Static and dynamic properties of shell-shaped condensates

Abstract

Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.arXiv:1712.04428v2 [cond-mat.quant-gas]

Ground state and collective excitations of a dipolar Bose-Einstein condensate in a bubble trap

“…Morover, these parameters are in the range of those used in the TSL of Ref. 29 in order to allow for a direct comparison, where possible, in the vanishing dipole-dipole interaction limit. Therefore, the variational parameters of interest in the thin-shell limit are contained in the angular part |h(θ , φ )| 2 , which we proceed to optimize numerically by minimizing the total energy.…”

The Bose-Einstein Condensate and Cold Atom Laboratory

“…Laser cooling and the creation of Bose-Einstein condensates (BECs) [1] have opened up the field of dilute ultracold quantum gases. These systems enable the study of fundamental aspects of quantum mechanics, such as the evolution of matter waves [2], the transition of quantum statistic to classical thermodynamics [3], the impact of the dimensionality and topology of the gases [4] and may also probe the interface between quantum mechanics In the absence of any gravitational sag, the trapping potentials perfectly overlap, while in a gravitational field the two species experience a differential sag and the atomic clouds are (partially) separated. In addition, the traps have to be steeper than in microgravity to prevent the atoms from falling out of the confinement.…”

Shell potentials for microgravity Bose–Einstein condensates

“…13 More recent theoretical work has focused on the collective modes of shell condensates, and the signatures of a condensate transitioning to a hollow shell from a conventional topology. 14,15 Interesting effects are predicted to occur when a shell condensate is released into time-of-flight expansion; different regions of the shell BEC will interfere with each other, resulting in spatial matter-wave interference patterns that are quite sensitive to the shape of the shell potential and (via mean-field interactions) the number of atoms in the condensate. 16 Recent work has also been done exploring the basic physics of BEC on the surface of a sphere.…”