From Coherent Modes to Turbulence and Granulation of Trapped Gases

Abstract

The process of exciting the gas of trapped bosons from an equilibrium initial state to strongly nonequilibrium states is described as a procedure of symmetry restoration caused by external perturbations. Initially, the trapped gas is cooled down to such low temperatures, when practically all atoms are in Bose-Einstein condensed state, which implies the broken global gauge symmetry. Excitations are realized either by imposing external alternating fields, modulating the trapping potential and shaking the cloud of trapped atoms, or it can be done by varying atomic interactions by means of Feshbach resonance techniques. Gradually increasing the amount of energy pumped into the system, which is realized either by strengthening the modulation amplitude or by increasing the excitation time, produces a series of nonequilibrium states, with the growing fraction of atoms for which the gauge symmetry is restored. In this way, the initial equilibrium system, with the broken gauge symmetry and all atoms condensed, can be excited to the state, where all atoms are in the normal state, with completely restored gauge symmetry. In this process, the system, starting from the regular superfluid state, passes through the states of vortex superfluid, turbulent superfluid, heterophase granular fluid, to the state of normal chaotic fluid in turbulent regime. Both theoretical and experimental studies are presented.Comment: Latex file, 25 pages, 4 figure

Quantum turbulence in trapped atomic Bose–Einstein condensates

“…Among the particular aspects of the granular phase we can distinguish the following: (i) it appears as a heterogeneous phase, with grains of high density surrounded by a rarefied gas -both components however are formed by the [194]. same atoms; (ii) grains are randomly distributed in space; (iii) the grains have well defined phases despite the lack of vortices (zero circulation), which means that the system is overall coherent but not locally, since the phases are not the same among the grains.…”

Realization of inverse Kibble–Zurek scenario with trapped Bose gases

“…The modulation amplitude and time can be varied in a wide range, thus, varying the energy injected into the system. The injected energy per atom can be evaluated [31,32] as…”

Strongly Nonequilibrium Bose-Condensed Atomic Systems

“…Keeping in mind the setup of experiments [14][15][16]20] with 87 Rb, we have the trap characteristics…”

“…Energy is injected into the system by modulating the trapping potential as described in Refs. [14,15,16,20]. Injecting energy into the trap produces a sequence of nonequilibrium states that we have studied experimentally as well as by computer simulations for the order-function equation (1), adding there the attenuation by replacing in Eq.…”

“…Instead, the increasing number of vortices forms a random tangle corresponding to quantum turbulence [10][11][12][13]. This vortex turbulence of trapped atoms has been observed in three-dimensional traps [14][15][16] as well as in quasi-two-dimensional traps [17], and is summarized in the review articles [18][19][20].…”