The article does not propose what you describe. RTFA. Humans are not going.
The article proposes accelerating a bunch of tiny probes to 0.2c via earth-based lasers. There is no plan for decelerating. Instead, the surviving probes will radio back what they see as they fly by their target at 0.2c, giving earthlings a close glimpse of nearby solar systems.
Probably should debug the probes using Mars fly-bys. Experiment is over in hours vs decades (experimental probe goes on to reach Pluto's orbit in a day or so).
Should mount the lasers on the spacecraft itself. Laser light travels at the speed of light for any observer, so where it is sourced is immaterial. Then, braking is a non-issue, with a turning maneuver about half-way.