Solitons are among the most distinguishing fundamental excitations in a wide range of non-linear systems such as water in narrow channels, high speed optical communication, molecular biology and astrophysics. Stabilized by a balance between spreading and focusing, solitons are wavepackets, which share some exceptional generic features like form-stability and particle-like properties. Ultracold quantum gases represent very pure and well-controlled non-linear systems, therefore offering unique possibilities to study soliton dynamics. Here we report on the first observation of long-lived dark and dark-bright solitons with lifetimes of up to several seconds as well as their dynamics in highly stable optically trapped 87 Rb Bose-Einstein condensates. In particular, our detailed studies of dark and dark-bright soliton oscillations reveal the particle-like nature of these collective excitations for the first time. In addition, we discuss the collision between these two types of solitary excitations in Bose-Einstein condensates. The dynamics of non-linear systems plays an essential role in nature, ranging from strong non-linear interactions of elementary particles to non-linear wave phenomena in oceanography and meteorology. A special class of non-linear phenomena are solitons with interesting particle and wave-like behaviour. Reaching back to the observation of "waves of translation" in a narrow water channel by Scott-Russell in 1834 [1], solitons are nowadays recognized to appear in various systems as different as astrophysics, molecular biology and non-linear optics [2]. They are characterized as localized solitary wavepackets that maintain their shape and amplitude caused by a self-stabilization against dispersion via a non-linear interaction. While an early theoretical explanation of this non-dispersive wave phenomenon was given by Korteweg and de Vries in the late 19th century it was not before 1965 that numerical simulations of Zabusky and Kruskal theoretically proved that these solitary waves preserve their identity in collisions [3,4]. This revelation led to the term "soliton" for this type of collective excitation. Nowadays solitons are a very active field of research in many areas of science. In the field of non-linear optics they attract enormous attention due to applications in fast data transfer. Bose-Einstein condensates (BEC) of weakly interacting atoms offer fascinating possibilities for the study of nonlinear phenomena, as they are very pure samples of ultracold gases building up an effective macroscopic wave function of up to mm size. Non-linear effects like collective excitations [5], four-wave mixing [6] and vortices [7,8] have been studied, to name only a few examples. The existence and some fundamental properties of solitons have been deduced from few experiments employing ultra-cold quantum gases. Bright solitons, characterized as non-spreading matter-wave packets, have been observed in BEC with attractive interaction [9,10,11] where they represent the ground state of the system. In a repulsively...

We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of 87 Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular we measure conversion rates in the range of 10 −12 cm 3 s −1 for spin changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10 −13 cm 3 s −1 for hyperfine-changing collisions. From our data we observe a polar behavior in the F=2 ground state of 87 Rb, while we measure the F=1 ground state to be ferromagnetic. Furthermore we see a magnetization for condensates prepared with non-zero total spin.PACS numbers: 03.75. Mn, 34.50.Pi, 03.75.Hh The investigation of atomic spin systems is central for the understanding of magnetism and a highly active area of research e.g. with respect to magnetic nanosystems, spintronics and magnetic interactions in high T c superconductors. In addition entangled spin systems in atomic quantum gases show intriguing prospects for quantum optics and quantum computation [1,2,3,4,5]. Bose-Einstein condensates (BEC) of ultra-cold atoms offer new regimes for studies of collective spin phenomena [6,7,8,9,10,11,12,13]. BECs with spin degree of freedom are special in the sense that their order parameter is a vector in contrast to the "common" BEC where it is a scalar. Recent extensive studies have been made in optically trapped 23 Na in the F=1 state [10,11,12,13]. In addition evidence of spin dynamics was demonstrated in optically trapped 87 Rb in the F=1 state [14]. There is current interest in extending the systems under investigation to F=2 spinor condensates [15,16,17,18,19,20], which add significant new physics. F=2 spinor condensates offer richer dynamics, an additional magnetic phase, the so-called cyclic phase [16,18], as well as intrinsic connections to d-wave superconductors [21].In this letter we present first studies of optically trapped 87 Rb F=2 spinor condensates. We measure rates for spin changing collisions for different channels within the F=2 manifold and discuss the steady state for various initial conditions. Additionally we observe and discuss the thermalization of dynamically populated m F condensates. We also present measurements of spin-dependent hyperfine decay rates of the F=2 state in 87 Rb, as a key to further understanding the intensively studied collisional properties of 87 Rb [22,23].Our experimental setup consists of a compact double MOT apparatus which produces magnetically trapped 87 Rb Bose-Einstein condensates containing 10 6 atoms in the F=2, m F = 2 state. To confine the atoms independently of their spin state they are subsequently transferred into a far detuned optical dipole trap. It is operated at 1064 nm generating trapping frequencies of typically 2π × 891 Hz vertically, 2π × 155 Hz horizontally and 2π × 21.1 Hz along the beam direction. After transfer we further cool the ensemble for 500 ms by selective parametric excitation [24] resulting in ...

Over the last years the exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand for experimental environments with non-cubic lattice geometries. In this paper we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step the superfluid-Mott insulator (SF-MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this we study the physics of spinor Bose-Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF-MI transition. Our results suggest that below the SF-MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly this opens new perspectives for a lattice driven tuning of a spin dynamics resonance occurring through the interplay of quadratic Zeeman effect and spin-dependent interaction. We finally discuss further lattice configurations which can be realized with our setup.

We present experimental data showing the head-on collision of dark solitons generated in an elongated Bose-Einstein condensate. No discernable interaction can be recorded, in full agreement with the fundamental theoretical concepts of solitons as mutually transparent quasiparticles. Our soliton generation technique allows for the creation of solitons with different depths; hence, they can be distinguished and their trajectories be followed. Simulations of the 1D-Gross-Pitaevskii equation have been performed to compare the experiment with a mean-field description.

We present measurements and a theoretical model for the interplay of spin dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features like quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F = 1 87 Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to thermal equilibration.PACS numbers: 03.75. Mn,03.75.Gg,32.60.+i Multi-component Bose-Einstein condensates with spin degree of freedom, the so called spinor condensates, are experiencing rapidly growing attention. These ultra-cold quantum gas systems are interesting in several respects, e.g. they show intriguing static and dynamic magnetic properties [1,2,3], they represent a well controlled thermodynamic model system [4,5] and they promise unique insights into mesoscopic multi-component entanglement and decoherence processes [6].Pioneering experiments on F = 1 23 Na spinor condensates, found to be anti-ferromagnetic, and quasispin-1/2 systems in 87 Rb have shown fascinating demixing dynamics, metastability and domain formation processes [3,7]. Recently the spinor systems under study have been extended to 87 Rb, which behaves ferromagnetic in the F = 1 state [8,9] and anti-ferromagnetic in F = 2 [8]. In particular, these experiments also showed spinor oscillations and shifted the research interest towards dynamic spin conversion effects. Recent studies have demonstrated a magnetic field dependence of the oscillation amplitude and frequency [10,11,12], which was also theoretically assigned to an interesting resonance phenomenon [13]. The coherent evolution in these experiments at short timescales is opposed to the incoherent thermodynamic behavior at long timescales, e.g. decoherence driven cooling [4], constant temperature BEC [5] or temperature driven magnetization [11].The coherent and thermodynamic regime are conceptually very different, as the first relies on the assumption of each atom in the ensemble being in the same superposition state, while there are presumably different and independent ensembles for each spin state in the second regime, i.e. here an atom is either in states |F = 1, m F = ±1 or |F = 1, m F = 0 . It is still under discussion, how and at which point the crossover from the "pure state" ensemble to a "mixed state" arises and how this is connected to decoherence and dephasing mechanisms in spinor systems. This question can be generalized to the understanding of decoherence in arbitrary multicomponent systems and its dependence on the number of constituents, which might have important consequences for quantum information theory. So far studies on the relative phases of different components have only been performed in quasi-spin 1/2 systems [4,14,15] based on the preparation of mixtures with well defined phase, while investigations on spinor systems were essentially restricted to population-based state preparation without phase control.In this paper we ...