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Register a new userHeavily Damped Motion of One-Dimensional Bose Gases in an Optical Lattice
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We study the dynamics of strongly correlated one-dimensional Bose gases in a combined harmonic and optical lattice potential subjected to sudden displacement of the confining potential. Using the time-evolving block decimation method, we perform a first-principles quantum many-body simulation of the experiment of Fertig {it et al.} [Phys. Rev. Lett. {bf 94}, 120403 (2005)] across different values of the lattice depth ranging from the superfluid to the Mott insulator regimes. We find good quantitative agreement with this experiment: the damping of the dipole oscillations is significant even for shallow lattices, and the motion becomes overdamped with increasing lattice depth as observed. We show that the transition to overdamping is attributed to the decay of superfluid flow accelerated by quantum fluctuations, which occurs well before the emergence of Mott insulator domains.
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We discuss two complementary problems: adiabatic loading of one-dimensional bosons into an optical lattice and merging two one-dimensional Bose systems. Both problems can be mapped to the sine-Gordon model. This mapping allows us to find power-law scalings for the number of excitations with the ramping rate in the regime where the conventional linear response approach fails. We show that the exponent of this power law is sensitive to the interaction strength. In particular, the response is larger, or less adiabatic, for strongly (weakly) interacting bosons for the loading (merging) problem. Our results illustrate that in general the nonlinear response to slow relevant perturbations can be a powerful tool for characterizing properties of interacting systems.
Low-dimensional systems are beautiful examples of many-body quantum physics. For one-dimensional systems the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regime. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1d Bose gases. Dynamic splitting is used to create two 1d systems in a phase coherent state. The time evolution of the coherence is revealed in local phase shifts of the subsequently observed interference patterns. Completely isolated 1d Bose gases are observed to exhibit a universal sub-exponential coherence decay in excellent agreement with recent predictions by Burkov et al. [Phys. Rev. Lett. 98, 200404 (2007)]. For two coupled 1d Bose gases the coherence factor is observed to approach a non-zero equilibrium value as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase locking two lasers by injection. The non-equilibrium dynamics of superfluids plays an important role in a wide range of physical systems, such as superconductors, quantum-Hall systems, superfluid Helium, and spin systems. Our experiments studying coherence dynamics show that 1d Bose gases are ideally suited for investigating this class of phenomena.
We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time of flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii or Bogoliubov type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behaviour.
We study equilibrium properties of Bose-Condensed gases in a one-dimensional (1D) optical lattice at finite temperatures. We assume that an additional harmonic confinement is highly anisotropic, in which the confinement in the radial directions is much tighter than in the axial direction. We derive a quasi-1D model of the Gross-Pitaeavkill equation and the Bogoliubov equations, and numerically solve these equations to obtain the condensate fraction as a function of the temperature.
In this work we analyze the dynamical behavior of the collision between two clouds of fermionic atoms with opposite spin polarization. By means of the time-evolving block decimation (TEBD) numerical method, we simulate the collision of two one-dimensional clouds in a lattice. There is a symmetry in the collision behaviour between the attractive and repulsive interactions. We analyze the pair formation dynamics in the collision region, providing a quantitative analysis of the pair formation mechanism in terms of a simple two-site model.
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