The spins of alkali atoms in a vapor at room temperature or above are in thermal equilibrium, disordered and unpolarized. Most often, optical pumping with circularly-polarized light is used for driving the atomic spins into a particular orientation. Here we study unique pumping conditions that lead to bifurcation of the total spin orientation, i.e., to alignment of all spins (randomly) either parallel or anti-parallel to a defined axis. The bifurcation mechanism requires constituent atoms with spin S≥1, a unique optical pumping that drives atoms towards larger |S| (i.e. symmetric to ±S), and importantly inter-atomic spin-exchange coupling that settles only when all spins point to the same direction.
We show theoretically and experimentally that this collective mechanism is associated with a non-equilibrium phase transition. The total spin in the vapor takes the role of an order parameter, while the optical pump power and the spin-exchange collision rate act as normalized temperatures in the statistical model. We identify critical exponents (β,γ,δ) near the phase transition conditions and observe critical slowing down of the spin buildup time, which reaches several seconds, 2-3 orders of magnitude larger than the single-atom life time. Moreover, we observe similar substantial increase in the 'life-time' of the symmetry-broken spin when approaching the critical point.
This system can be used to investigate critical phenomena in out-of-equilibrium scenarios, with a very simple experimental setup. Furthermore, considering a single ensemble as one 'collective' Ising spin, an array of such spin, coupled using light, may function as an element in an Ising machine or other condensed-matter spin models.