Multiresonant Spinor Dynamics in a Bose-Einstein Condensate

We analyze the spinor dynamics of a ${}^{87}\mathrm{Rb}$ $F=2$ condensate initially prepared in the $m_F=0$ Zeeman sublevel. We show that this dynamics, characterized by the creation of correlated atomic pairs in $m_F=\pm 1$, presents an intriguing multiresonant magnetic-field dependence induced by the trap inhomogeneity. This dependence is directly linked to the most unstable Bogoliubov spin excitations of the initial $m_F=0$ condensate, showing that, in general, even a qualitative understanding of the pair-creation efficiency in a spinor condensate requires a careful consideration of the confinement.

Figure 1

Illustration of the resonances in the spinor dynamics of a Bose-Einstein condensate initially in the $|m_F=0⟩$ state. For certain magnetic fields, the production efficiency of atoms in the $|m_F=\pm 1⟩$ states is resonantly enhanced due to the excess energy released by the quadratic Zeeman effect. The column densities of all three Zeeman components in the plane of strongest confinement are shown in (a) and (c) in both a 3D and a density plot. Note that condensates in the $|m_F=\pm 1⟩$ states are created in characteristic spatial modes depending on the particular resonance.

Figure 2

(a) Fraction of atoms transferred into $|m_F=\pm 1⟩$ within 21 ms as a function of the quadratic Zeeman energy $q$. To obtain this fraction, the number of transferred atoms per state was divided by the sum of transferred $|m_F=\pm 1⟩$ and condensed $|m_F=0⟩$ atoms. Because of strong shot-to-shot fluctuations 15 independent realizations were averaged at each magnetic field. The error bars indicate statistical uncertainties. The blue line is a triple Gaussian fit to guide the eye. (b) Instability rate, given by the imaginary part of the most unstable spin Bogoliubov mode, corresponding to the pair-creation efficiency into $|m_F=\pm 1⟩$ (solid line). The maximal instability rate for an effective homogeneous case (dashed line) lacks any resonant features.

Figure 3

Position of the lowest energy spinor dynamics resonance, recorded for various atom numbers $N$ of the initial condensate in the $|m_F=0⟩$ state. The blue line represents a fit to a power law $N^{\gamma }$, yielding an exponent of $\gamma =0.36\pm 0.02$.

Figure 4

Instability rate as a function of the quadratic Zeeman energy for the parameters of Ref. [9], $({\omega }_x,{\omega }_y,{\omega }_z)=2\pi \times (440,39,4.2)\mathrm{Hz}$ and $N=2\times {10}^6$ atoms. A constant maximal instability rate for $0<q<6\mathrm{Hz}$ is followed by a significant decay of the conversion efficiency for $q<0$.