Defect generation and dynamics during quenching in finite size homogeneous ion chains

An equally spaced linear chain of ions provides a test-bed for studying the defect formation during a topological phase transition from a linear to a zig-zag configuration. By using a particular axial potential leading to an homogeneous ion chain, the boundary conditions are not needed, allowing new rich defect dynamics to appear on an homogeneous system. A semi-empirical expression for the critical transition frequency provides an excellent agreement to the numerical results for low ion numbers. The non-adiabatic crossing of the phase transition shows different power-laws for the defect probability density for different quench rates regions. Information regarding defect dynamics is obtained through the measurement of the defect density at different times during the quench. By comparing the defect density and the correlation length dynamics among the different number of trapped ions, the role of the different defect loss mechanism can be deduced. An excellent agreement with the predictions given by the homogeneous Kibble-Zurek model is found on a finite size system of 30 ion system which can be tested in present ion trap experimental set-ups.