Rotational tuning of the dipole-dipole interaction in a Bose gas of magnetic atoms

Abstract

We investigate the dynamics of a Bose-Einstein condensate of magnetic atoms in which the dipoles are rotated by an external magnetic field. The time-averaged dipole-dipole interaction between the atoms is effectively tuned by this rotation, however recent experimental and theoretical developments show that dynamic instabilities emerge that may cause heating. We present simulations of a realistic tuning sequence in this system, and characterize the system behavior and the emergence of instabilities. Our results indicate that the instabilities develop more slowly as the rotation frequency increases, and indicate that experiments with tuned dipole-dipole interactions should be feasible.

Vortex lattice formation in dipolar Bose-Einstein condensates via rotation of the polarization

“…In this system the properties of Branch II (α < 0 ∀ Ω ∈ [Ω b , ∞)) have been studied in previous investigations into the effective rotational tuning of dd [62,64]. Instead we are interested in Branch I of the stationary solutions (α ≥ 0) in the presence of a spherically-symmetric trap, that is, γ = 1.…”

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

“…However, in Sec. V we find that the dynamical instabilities that have previously been demonstrated to plague the TF stationary states, when the in-plane-aligned dipole polarization rotates rapidly [37,38], are also present for almost all dipole tilting angles whenever the atomic dipole moment is finite. In the TF regime we also find that the dimensionless chemical potential of the stationary solution predicted by the timeaveraged dipolar interaction is at least 10 times higher than the in-plane trapping frequency.…”

“…Similarly, if the final value of θ is less than π/2, this branch does not extend to infinity but terminates at the rotation frequency = (1 + γ )ω ⊥ and any rotation frequency tuning procedure would need to avoid this terminal. Instead, if the quasiadiabatic ramp-up of θ from zero is initialized at values of higher than b2 , the stationary solution branch that are accessed by the condensate is always branch V [38]. As such, we predict that at least three out of the five stationary solution branches may readily be accessed through parameter tuning protocols; it may not be possible to access branches II and IV via such procedures.…”

“…Subsequent theoretical studies addressing this unexpectedly short condensate lifetime proposed that a dynamical instability associated with the small, but nonetheless finite, time-dependent effects at high rotation frequency were responsible for an exponential deviation from the ground state of the Thomas-Fermi hydrodynamic equations ( 1) and (2) over long timescales [37,38]. However, while it has been possible to simulate this scenario via direct solution of the dGPE for a magnetic field aligned at any given value of θ [38], the complementary semi-analytical methods are only applicable when the magnetic field is aligned along one of the trap's principal axes at t = 0, i.e., θ = 0 or θ = π [34,37].…”

“…Since the time-averaged interaction is dependent on the angle made by the rotating dipole polarization with respect to the rotation axis, experimentalists are able to effectively tune the dipolar interaction strength, and sign, by altering the orientation of the rapidly rotating magnetic field. However, the experimental realization of the rotational tuning scheme reported a significantly diminished condensate lifetime, and subsequent theoretical analyses of dipolar BECs polarized in the plane orthogonal to the rotation axis demonstrated that dynamical instabilities seeded by the rotation may have been a contributing factor to this unexpectedly short lifetime [37,38].…”