We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.

Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.

We report on the realization of a doublewell potential for Rubidium-87 Bose-Einstein condensates. The experimental setup allows the investigation of two different dynamical phenomena known for this system -Josephson oscillations and self-trapping. We give a detailed discussion of the experimental setup and the methods used for calibrating the relevant parameters. We compare our experimental findings with the predictions of an extended two-mode model and find quantitative agreement.

Bose-Einstein condensates in designed potentials represent a model system for the investigation of nonlinear matter wave dynamics, since both the nonlinearity and the potentials can be very well controlled experimentally. The nonlinearity arising from the atom-atom interaction can be adjusted through the atom number. The potentials can be readily realized by employing the atom-light interaction leading to potentials which are proportional to light intensity. Since the techniques for manipulation of light are very well developed almost arbitrary potentials can be realized. In our experiments we employ the most simple light intensity configurations such as focused laser beam and standing light waves.The first experiment we will discuss deals with the realization of a bright atomic-gap solitonsa paradigm of nonlinear matter wave dynamics. These solitons exist in the presence of weak periodic potentials, which modify the free dispersion relation represented by the well known band structure. Preparing a condensate at the Brillouin zone edge anomalous dispersion can be realized. Thus a bright soliton can be formed since anomalous dispersion can compensate the repulsive atom-atom interaction of 87Rb. The systematic investigations reveal that the realized solitons exhibit the expected dependence of the atom number and the width of the soliton on the strength of the dispersion [1].Our experimental system allows in a very direct way to investigate also the regime of discrete nonlinear systems by just increasing the depth of the periodic potential i.e. increasing the light intensity, which leads to an array of weakly coupled condensates. In this regime also non-spreading wave packets exist, but in contrast to the gap-soliton the localization originates from the local dynamics of few wells at the edge of the wave packet. In our experiments we have observed this new localization process which leads to rectangular wave packetsnonlinear self trapping. We also confirm the predicted scaling behavior of the critical density which has to be surpassed to lead to nonlinear self trapping. Our theoretical model -discrete nonlinear Schrodinger equation with modified nonlinearity due to transverse Thomas Fermi distributioncaptures very well our observation. Furthermore it reveals clearly the importance of the local dynamics near the edges of the non-spreading wave packets [2].Combining a periodic potential with 5pgm period with a harmonic potential realized with a focussed laser beam leads to a well controllable double-well potential. Since our optical imaging system has a resolution of 2.8(2)gm, the population of the individual wells can be imaged in situ and the dynamics of the populations can be studied in real space. If the potentials are switched of and the atomic cloud is observed in time of flight (far field) the expected double slit interference pattem are observed. This allows the deduction of the relative phase between the two condensates and the fill characterization of the dynamics of the wave functions in the two mode approx...