  Here we demonstrate an on-chip electro-optic frequency shifter that is
precisely controlled using only a single-tone microwave signal. This is
accomplished by engineering the density of states of, and coupling between,
optical modes in ultra-low loss electro-optic waveguides and resonators
realized in lithium niobate nanophotonics. Our device provides frequency shifts
as high as 28 GHz with measured shift efficiencies of ~99% and insertion loss
of <0.5 dB. Importantly, the device can be reconfigured as a tunable
frequency-domain beam splitter, in which the splitting ratio and splitting
frequency are controlled by microwave power and frequency, respectively. Using
the device, we also demonstrate (non-blocking) frequency routing through an
efficient exchange of information between two distinct frequency channels, i.e.
swap operation. Finally, we show that our scheme can be scaled to achieve
cascaded frequency shifts beyond 100 GHz. Our device could become an essential
building-block for future high-speed and large-scale classical information
processors as well as emerging frequency-domain photonic quantum computers.
