Fig. 1: An ultracold atomic reaction undergoing a (non-adiabatic/quasi-adiabatic) passage through, respectively.
From: Parametric tuning of quantum phase transitions in ultracold reactions
a, b the first-order and (d, e) the second-order quantum phase transition. a For the first-order transition, both molecules and atoms can be in the local energy minima simultaneously, whereas (d), for the second-order transition, a high efficiency of the chemical reaction can be achieved by an adiabatic transition between the molecular and atomic energy minima. b–e The mean-field ground energy as a function of the order parameter in the first-order and second-order quantum phase transition, respectively (arrows indicate the direction of time) (c) The numerically obtained phase diagram describing the dependence of the number of nonadiabatic excitations, nex, as a function of the inverse sweep rate, \(1/{\beta }_{{{\rm{eff}}}}\equiv {g}^{2}/(\beta \ln N)\) (x-axis), and the molecular interaction strength, κ = r/g in Eqs. (1) and (3), (y-axis). For the model (2), κ = −1 separates the regimes with first (κ < − 1) and second (κ > − 1) order phase transitions. This explains the fast increase of the excitation numbers below the κ = −1 line.
