  Modern advanced photonic integrated circuits require dense integration of
high-speed electro-optic functional elements on a compact chip that consumes
only moderate power. Energy efficiency, operation speed, and device dimension
are thus crucial metrics underlying almost all current developments of photonic
signal processing units. Recently, thin-film lithium niobate (LN) emerges as a
promising platform for photonic integrated circuits. Here we make an important
step towards miniaturizing functional components on this platform, reporting
probably the smallest high-speed LN electro-optic modulators, based upon
photonic crystal nanobeam resonators. The devices exhibit a significant tuning
efficiency up to 1.98 GHz/V, a broad modulation bandwidth of 17.5 GHz, while
with a tiny electro-optic modal volume of only 0.58 $\mu {\rm m}^3$. The
modulators enable efficient electro-optic driving of high-Q photonic cavity
modes in both adiabatic and non-adiabatic regimes, and allow us to achieve
electro-optic switching at 11 Gb/s with a bit-switching energy as low as 22 fJ.
The demonstration of energy efficient and high-speed electro-optic modulation
at the wavelength scale paves a crucial foundation for realizing large-scale LN
photonic integrated circuits that are of immense importance for broad
applications in data communication, microwave photonics, and quantum photonics.
