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Register a new userExcitations of Bose-Einstein condensates in a one-dimensional periodic potential
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We report on the experimental investigation of the response of a three-dimensional Bose-Einstein condensate (BEC) in the presence of a one-dimensional (1D) optical lattice. By means of Bragg spectroscopy we probe the band structure of the excitation spectrum in the presence of the periodic potential. We selectively induce elementary excitations of the BEC choosing the transferred momentum and we observe different resonances in the energy transfer, corresponding to the transitions to different bands. The frequency, the width and the strength of these resonances are investigated as a function of the amplitude of the 1D optical lattice.
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We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as $ell(omega)sim 1/omega^alpha$. We show that the well known result $alpha=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $alpha$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $alpha=1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.
The cubic nonlinear Schrodinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrodinger equation nor in the integrable nonlinear Schrodinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schrodinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.
Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schrodinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrodinger equation nor in the integrable nonlinear Schrodinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.
We report on measurements of resonantly enhanced tunneling of Bose-Einstein condensates loaded into an optical lattice. By controlling the initial conditions of our system we were able to observe resonant tunneling in the ground and the first two excited states of the lattice wells. We also investigated the effect of the intrinsic nonlinearity of the condensate on the tunneling resonances.
We investigate both experimentally and theoretically disorder induced damping of Bloch oscillations of Bose-Einstein condensates in optical lattices. The spatially inhomogeneous force responsible for the damping is realised by a combination of a disordered optical and a magnetic gradient potential. We show that the inhomogeneity of this force results in a broadening of the quasimomentum spectrum, which in turn causes damping of the centre-of-mass oscillation. We quantitatively compare the obtained damping rates to the simulations using the Gross-Pitaevskii equation. Our results are relevant for high precision experiments on very small forces, which require the observation of a large number of oscillation cycles.
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