Enhancing nanomechanical squeezing by atomic interactions in a hybrid atom-optomechanical system

In a hybrid atom-optomechanical system, the optical coupling of a mechanical mode of a nanomembrane in an optical cavity with a distant interacting atom gas permits highly nonclassical quantum many-body states. We show that the mechanical mode can be squeezed by the backaction of internal excitations of the atoms in the gas. A Bogoliubov approach reveals that these internal excitations form a fluctuating environment of quasiparticle excitations for the mechanical mode with a gaped spectral density. Nanomechanical squeezing arises due to quasiparticle excitations in the interacting atom gas when the mechanical frequency is close to resonance with the internal atomic transitions. Interestingly, nanomechanical squeezing is enhanced by atom-atom interactions.

Figure 1

Hybrid atom-optomechanical system: a nanomechanical membrane in an optical cavity is coupled to the internal states of a distant atom gas residing in an optical lattice potential.

Figure 2

(a) Approximated zero-temperature spectral density $G_{T=0}\left(\omega \right)$ with $J=0.2{\mathrm{\Omega }}_{\text{a}}$ for different $nU$. (b) Spectral density $G\left(\omega \right)$ with $\beta {\mathrm{\Omega }}_{\text{a}}=1000,J=5{\mathrm{\Omega }}_{\text{a}}$, and $L=1000$.

Figure 3

(a) Variances of the nanomembrane displacement (solid lines) and the atomic internal state (dash-dotted lines) as a function of the atomic frequency ${\mathrm{\Omega }}_{\text{a}}$ with $nU=0.5{\mathrm{\Omega }}_{\text{m}}$. Other parameters chosen are $L=200,N={10}^6,\lambda =2\times {10}^{-4}{\mathrm{\Omega }}_{\text{m}}^{3/2}$, and $J=0.1{\mathrm{\Omega }}_{\text{m}}$. Moreover, the nanomembrane displacement variance (b) and the number of depleted particles (c) are shown as a function of the interaction strength $nU$. For (b) and (c), we have chosen $J=0.5{\mathrm{\Omega }}_{\text{m}},{\mathrm{\Omega }}_{\text{a}}=1.04{\mathrm{\Omega }}_{\text{m}},N={10}^3,L=200$, and $\sqrt{2}\lambda =0.015{\mathrm{\Omega }}_{\text{m}}^{3/2}$. Different colors mark a different inverse temperature as indicated.