Cavity-Electromechanics with Phonons
Imran Mahboob, Katsuhiko Nishiguchi, Hajime Okamoto, and Hiroshi Yamaguchi
Physical Science Laboratory
Cavity-opto/electromechanical systems exploit the parametric coupling between a photonic cavity and a mechanical resonator . The parametric coupling arises from the motion of the mechanical element that can modulate the cavityĀfs frequency. This results in the emergence of side-bands at the sum (blue) and difference (red) frequency of the constituent resonators. By optically pumping on the side-bands, the coupling between the two systems can be enhanced. This in turn can induce an EIT-like transparency in the cavity where energy is transferred to the mechanical resonator. Alternatively, the cavity can also manipulate the oscillation dynamics of the mechanical resonator and even cool it into its quantum ground state i.e. energy is transferred to the cavity from the mechanical resonator.
In this work, we demonstrate an all-phonon analogue of a photonic cavity-opto/electromechanical system where the mechanical oscillation of interest is composed by the 1st oscillation mode and role of the phonon cavity is played by the 2nd oscillation mode. The parametric coupling between the modes is created by modulating the tension in the electromechanical resonator at the sideband frequencies. This in turn modifies the oscillation dynamics of the constituent modes that can drive the parametric coupling between them.
The experiments were performed in a piezoelectrically active GaAs/AlGaAs electromechanical resonator which sustained the 1st and 2nd modes at 171.3 kHz and 470.9 kHz respectively (Fig. 1). The piezoelectric transducer enabled the tension in the mechanical resonator to be modulated at the sidebands. The creation of parametric coupling is demonstrated by probing the 2nd mode whilst pumping on the red-side band (see Fig. 2). This results in energy from the 2nd mode being transferred to the 1st mode. As the pump amplitude is increased, the coupling between modes is made so strong that it results in parametric normal mode splitting where the modes are no longer distinct but rather a hybrid. We exploit the dynamic nature of this parametric coupling to create a transparency in the phonon cavity and to cool the 1st mode .
 T. Kippenberg and K. Vahala, Science 321 (2008) 1172.
 I. Mahboob et al., Nature Physics 8 (2012) 387.
Fig. 1. An SEM image of the electromechanical resonator and simple circuit schematic.
Fig. 2. The 2nd mode being probed at large red-pump amplitudes which undergoes parametric normal mode splitting indicating that it is strongly coupled to the 1st mode.