A mechanism with positive feedback governing the transitions in super-low temperature physics studied via a two-species condensate with spin-1 atoms.

The ground states of two-species condensates with spin-1 atoms have been studied analytically and numerically. All the results from the analytical approach are checked by the latter. The [Formula: see text] channel has been neglected, where λ is the coupled spin of two different atoms. A complete phase diagram has been plotted against the whole parameter space which has been divided into regions associated with different phases. All the boundaries separating the regions have been analytically obtained. Let p- denote the phase of a species in which all the atoms are two by two in singlet-pairs, f- denote that all the spins are lying along a common direction (fully polarized), and q- denote a mixture of the above two phases, namely, some singlet-pairs together with a fully polarized subsystem. Then, we found that the p-phase cannot coexist with the q- or f-phase (the p-f or f-p phase could exist only if the species in the f-phase is a few-body system). The q-q phase also does not exist. Thus, once a few atoms of a species are aligning (i.e., in the q-phase), the singlet-pairs of the other species must all be broken and become fully polarized. This is an important feature of multi-species spin-1 systems arising from the basic character of the inter-species interaction via a mechanism with positive feedback. Note that, when both species are in the p-phase, there is no special direction. However, once a few of A-(or B-)atoms are aligning, a special direction is established, and the inter-species interactions from them will be unified and thereby promote the spin-alignment in the other pieces, and vice versa. This is the positive feedback, that is, the alignments in both species are mutually promoted. This explains why a q-phase causes the full polarization of the other species. In particular, the transition from p-p to q-f, f-q or f-f is governed by this mechanism. It leads to a sudden breaking of all the singlet-pairs and is expected to be popular in various multi-species spin-1 systems in the neighborhood of temperature zero.