Two-Mode Squeezing in an Electromechanical Resonator

Imran Mahboob, Hajime Okamoto, and Hiroshi Yamaguchi
Physical Science Laboratory

The widespread availability of quantum entanglement with photons, in the guise of two-mode squeezed states, can be attributed to the phenomenon of parametric down-conversion. A reinterpretation of this effect with macroscopic mechanical objects can offer a route towards a purely mechanical entanglement and the unique possibility of probing the quantum mechanical nature of our everyday classical world. In spite of this prospect, mechanical two-mode squeezed states have remained elusive due to the inability to recreate the nonlinear interaction at the heart of this phenomenon in the mechanical domain.

To address this we have developed a non-degenerate parametric down-converter, in a mechanical resonator integrated with electrical functionality, which enables mechanical nonlinearities to be dynamically engineered to emulate this interaction [1]. In this configuration, phonons are simultaneously generated in pairs in two macroscopic vibration modes which results in the amplification of their motion by more than 20 dB. In parallel, mechanical two-mode squeezed states are also created which exhibit fluctuations 5 dB below the thermal level of their constituent modes as well as harbouring correlations between the modes that become almost perfect as their amplification is increased. This remarkable observation of correlations between two massive phonon ensembles paves the way towards an entangled macroscopic mechanical system at the single phonon level.

This work was supported by KAKENHI

[1]
I. Mahboob et al., Phys. Rev. Lett. 112 167203 (2014).

Fig. 1. (a) An electron micrograph of the coupled GaAs based electromechanical resonator, sustaining a symmetric (S) and an asymmetric mode (A), whose profiles extracted from a finite element analysis are also depicted. The mechanical elements are integrated with piezoelectric transducers that can induce tension and parametrically modulate the spring constant. (b) The thermal Langevin force driven motion of the symmetric XS:YS (red points) and asymmetric XA:YA (not shown) modes yield a circular distribution in phase space indicating their uncorrelated random nature. Piezoelectrically activating the non-degenerate parametric down-conversion, at the sum frequency of both modes (ωS+ωA), results in two-mode squeezing which can be observed in the cross-quadratures namely XA:YS (black points) and XS:YA (not shown). (c) The two-mode squeezed state corresponds to the fluctuations in both modes becoming correlated which can be readily observed via the non-zero off-diagonal elements in the corresponding Pearson correlation coefficient matrix.