Our experiments aim at exploring fundamental properties of Bose-Einstein condensates and to develop tools for using BECs in atom optical applications. After having realized BEC since 1998, coherent mirrors, beam splitters and phase shifters based on optical dipole potentials were developed in 1999. Subsequently, it was shown theoretically that such phase shifts can be used to generate fundamental excitations like solitons and vortices. With this phase imprinting method we succeeded in generating solitons in Bose-Einstein condensates for the first time. Blue detuned dipole potentials were also used to demonstrate a waveguide for BECs, which should in principle allow for the construction of guided atom interferometers. Furthermore we studied the coherence properties of BECs. In particular, we have demonstrated the existence of significant spatial and temporal fluctuations of the phase in very elongated condensates for the first time. Our most recent measurements study disordered 1D optical lattices. We superimpose a randomly structured disorder pattern radially onto our 1D optical lattice and investigate the ground state properties of BEC in this combined optical potential.
The coherence properties of Bose-Einstein condensates are essential for both the conceptual understanding of BEC and their use in many promising applications like atom lasers and interferometers. In photon optics, the properties of lasers are dramatically different from those of thermal light sources due to their coherence. In the same way the coherence properties distinguish Bose-Einstein condensates from thermal atomic distributions.
Because of their central role the coherence properties have attracted a lot of theoretical and experimental interest since the first realization of BEC in atomic gases in 1995. In particular, high contrast interference between two independent BECs was observed confirming the long-range coherence [1]. Furthermore, spectroscopic [2] and interferometric [3] methods and atom laser outcoupling [4] have been used to quantitatively determine the phase coherence properties. All these experiments were consistent with a uniform phase across the condensate.
However, in low dimensional systems the situation drastically changes. Since the 1960's it is theoretically known that no Bose-Einstein condensation occurs in homogeneous (i.e. untrapped) Bose gases in 1D (even for T=0) and in 2D for T>0. The absence of BEC in these systems is expressed by the Mermin-Wagner-Hohenberg-Theorem [5] and is caused by long-wavelength fluctuations of the phase, which destroy the long-range coherence. Recently, it has been predicted that such temporal and spatial fluctuations of the phase caused by thermal excitations of the low energy modes of the condensate also occur in trapped 1D and even in strongly elongated 3D-condensates [6].
The existence of phase fluctuations was first demonstrated by our group using a ballistic expansion method. It was observed that depending on the system parameters ballistically expanded condensates show pronounced stripes in their density distribution. We have shown that these stripes originate from phase fluctuations within the trapped condensate and therefore can be used to measure those fluctuations. The typical distance over which the coherence is lost is called phase coherence length. This length can be much smaller than the condensate length. Nevertheless phase fluctuating condensates locally behave like pure condensates (as long as the phase coherence length exceeds the healing length) and therefore are called 'quasicondensates'. In particular, the theoretical description of such condensates is based on the prediction that density fluctuations are suppressed for the trapped condensate. We have verified this suppression by measuring the release energy.
In a further set of measurements we have used an interferometric scheme based on Bragg-diffraction pulses to directly compare the phases at different positions within the condensate. In both output ports of the atom interferometer we constructed two copies of the original condensates. They are superposed with a variable spatial displacement d. Since the measured intensity crucially depends on the phase imprinted by the interferometer, a measurement of the interferometric contrast ('visibility') suffers from all uncontrolled effects which affect this global phase. Therefore we have developed a new method which is based on intensity correlations. This method is in many respects analogous to the Hanbury-Brown-Twiss stellar interferometer. In the same way as their interferometer is insensitive to atmospheric fluctuations, our method is not affected by variations of the phase imprinted by the interferometer. With this method we succeeded in measuring the spatial correlation function of phase fluctuating BECs. This function directly yields the phase coherence length. The theoretically expected functional form and phase coherence length were verified.
With the help of optical lattices it is possible to investigate effects traditionally related to condensed matter physics. The perfect periodicity of the optical lattice and the experimental control over the lattice depth and spacing make optical lattices to a valuable tool of modern atom physics. We create a one dimensional optical lattice by retro reflection of a Titanium Saphire laser at 825nm along the axial direction of the condensate. The resulting standing wave creates a lattice structure of intensity maxima and minima. Due to the AC-Stark effect the atoms feel an attractive potential at the intensity maxima. The condensate in the optical lattice can be described by Bloch functions analogous to solid state physics. The properties of the sample can be investigated in time of flight measurements. The spatial periodicity of the atoms in the lattice potential causes discrete peaks in the momentum distribution of the atom at 2 ћk and higher orders, as it can be seen in the figure. Shown are time of flight measurements (fixed time for all pictures) of oscillations in the momentum distribution.
The perfect periodicity of the lattice is disturbed by superimposing a randomly structured pattern radially onto the condensate. This changes the ground state of the lattice gas. The atoms have to adjust to the additional disordered potential and the resulting increase in mean field energy causes an according increase of the width of the central peak, as shown in the picture beneath.
