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We study photon/phonon statistics of a qubit-plasmon-phonon hybrid system inthe ultrastrong coupling regime. The introduced qubit coupling causes parityconserving and non-conserving situations. We employ an analytic approximationapproach for the parity conserving case to reveal the statistical behaviors ofphotons and phonons. It indicates that both photons and phonons show strongantibunching at the same frequency. Even though the bunching properties ofphotons/phonons occupy the dominant regions of the considered frequencies,phonons tend to weakly antibunching within the photonic strong-bunching area.In contrast, one can find that the configurations of correlation functions forboth photons and phonons in the parity conserving case are squeezed towards thecentral frequency by parity breaking, which directly triggers the reversestatistical behaviors for the different parties at the low-frequency regionsand the strong bunching properties at other frequency regions. Thephoton-phonon cross-correlation function also demonstrates similarparity-induced differences, indicating that the non-conserving parity inducesthe photon-phonon bunching behavior. We finally analyze the delayedsecond-order correlation function with different driving frequencies, whichillustrates striking oscillations revealing the occurrence of simultaneousmultiple excitations.

Photon and phonon statistics in a qubit-plasmon-phonon ultrastrong coupling system