Controling the dynamics across a quantum phase transition*

When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a universal power-law predicted by the Kibble-Zurek mechanism (KZM). The scaling theory of phase transitions can however be used to determine the full counting statistics of topological defects, beyond the KZM. Knowledge of the distribution of topological defects provides new insights into the breakdown of adiabaticity.
In addition, the quantum critical dynamics can be controlled. One approach relies on quantum monitoring via continuous quantum measurements. A second approach is based on local driving of the phase transition. We shall present theoretical and experimental progress based on these approaches.

A. del Campo, Universal Statistics of Topological Defects Formed in a Quantum Phase Transition, arXiv:1806.10646
L. P. García-Pintos, D. Tielas, A. del Campo, Spontaneous symmetry breaking induced by quantum monitoring, arXiv:1808.08343
F. J. Gómez-Ruiz, A. del Campo, Universal dynamics of inhomogeneous quantum phase transitions: suppressing defect formation, arXiv:1805.00525