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Register a new userFormation of granular structures in trapped Bose-Einstein condensates under oscillatory excitations
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We present experimental observations and numerical simulations of nonequilibrium spatial structures in a trapped Bose-Einstein condensate subject to oscillatory perturbations. In experiment, first, there appear collective excitations, followed by quantum vortices. Increasing the amount of the injected energy leads to the formation of vortex tangles representing quantum turbulence. We study what happens after the regime of quantum turbulence, with increasing further the amount of injected energy. In such a strongly nonequilibrium Bose-condensed system of trapped atoms, vortices become destroyed and there develops a new kind of spatial structure exhibiting essentially heterogeneous spatial density. The structure reminds fog consisting of high-density droplets, or grains, surrounded by the regions of low density. The grains are randomly distributed in space, where they move. They live sufficiently long time to be treated as a type of metastable objects. Such structures have been observed in nonequilibrium trapped Bose gases of $^{87}$Rb, subject to the action of alternating fields. Here we present experimental results and support them by numerical simulations. The granular, or fog structure is essentially different from the state of wave turbulence that develops after increasing further the amount of injected energy.
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This review explores the dynamics and the low-energy excitation spectra of Bose-Einstein condensates (BECs) of interacting bosons in external potential traps putting particular emphasis on the emerging many-body effects beyond mean-field descriptions. To do so, methods have to be used that, in principle, can provide numerically exact results for both the dynamics and the excitation spectra in a systematic manner. Numerically exact results for the dynamics are presented employing the well-established multicongurational time-dependent Hartree for bosons (MCTDHB) method. The respective excitation spectra are calculated utilizing the more recently introduced linear-response theory atop it (LR-MCTDHB). The latter theory gives rise to an, in general, non-hermitian eigenvalue problem. The theory and its newly developed implementation are described in detail and benchmarked towards the exactly-solvable harmonic-interaction model. Several applications to BECs in one- and two-dimensional potential traps are discussed. With respect to dynamics, it is shown that both the out-of-equilibrium tunneling dynamics and the dynamics of trapped vortices are of many-body nature. Furthermore, many-body effects in the excitation spectra are presented for BECs in different trap geometries. It is demonstrated that even for essentially-condensed systems, the spectrum of the lowest-in-energy excitations computed at the many-body level can differ substantially from the standard mean-field description. In general, it is shown that bosons carrying angular momentum are more sensitive to many-body effects than bosons without. These effects are present in both the dynamics and the excitation spectrum.
The problem of understanding how a coherent, macroscopic Bose-Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly-interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation, and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases.
We report on the creation of three-vortex clusters in a $^{87}Rb$ Bose-Einstein condensate by oscillatory excitation of the condensate. This procedure can create vortices of both circulation, so that we are able to create several types of vortex clusters using the same mechanism. The three-vortex configurations are dominated by two types, namely, an equilateral-triangle arrangement and a linear arrangement. We interpret these most stable configurations respectively as three vortices with the same circulation, and as a vortex-antivortex-vortex cluster. The linear configurations are very likely the first experimental signatures of predicted stationary vortex clusters.
We investigate the occurrence of rotons in a quadrupolar Bose-Einstein condensate confined to two dimensions. Depending on the particle density, the ratio of the contact and quadrupole-quadrupole interactions, and the alignment of the quadrupole moments with respect to the confinement plane, the dispersion relation features two or four point-like roton minima, or one ring-shaped minimum. We map out the entire parameter space of the roton behavior and identify the instability regions. We propose to observe the exotic rotons by monitoring the characteristic density wave dynamics resulting from a short local perturbation, and discuss the possibilities to detect the predicted effects in state-of-the-art experiments with ultracold homonuclear molecules.
Generation of different nonequilibrium states in trapped Bose-Einstein condensates is studied by numerically solving nonlinear Schrodinger equation. Inducing nonequilibrium states by shaking the trap, the following states are created: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.
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