Kibble-Zurek Mechanism

We have proposed to use the ion chain as a test bed for the Kibble Zurek mechanism. In particular we have proposed to use the crossover between the linear to the Zig Zag configuration:

 

The number of the produced defects is controlled by the rate of the quench as can be seen in the following movie: Movie1

In the following work we have identified the critical exponents that dictate the density of kinks.

Structural Defects in Ion Chains by Quenching the External Potential: The Inhomogeneous Kibble-Zurek Mechanism. Phys. Rev. Lett. 105, 075701 (2010)

Moreover, in a linear Paul trap the axial density of ions is higher in the center of the chain and the transition becomes inhomogeneous.

As a result, while decreasing the transverse confinement, the mechanical instability is first crossed in the center of the chain, and spreads towards the edges of the chain. The velocity of teh associated fornt turns out to play a key role in the nucleation of kinks. Indeed, if it is smaller than the sound velocity, the dynamics becomes adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the Kibble-Zurek mechanism, which lacks experimental evidence to date.