Abstract
We demonstrate the self-interference of a single Bose–Einstein condensate on a non-simply connected geometry, focussing on a toroidally trapped ring-shaped condensate. First, we show how the opposite parts of the ring can interfere using the Wigner function representation. Then, using analytical expressions for the time-evolution of a freely expanding ring-shaped condensate with and without a persistent current, we show that the self-interference of the ring-shaped condensate is possible only in the absence of the persistent current. We conclude by proposing an experimental protocol for the creation of ring dark solitons using the toroidal self-interference.
Highlights
Following the pioneering demonstration of interference between two freely expanding Bose-Einstein condensates (BECs) [1], self-interference of a single condensate has been experimentally and numerically observed in hard-wall reflections [2, 3]
These results suggest that if we start with a toroidal condensate at some finite radius and let the ring expand towards the origin, we should observe circular fringes when the opposite and in general different parts of the ring overlap with each other
ring dark solitons (RDSs) have not been experimentally observed in cold atomic quantum liquids, and here, we propose an alternative protocol that involves the use of the toroidal self-interference as a density imprinting mechanism for their creation
Summary
Following the pioneering demonstration of interference between two freely expanding Bose-Einstein condensates (BECs) [1], self-interference of a single condensate has been experimentally and numerically observed in hard-wall reflections [2, 3]. In a self-interference setting, the wavefunction splits up into two (or more) pieces, which travel different paths; subsequently the self-interference arises when both parts are later spatially recombined This process can happen next to a hard-wall potential, as mentioned, whereby the condensate interferes with its reflection. For non-zero radii, on the other hand, we demonstrate a possible experimental way to observe the self-interference by letting the ring expand freely and overlap with itself to produce circular fringes. Based on the toroidal self-interference, we propose a protocol for the experimental creation of ring dark solitons
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