Competition between Bose-Einstein Condensation and Spin Dynamics

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

Figure 1

(a) Experimental sequence showing the reduction in the ODT intensity in a duration $t_S$. An absorption image is taken after a time $t$ and Stern-Gerlach separation. (b) Simple sketch of the evolution of the momentum distributions [$p(k)$] of atoms in the three lowest spin-excited states, illustrating the difficulty of achieving a BEC (a peak on top of the broad thermal $k$ distribution) in spin-excited states due to spin dynamics. Absorption pictures showing (c) a BEC in $m_s=-3$, and a thermal gas in other spin states for a gas initially prepared with magnetization $M=-2.5\pm 0.25$, and (d) a small multicomponent BEC for $M=-2.00\pm 0.25$.

Figure 2

(a) Number of thermal atoms in $m_s=-3$ (the black diamonds) and $m_s=-2$ (the red disks) as a function of time $t$ for a shock cooling time $t_S=500\mathrm{ms}$. (b) Corresponding condensate fractions in $m_s=-3$ (the black diamonds) and $m_s=-2$ (the red disks). The shaded region highlights when both $m_s=-3$ and $m_s=-2$ thermal clouds are saturated, but only $m_s=-3$ atoms condense.

Figure 3

Numerical results. Evolution of the condensate fractions for different values of $a_4$ (blue diamonds, $m_s=-3$; red circles, $m_s=-2$). Filled markers correspond to the experimental case: $a_4=64a_B$ and $a_6=102.5a_B$ [16], where $a_B$ is the Bohr radius. Empty markers correspond to simulations where $a_4$ is set equal to $a_6$ to suppress spin dynamics. A significative BEC fraction in $m_s=-2$ is then obtained.

Figure 4

(a) Absorption images after shock cooling experiments performed with $t_S=50\mathrm{ms}$ and an initial magnetization $M=-2\pm 0.25$. A small BEC is present in the three lowest spin states; i.e., $m_s=-3,-2$, and $-1$. The different images illustrate the fluctuations of magnetization of the condensate fraction. (b) Numerical results after evaporation, for three initial relative sets of phases. (c) Total condensate fraction of the multispin component gas for $t=t_S$ and $M=-2\pm 0.25$ as a function of $t_S$. We observe small multicomponent condensates in the three lowest energy states. The solid line is a guide for the eye.