A first set of experiments demonstrated the possibility to influence the linear dispersion of matter waves by changing the quasi-momentum of the atoms in a periodic potential. In particular wave packets with anomalous dispersion were prepared at the brillouin zone edge in quasi-momentum space. Their behaviour is equivalent to particles with a negative effective mass, which was be confirmed by reversing the time evolution of an expanding wave packet. This demonstration of a negative effective mass of wave packets was an essential prerequisite for the creation of atomic solitons. Their formation was observed having prepared Bose-Einstein condensates of only 1000 atoms. A further set of systematic experiments was performed confirming the solitonic behaviour of the wave packets. This was the first realisation of atomic solitons with repulsive interaction also called Gap-Solitons.
The objective of this PhD thesis was the examination of the dynamical behaviour of coherent wave packets realised by Bose-Einstein condensates (BEC) out of 87Rubidium atoms. Their dynamics is mainly affected by linear dispersion due to momentum uncertainty and by nonlinear atomic interaction due to s-wave scattering. The primary objective was the realisation of bright atomic solitons, which represent density distributions with time-independent shape. They only exist if the effects of dispersion and nonlinearity cancel out each other. For 87Rb atoms with repulsive interaction this requires the dispersion of the ensemble to be anomalous. The dispersion of the wave packet can be influenced in sign and in magnitude by superimposing a periodic potential and by changing the quasi-momentum of the atoms. For that purpose an apparatus to produce Bose-Einstein condesates as source of coherent matter waves was build up and characterised. The phase transition was observed as well in magnetic as in optical dipole traps. Experiments related to the dynamic of wave packets were conducted in a twodimensional optical trap retaining the atoms against gravity and allowing them to propagate along the axis of the trap. The periodic potential to influence the dispersion results from two counterpropagating interfering laser beams superimposed to the dipole trap. A first set of experiments demonstrated the possibility to influence the linear dispersion of matter waves by changing the quasi-momentum of the atoms in a periodic potential. In particular wave packets with anomalous dispersion were prepared at the brillouin zone edge in quasi-momentum space. Their behaviour is equivalent to particles with a negative effective mass, which was be confirmed by reversing the time evolution of an expanding wave packet. This demonstration of a negative effective mass of wave packets was an essential prerequisite for the creation of atomic solitons. Their formation was observed having prepared Bose-Einstein condensates of only 1000 atoms. A further set of systematic experiments was performed confirming the solitonic behaviour of the wave packets. This was the first realisation of atomic solitons with repulsive interaction also called Gap-Solitons.
In this thesis I report on experiments on the quantum dynamics of matter waves in a onedimensional lattice potential. A 87Rb Bose-Einstein condensates is prepared in a one-dimensional waveguide in the lowest band of a superimposed optical lattice potential. The action of a weak lattice potential allows to modify the linear wave dispersion. We realized dispersion management by switching from normal to anomalous dispersion during the evolution. In this way the initial expansion of a wave packet is reversed to a compression and thus the effective spreading can be suppressed. By preparing a BEC at the Brillouin zone edge, we observed bright atomic gap solitons – non-spreading wave packets. They form, if the atom number and the lattice potential depth is tuned such that the effect of the repulsive atomic interaction and the anomalous dispersion cancel. For deep lattice potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping for matter waves. The transition from the diffusive regime, characterized by an continuous expansion of the condensate, to the self-trapping regime is accomplished by increasing the atomic density. Due to the corresponding increase of the repulsive atomic interaction the initial expansion stops and the width of the wave packet remains finite. The comparison with a numerical analysis reveals that the effect is due to an inhibition of the site-to-site tunneling induced by the nonlinear phase evolution.
This thesis presents the development of an experimental apparatus to produce Bose-Einstein condensates (BECs) with tunable interparticle interactions. The ability to precisely control the strength of these interactions, and even to switch them from repulsive to attractive, allows one to probe novel regimes of condensate physics, from the collapse of attractively interacting BECs and the formation of solitary matter-waves to the observation of beyond mean-field effects in strongly repulsive condensates. The construction and characterisation of both a single and crossed beam optical dipole trap is presented. In the single beam case we develop a technique allowing the guided transport of atoms along the beam and up to a room-temperature surface; a technique which can be used to evaporatively cool the trapped atomic cloud. We produce Bose-Einstein condensates of 87Rb in the F=1, mF=-1 state in this trap, comparing the effect of beam waist on the evaporation trajectory. In the crossed beam trap Bose-Einstein condensation of 87Rb is realised in three distinct trapping configurations, along with a 1D optical lattice formed by changing the polarisation of the beams. A method of direct cooling of 85Rb atoms in the crossed trap is developed using a magnetic Feshbach resonance to precisely tune both the elastic and inelastic scattering properties of the atoms. The resonance used for this work occurs at 155G in collisions between atoms in the F=2, mF=-2 state of 85Rb. Bose-Einstein condensates of up to 40,000 85Rb atoms are formed in this trap and we demonstrate the presence of tunable interatomic interactions, exploring the collapse phenomenon associated with attractive condensates. By loading the 85Rb condensate into a quasi-1D waveguide we show that stable attractive condensates can be created, taking the form of bright solitary matter-waves. We observe a solitary wave of ~2,000 atoms which propagates, without dispersion, along the waveguide over a distance of ~1.1mm. The particle-like nature of the solitary wave is demonstrated by classical reflection of the wavepacket from a repulsive Gaussian barrier.
We report on the first experimental observation of bright matter wave solitons for 87Rb atoms with repulsive atom-atom interaction. This counterintuitive situation arises inside a weak periodic potential, where anomalous dispersion can be realized at the Brillouin zone boundary. If the coherent atomic wave packet is prepared at the corresponding band edge, a bright soliton is formed inside the gap. The strength of our system is the precise control of preparation and real time manipulation, allowing the systematic investigation of gap solitons.
Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
This dissertation presents a theoretical analysis of methods to manipulate and control the momentum state of coherent matter waves. Of particular interest is the coherent acceleration of a quantum-degenerate atomic system, which, as a direct consequence of the form of the de Broglie wavelength, results in tunable source of matter waves. Such sources are of considerable importance for a number of potential applications in the field of atom optics, including the development of highly sensitive gyroscopes, accelerometers, gravity gradiometers or atom lithography and holography, as well as for potential uses in integrated atom optics. Our basic setup consists of a Bose-Einstein condensate in a moving optical lattice created by a pair of frequency-chirped counterpropagating laser beams acting as a "conveyor belt'' for ultracold atoms. Whereas the acceleration of ultracold but non-condensed atoms in such a lattice was demonstrated earlier, we extend this scheme to the case of Bose-Einstein condensates. As a first step, we investigate the acceleration efficiency for various acceleration rates and nonlinear interaction strengths. We find parameter regimes where efficient acceleration is possible, i.e. all atoms are accelerated to the same velocity and the initially sharp momentum distribution and thus its monochromaticity is preserved. However, in general we identify switch-on effects of the lattice, dynamical loss and nonlinear effects to be responsible for deterioration of the monochromaticity of the condensate: On the one hand, switch-on effects and dynamical loss induce a coupling of the initially populated momentum mode to other modes, thereby distributing the momentum over several modes. On the other hand, the nonlinear release of mean field energy during the acceleration process causes the mode profile itself to broaden, also leading to a contamination of the initial monochromaticity. As a second step, we discuss ways to improve this scheme by removing the restriction of constant accelerations. We employ genetic algorithms to optimize the time-dependent motion of the lattice. We show that with such flexibility, it is possible to achieve a fast and highly efficient coherent acceleration of condensates, even when mean-field effects cannot be neglected. The same scheme also enables the creation of arbitrary coherent superposition states in momentum space. The technique is thus suitable for building highly efficient momentum state beam splitters. In addition to simply accelerating condensates, it is desirable for many potential applications to transport atomic wave packets without dispersion over large distances. This can be achieved by launching bright atomic solitons, where the effects of the nonlinearity counterbalance the dispersion. Placing a Bose-Einstein condensate with repulsive interactions in a lattice, one can create a negative effective mass. Under these circumstances bright and stable soliton solutions exist, so-called gap solitons. After a careful analysis of the soliton properties, we use the tools we developed for condensate acceleration and demonstrate two feasible schemes to excite the solitons. Experimental data released after publication of our results demonstrating the acceleration of Bose-Einstein condensates in moving lattices and the very recent observation of atomic gap solitons indicates that our theoretical analysis was timely and indeed experimentally feasible. As an outlook, we briefly comment on a new direction in the field of atom optics that holds promise for future applications: the use of quantum degenerate Fermi gases. In atomic as well as in optical physics one often encounters situations where there exists a coupling between several modes of a system. Here, we illustrate the "toy model'' of a fermionic coupler where transitions between two internal states are induced by Raman coupling. Due to Fermi statistics and interatomic interactions, this is a simple example of a nonlinear multimode coupler. Investigation of this system consisting of only a few fermions already clearly illustrates the basic differences between bosonic and fermionic dynamics and sheds light on the role of two-body collisions. Understanding the basic mechanisms of this system is a first step towards more sophisticated coherent control of fermionic systems.