  We propose a new method for frequency conversion of photons which is both
versatile and deterministic. We show that a system with two resonators
ultrastrongly coupled to a single qubit can be used to realize both single- and
multiphoton frequency-conversion processes. The conversion can be exquisitely
controlled by tuning the qubit frequency to bring the desired
frequency-conversion transitions on or off resonance. Considering recent
experimental advances in ultrastrong coupling for circuit QED and other
systems, we believe that our scheme can be implemented using available
technology.
