Parametric Frequency Conversion and Logic Operations Using Electromechanical Resonators


Imran Mahboob, Emmanuel Flurin, Katsuhiko Nishiguchi, Akira Fujiwara, and Hiroshi Yamaguchi
Physical Science Laboratory

 The pioneering mechanical computer has been largely forgotten with the advent of Boolean logic, the semiconductor transistor and integrated circuits which have given rise to logic gates that underpin all modern computation [1]. However as conventional computers toil to conserve Moore’s law, the nanoelectromechanical computer was proposed which has acquired urgency as it offers the tantalizing prospect of low power consumption. In spite of some recent experimental effort, a universal electromechanical logic gate based on Boolean algebra has remained beyond reach. To address this, we realise a practical logic device in an electromechanical resonator operated in the non-degenerate parametric amplification regime [2, 3].
 Widely used in optics, non-degenerate parametric amplifiers can enable the frequency of a laser to be tuned. Frequency conversion is realised by exploiting the interaction of an intense high frequency pump beam (fp) with a less intense lower frequency signal beam (fs) in a crystal with a nonlinearity due for example to the Kerr effect which both amplifies the signal beam as well as generating an idler beam (fi) where this process conserves energy i.e. hfp=hfs + hfi and h is Planck’s constant.
 Here we exploit this concept in a tiny mechanical resonator (Fig. 1) where multiple channels of binary information are encoded via the pump as nanometre scale oscillations at different frequencies. The parametrically activated nonlinearity in the mechanical resonator can mix the input binary channels resulting in a rich idler spectrum of output oscillation states that can be used to not only construct all the primary logic gates and multi-bit logic circuits (Fig. 2) but also to execute Boolean logic functions in parallel all in just a single mechanical oscillator. These results suggest that a nanomechanical computer based on these ground breaking techniques could have potentially unrivalled data processing power.

[2] I. Mahboob et al., Nature Commun. 2 (2011) 198.
[3] I. Mahboob et al., Appl. Phys. Lett. 97 (2010) 253105.

Fig. 1. An SEM image of the parametric amplifier consisting of a doubly
clamped beam with an out-of-plane oscillation mode. Application
of a.c. bias to the resonator can piezoelectrically induce both
harmonic and parametric resonances. Also shown are the input
pump and signal excitations and the output amplified
signal and idler oscillations.
Fig. 2. Application of 3 pumps A, B and C at
different pump frequencies results in
a rich idler spectrum which can be
used to realise multi-bit logic circuits in parallel.

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