Symmetry breaking phase transitions and their dynamics are at the heart of a broad range of physical phenomena ranging from the physics of the early universe to solid state physics. Of particular interest are dynamical properties when traversing such a symmetry-breaking second-order phase transition at a finite rate as then spatially separated parts of the system may chose symmetry-broken phases independently and where such choices are incompatible, defects form whose number dependence on the quench rate is given by simple power laws.
Here we study the dynamics of symmetry breaking phase transitions in the formation of helical ion strings that are being held in ion traps that are rotationally invariant around one trap axis. The structures that can occur can be visualised by taking a belt from your trouser and holding it front of you with both hands. Turning one end of the belt creates a helical structure with a winding number that depends on the number of turns. When you go through a phase transition in which the planar structure becomes unstable, we will end up with a finite winding number depending on how fast we traverse the phase transition. We derive analytical scaling laws and confirm them with extensive numerical simulations.