https://doi.org/10.1140/epjd/s10053-022-00384-9
Regular Article – Quantum Optics
Phonon blockade in a system consisting of two optomechanical cavities with quadratic cavity–membrane coupling and phonon hopping
Optic and Laser Group, Faculty of Physics, Yazd University, Yazd, Iran
Received:
18
May
2021
Accepted:
10
March
2022
Published online:
28
March
2022
Quantum control of phonons has become a focus of development for quantum technologies. Here, we propose a scheme to realize phonon blockade in a system that contains two optomechanical cavities in the presence of quadratic cavity–membrane coupling as well as phonon hopping. In fact, each cavity has a movable membrane placed in the node (or antinode) of the cavity field, and the two membranes are connected by a coupling constant 
. In addition, we take into account the decay rate of mirrors. To examine phonon statistics, we study the equal-time second-order correlation function 
for the mechanical mode, by which we are able to investigate the phonon blockade analytically. Due to weakness of the considered laser pumping intensity, we limited our study to the Hilbert space states with two-phonon excitations. The results show that by tuning the coupling constant between the two mechanical modes, phonon blockade can be observed at different frequencies. Examining the effect of phonon loss rate, we found that the minimum of the equal-time second-order correlation function decreases under the influence of mechanical decay rates, and the phonon blockade is more likely to occur.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
