Spontaneous Demagnetization of a Dipolar Spinor Bose Gas in an Ultralow Magnetic Field

We study the spinor properties of $S=3$ ${}^{52}\mathrm{Cr}$ condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.

Figure 1

Chromium BEC spin composition at low fields, revealed by Stern-Gerlach analysis (see 18). The BEC spontaneously depolarizes as the magnetic field is lowered. Absorption pictures after 155 ms of hold time, in a field of (a) 1 mG, (b) 0.5 mg, (c) 0.25 mG, and (d) 0 mG. At the lowest magnetic field, the spin distribution is $\{17.5\pm 9,18\pm 4,14\pm 1.5,15\pm 3,17\pm 3,12.5\pm 4,6\pm 2\}\%$ corresponding to a magnetization of $-0.5g_S{\mu }_B$.

Figure 2

Demagnetization curve for 3D BECs and for 1D quantum gases: $m_S=-3$ final population as a function of the magnetic field. Full circles give the results for 3D-BECs and triangles for 1D tubes. Inset: final gas magnetization as a function of the magnetic field in the lattice, for two orthogonal orientations of the field with respect to axis of the lattice tubes. Lines are Gaussian fits to the data.

Figure 3

Time evolution of the $m_S=-3$ population, as a function of the time delay between the moment at which the magnetic field control is set to zero and the beginning of the Stern-Gerlach procedure. (a) dynamics for 3D BECs; (b) dynamics for 1D quantum gases. Full lines are guides to the eye. Depolarization starts after a delay, corresponding to the time for $B(t)$ to reach $B_c$ (see text).

Figure 4

Stern-Gerlach monitoring of the spin composition, for the BEC case, using our second Stern-Gerlach procedure (see 18) which insures simultaneously spin separation and a measurement of the momentum distribution of each Zeeman component. The three curves, vertically offset for better clarity, correspond to the absorption pictures shown in the inset, taken at three steps of depolarization separated by a few ms. Solid lines result from multiple Gaussian fits. The width of the narrow peaks shows that atoms in different spin states remain Bose condensed. A broad additional pedestal reveals the presence of a thermal component.