Resonant Spin-Changing Collisions in Spinor Fermi Gases

The compensation of quadratic Zeeman effect and trap energy in high-spin fermions is shown to lead to resonances in the spin-changing collisions that are typically absent in spinor condensates and spin-$1/2$ fermions. We study these resonances in lattice fermions, showing that they permit the targeting of a particular spin-changing channel while suppressing the rest and the creation of magnetically insensitive superpositions of many-body states with entangled spin and trap degrees of freedom. Finally, the intersite tunneling may lead to a quantum phase transition described by a quantum Ising model.

Figure 1

States involved in the resonant dynamics at $\alpha \simeq -1/2$ for $f=3/2$. The lines indicate from bottom to top the three trap levels. The spin states are indicated by filled and open squares ($m=\pm 1/2$) and circles ($m=\pm 3/2$).

Figure 2

$f=3/2$. Time-averaged population ($N_{3/2}$) in $m=\pm 3/2$ as a function of $\alpha$, for ${\tilde{g}}_{0,2}=0.08,0.10$ [15] and $\overline{n}=2.0$ (thin red line) and 2.5 (thick line).

Figure 3

$f=5/2$. Time-averaged population $N_{3/2}$ in $m=\pm 3/2$ (thick line) and $N_{5/2}$ in $m=\pm 5/2$ (thin red line) for $\overline{n}=2.0$ and ${\tilde{g}}_{0,2,4}=0.08,0.10,0.05$ [15].