Phonon Blockade In Nanomechanical Resonators

With the development of micro-and nanotechnologies,the quality factors of the Nanomechanical resonators become higher and the couplings of mechanical resonators to other systems become stronger.Now,mechanical resonators can be used for information processing.In particular,the emergence of phonon lasers and the theoretical proposals of single phonon source lay a foundation for quantum information processing based on nanomechanical resonators.As one of the physical mechanisms to realize single phonon source,phonon blockade has attracted much attention in recent years.In this dissertation,we study the statistical properties of phonons for different quantum systems coupled with the nanomechanical resonators,and propose theoretical schemes to realize phonon blockade.(1)we propose to observe a phonon blockade in multimode optomechanical system.Under the interaction of the strong optical driving field,the multimode optomechanical system can be reduced to a much simple model for a mechanical mode linearly coupled to an optical mode with Kerr nonlinearity.Our calculations show that strong phonon antibunching effects can be observed even with weak optomechanical coupling.Moreover,the statistical properties of the phonons can be controlled by regulating the strength ratio and the relative phase between the weakly driving fields,and this provides us an effective way to realize tunable single-phonon sources.(2)we study the phonon statistics of a quadratically coupled optomechanical system,in which an effective second-order nonlinear interaction between an optical mode and a mechanical mode is induced by a strong optical driving field on two-phonon red-sideband resonance.We show that strong phonon antibunching can be observed even if the strength of the effective second-order nonlinear interaction is much weaker than the decay rates of the system.Moreover,the phonon statistics can be dynamically controlled by tuning the strengths and the phase difference of the weak driving fields.The scheme proposed here provides us another effective way to realize tunable single-phonon sources.(3)we investigate the phonon statistics in a nanomechanical resonator,which is quadratically coupled to a two-level system,by driving the nanomechanical resonator and two-level system simultaneously.We find that unconventional phonon blockade can be observed when driven fields are weak.By increasing the strengths of the driving fields,we show the crossover from the unconventional phonon blockade to the conventional phonon blockade.Moreover,under the strong coupling condition for conventional phonon blockade,quantum interference effect can also be used to enhance the phonon blockade by optimizing the phase difference of the two external driving fields.(4)we study photon,phonon statistics and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system.Unconventional photon blockade,phonon blockade,and strong anticorrelation between photons and phonons can be observed in the same parameter regime.The combination of photon blockade,phonon blockade,and strongly anticorrelated photons and phonons provides us a way to generate anticorrelated single photons and single phonons.Furthermore,in the strongly nonlinear coupling condition,photon pairs and phonon pairs can be generated simultaneously,and the photon and phonon pairs are correlated with each other,which can be used to generate two-photon gateway,two-phonon gateway,and the correlated photon-phonon gateway.Our study will help to deepen the understanding of phonon blockade in nanomechanical resonators and lay a theoretical foundation for the realization of single phonon source.