Avoiding infrared catastrophes in trapped Bose-Einstein condensates

Abstract

This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in "cigar-shaped" (1D) attractive BECs and the transverse instability of dark solitons in "pancake" (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to "engineer" the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior.

Dark-soliton dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential

“…The snake stability of dark solitons of superfluid Fermi gases in the unitarity limit can be studied by monitoring the evolution of a standing dark soliton created at the trap center [52][53][54][55][56]. The development of the snake instability and the concomitant vortex rings for a wide range of the numbers of atom pairs with λ = 6.5 are displayed in Fig.4 where the superfluid density is depleted, and so the slice of the vortex ring appears as two dark spots separated vertically.…”

“…Dark solitons have 1D character, which are stable in the quasi-1D regime, but feature a long-wavelength transverse instability known as the "snake instability" [52][53][54][55][56], when extended into higher dimensions. The snake instability originates from the transfer of the soliton kinetic energy to the transverse modes parallel to the soliton nodal plane.…”

“…The snake instability originates from the transfer of the soliton kinetic energy to the transverse modes parallel to the soliton nodal plane. Generally dark solitons undergo a snake deformation, causing the nodal plane collapse into vortex rings [54][55][56] in 3D (or vortex-antivortex pairs in two dimensions [53]). For atomic BECs, it has been shown that this instability leads to a strong bending of the nodal plane, which breaks down into vortex rings and sound waves, as experimentally observed [57,58].…”

Pattern Forming Dynamical Instabilities of Bose–einstein Condensates

“…Note that in terms of real physical units, the above mentioned critical value of Ω may correspond, e.g., to a weakly interacting 87 Rb pancake condensate, containing ≈ 10 3 atoms, confined in a trap with ω r = 2π × 5Hz and ω z = 2π × 50Hz. This condition was numerically tested in 88 and was found to be an overestimate of the critical trapping frequency for the transverse instability, of Ω cr ≈ 0.31. It was also found in 88 that for 0.18 Ω 0.31, while the stripe was dynamically unstable, there is not sufficient space for the instability-induced vortices to fully develop; as a result, after their formation, they subsequently recombine and disappear (cf.…”

“…In such cases, a simple criterion, involving physical parameters of a trapped condensate, for the suppression (or the onset) of the MI would be useful, especially for relevant experiments. As proposed recently in 88 , one can derive such a criterion in terms of the magnetic trap strength (which controls the size and the number of atoms of the condensate).…”