Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

Abstract

We consider, by means of the variational approximation ͑VA͒ and direct numerical simulations of the Gross-Pitaevskii ͑GP͒ equation, the dynamics of two-dimensional ͑2D͒ and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive ͑but not too large͒. Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

“…Thus the inclusion of three-body interaction seems to increase the stability of the condensates. The stability of trapless BEC with two-body interaction for constant (slowly varying) and oscillatory (rapidly varying) part has been already explored [28,32,33]. However, to the best of our knowledge, the effect on the inclusion of three-body interaction has not been studied in trapless BEC.…”

Nonstationary excitations in Bose–Einstein condensates under the action of periodically varying scattering length with time dependent frequencies

“…In Bose-Einstein conden-sates it is experimentally feasible to vary the scattering length by either magnetically or optically inducing a Feshbach resonance [4,14]. Earlier works on Bose-Einstein condensation report the periodic modulation with constant frequency of scattering length [5,7,8,9]. Along these lines, it is of potential interest to understand the dynamics of Bose-Einstein condensates under the action of periodically varying scattering length with slowly varying frequency.…”

“…According to the variational method we assume the Gaussian wave function in the form [7,8,9,19,20,21] φ(r, t) = A(t) exp − r 2 2a(t) 2 + ib(t) 2 r 2 2 + iδ(t) ,…”

“…In particular, temporal periodic modulation of scattering length by exploiting a Feshbach resonance is given a central importance in recent times. Earlier studies show that, in certain circumstances, periodically varying scattering length can stabilize the collapsing condensate [6,7,8,9]. However, very recently it has been shown that for a sign alternating nonlinearity an increase in the frequency of oscillations accelerates collapse [10].…”

“…The properties of the condensate wave function is usually described by a mean field Gross-Pitaevskii equation [3]. For the past couple of years, there has been increased interest in studying the properties of Bose-Einstein condensates with time varying trap potentials and scattering lengths both experimentally and theoretically [4,5,7,8,9]. In particular, temporal periodic modulation of scattering length by exploiting a Feshbach resonance is given a central importance in recent times.…”