Spontaneously Modulated Spin Textures in a Dipolar Spinor Bose-Einstein Condensate

Helical spin textures in a ${}^{87}\mathrm{Rb}$ $F=1$ spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. The formation of this modulated phase is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. The reduction of dipolar interactions by a sequence of rf pulses results in a suppression of the modulated phase, thereby confirming the role of dipolar interactions in this process. This study demonstrates the significance of magnetic dipole interactions in degenerate ${}^{87}\mathrm{Rb}$ $F=1$ spinor gases.

Figure 1

Spontaneous dissolution of helical textures in a quantum degenerate ${}^{87}\mathrm{Rb}$ spinor Bose gas. A transient magnetic field gradient is used to prepare transversely magnetized (b) uniform or (a),(c) helical magnetization textures. The transverse magnetization column density after a variable time $T$ of free evolution is shown in the imaged $x\mathrm{\text{−}}z$ plane, with orientation indicated by hue and amplitude by brightness (color wheel shown). (b) A uniform texture remains homogeneous for long evolution times, while (c) a helical texture with pitch $\lambda =60\mu \mathrm{m}$ dissolves over $\sim 200\mathrm{ms}$, evolving into a sharply spatially modulated texture.

Figure 2

Power spectrum of the spatial Fourier transform and the two-point correlation function $G(x,z)$ for the initial spin helix (a),(c) and the spontaneously modulated phase (b),(d). These data are derived from the same image sequence shown in Fig. 1c. The images (a),(c) correspond to an evolution time $T=0\mathrm{ms}$ while (b),(d) correspond to an evolution time $T=250\mathrm{ms}$. The short-range spatial order is defined as the integrated spectral power in the annular region shown in (b).

Figure 3

Growth of the spontaneously modulated phase (●) coincides with a reduction in the integrated energy in the low spatial frequency region (▪). The data shown correspond to an initial helical pitch of $60\mu \mathrm{m}$. Inset: The initial growth rate $\gamma$ of the modulated phase as a function of the helix wave vector. These were extracted from linear fits of the short-range order parameter at short evolution times.

Figure 4

Spatial power spectra (a) without or (b) with the application of rapid rf pulses during the 200 ms evolution following the preparation of the helical spin texture, are averaged over four experimental repetitions. Eliminating the dipolar interactions suppresses the short-range spatial modulation of the final spin texture. (c) The average number of detected spin vortices and (d) the short-range order parameter are shown vs evolution time. Square symbols indicate data obtained when the dipolar interaction is spatially averaged. In all cases, the initial helical pitch was $\lambda =80\mu \mathrm{m}$.