Phase Imprinting in Equilibrating Fermi Gases: The Transience of Vortex Rings and Other Defects

Abstract

We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases which are in good agreement with recent, independent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase imprinting tilt angle, and illustrate their dramatic effects. The former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines, as appears consistent with recent experimental claims. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.

Generic equilibration dynamics of planar defects in trapped atomic superfluids

“…Indeed, there has been significant controversy and debate over the characterization and decay processes of various defects, notably those associated with a phase imprint in which ∆Φ ∼ π. There the original defect was thought to be a heavy soliton [5], later a vortex ring [7], and still later, as was consistent with predictions from some of our co-authors [8], established to be a solitonic vortex [6]. Similarly, defects formed via the Kibble-Zurek mechanism, using a temperature quench across the BoseEinstein condensation (BEC) transition, were originally mis-identified as solitons [9] and later determined to be solitonic vortices [10].…”

“…These studies address only the condensate dynamics and do not include the effects of fermionic excitations. Considerable support for these numerics comes from previous related studies [8] of phase imprinting near ∆Φ = π where most aspects of the experiments [6] confirmed the earlier predictions. In such simulations it is important to avoid artificially symmetric situations which unphysically stabilize long-lived defects.…”

“…Similarly, defects formed via the Kibble-Zurek mechanism, using a temperature quench across the BoseEinstein condensation (BEC) transition, were originally mis-identified as solitons [9] and later determined to be solitonic vortices [10]. It should be noted that while this earlier work [8] with ∆Φ ∼ π is a special case leading to anomalously long-lived defects, nevertheless, the earlier stages of equilibration in this case too, are addressed by the defect sequence we report here.…”

“…Similar experiments have led to the observation of a variety of defects [1,[16][17][18], while other studies engineered localized excitations through phase imprinting [4][5][6][19][20][21]. The theory associated with these experiments has suggested that solitons, or vortices or vortex rings (in some combination or sequentially) are created in the process [4,[6][7][8][22][23][24][25].…”

“…We use a dimensionless fluctuation T χ temperature very close to the zero-temperature limit (well below a nanokelvin for cold gas systems) [32]. We stress that the inclusion of noise in our numerical approach is a significant addition [8]. This avoids unphysical effects due to spatial symmetries present in many other simulations [3,7,24].…”