As a manager, there are two ways to approach me.
The first is:
I came across this new technology which could help us with __.
Can I put together a small project demo project to see if it would
work? I expect to spend about X days on it.
The second is:
I came across this new technology and I put together a small demo
project at home. Can I show you how it works?
The first approach is to request regular company time to do some research. The second is saying that you've already spent your own time doing some research and want to show what you've found.
If you have the capability to research it on your own time, go that route as it shows that you are taking your career very seriously.
Now some managers will happily include whatever the latest tech is on a project without a real proof of concept. I'm not that guy. I want to eliminate as much risk as possible so the only way I'm going to say yes is if I see that someone has explored the good and bad things about the tech (and there are always downsides). If you can prove to me that you really understand it then I'll allow it to be used.