Additional Cues About Partial Overlap
This answer seems to be basically correct, but I'd add that many Gantt chart applications use the color-coding on the bars to give you a visual cue of which part of a task is a gating prerequisite for starting the following task. In your given example, the lead time between when the first task starts and when the second one should begin is one box (whatever time frame that represents; your diagram doesn't display that). The darker part of the first task is the minimum completion, and the additional space on the lighter part represents slack or other lead time being built into the dependency.
Note that the subsequent task also has a darker-colored section, presumably representing the same information for any subsequent tasks. While there currently isn't one, it seems likely that this is a subset of a larger work package so the coloring of the second bar may or may not be useful.
Rethink Your Dependency Graph
Now, whether or not this type of "partial completion" dependency is the best was to represent this work is arguable. I'd generally suggest either decomposing the work further so that there's less overlap, with the goal of having semi-parallel work represented in a less confusing way. For example, having
a1 -> b and
a1 -> a2 as separate activities just seems more manageable and a lot less ambiguous, but the trade-off is that it will require more composition and possibly more real estate on your planning document.
While most people using Gantt charts aren't doing agile project planning where done/not-done decomposition is largely considered de rigueur, slicing the salami thinner is not orthogonal to traditional project management. It may a beneficial practice for your project to adopt, regardless of your chosen framework or tooling.
Your mileage may vary, though.