Stationary states, dynamical stability, and vorticity of Bose-Einstein condensates in tilted rotating harmonic traps

Abstract

We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semianalytical prediction of their dynamical instability at high rotation frequencies against collective modes arising from environmental perturbations. Comparing the stationary states to direct simulations of the Gross-Pitaevskii equation, we predict the nucleation of quantum vortices in the dynamically unstable rotational regime. These vortex lines are aligned along the rotation axis despite the tilting of the rotating trap although the background density profile is tilted with respect to the trapping and rotation axes.

Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate

“…In line with the stationary solutions for the analogous nondipolar system of a nondipolar BEC in an rotating, tilted harmonic trap, we find that the solutions of Eqs. ( 21) and ( 22) are given by the TF density n TF (r) and the quadrupolar phase profile v TF (r), which are given by [41]…”

“…(21) and (22). However, it is not necessary to include a term proportional to ∇(zx) since the projection of upon theỹ axis is zero [41]. By substituting Eqs.…”

“…Equations ( 25) and ( 26) are equivalent to the definitions for the respective velocity amplitudes of the stationary states of a nondipolar BEC, in the TF regime, that is trapped by a tilted, rotating harmonic trap [41]. This quadrupolar condensate phase profile also coincides with the classical velocity potential of an inviscid fluid inside an ellipsoidal container rotating about a nonprincipal axis [57][58][59]; the dipolar BEC in a tilted, rotating frame represents a dipolar, quantum analog of the classical hydrodynamic system.…”

“…We work in the interaction-dominated Thomas-Fermi (TF) regime [40] and, in Sec. III, we merge the formalisms introduced in distinct studies for analyzing in-plane dipole rotation in dipolar BECs [37,39] and tilted rotation of the harmonic confinement of nondipolar BECs [41] to obtain self-consistency relations that completely specify the stationary solutions of this system. In Sec.…”

Spontaneous Formations of Dynamical Steady States in Polariton Condensates

“…1 to numerically simulate the dynamics of polariton BEC by a time-splitting Fourier pseudospectral method. Such an algorithm is unconditionally stable, and of spectral accuracy in space and second-order accuracy in time [35], and has been widely used to study dynamics of vortices and solitons in BECs [36][37][38]. In the following discussion, all results are tested for convergence and stability.…”