Multi-resonant Spin Dynamics
Spin changing collisions only occur if a resonance condition is fulfilled. This condition can be easily understood in terms of energy conservation: the energy of the atom pair in mF = 0 before the collision has to be equal to the combined energy of the atom in mF = +1 and the atom in mF = -1 after the spin changing collision.
Two energy contributions have to be taken into account. First, the internal energy of the atoms can change as depicted in (a). In F = 1 less energy is gained by the transfer of one atom to mF = +1 then is needed to transfer the other atom to mF = -1 due to the quadratic Zeeman effect. Hence, in sum the internal energy is increased by an amount that can be tuned by changing the magnetic field. In F = 2 the situation is inverse and the internal energy is decreased by the spin change. Additionally, the energy levels can be shifted by a microwave dressing as indicated in the figure for a red detuned microwave on the transition from F = 1, mF = -1 to F = 2, mF = -2.
The second energy scale is set by the effective potential seen by the atoms in mF = +1 and mF = -1 which is sketched in (b). It is a combination of the trapping potential created by the dipole laser beams (blue) and the repulsive mean field interaction with the remaining atoms in mF = 0 (grey area). Whenever the energy released by the internal state change matches the energy of an eigenstate of this effective potential, a resonance occurs. This can be seen in (c) where the fraction of atoms in mF = +1 and mF = -1 increases if the energy released by the internal state change is tuned to these resonances. Additionally, the spatial pattern of the populated eigenmodes of the effective potential become apparent in the absorption images of the atomic clouds.