How soon after purchase is it appropriate to raise the rent?
That will depend on whether the tenants have existing long term leases and what your state laws require for notice. If the tenants are on month to month agreements, and your state allows a 30 day notice, tenants do usually expect changes when ownership changes. Just be sure to check your market so that when tenants check around, they still find your units to be a good rate. If you overprice you won't keep or get tenants. But, if the existing tenants are a problem, then raising rents a sizable amount can be one way of encouraging them to move on.