You likely would qualify for an O-1 which is not subject to a lottery. You would be subject to a lottery for an H-1B unless the H-1B would be to work for a non

You likely would qualify for an O-1 which is not subject to a lottery. You would be subject to a lottery for an H-1B unless the H-1B would be to work for a non-profit entity engaged in basic research or another cap exempt entity. There are visas that allow for self employment or at least employment with a company created by the foreign national (O-1 sort of, E-1 and E-2, and IEPP) but oftentimes the path to "free agency" is through the green card process - which under certain circumstances can be applied for without company sponsorship - and with a PhD you likely would be able to apply for a green card on your own.