Usually the instruments in modern physics research are very high priced. So in general, the Physicist use to rely on the research laboratories set up by Governments for there research. But yeah! if you wish you can open your own research lab. In some cases, like if you want to do a research in High Energy Physics or Particle Physics, then you need to have a big ring of particle accelerator, which isn't possible for one to create those and fund those. So depending on your field of research, it may be possible to open a research lab of your own, but its not that much common, that a physicist opens its own lab.

I hope this helps. Wish you a great eve!