Abstract
We theoretically present an optomechanical cooling scheme of a double optical modes which are coupled with the same mechanical resonator by the radiation pressure to analyze the dynamical cooling of a micromechanical membrane. The mean value of the total second-order moments are obtained by solving linearized quantum Langevin equations. We discuss the effect of the significant parameters of the system on the instantaneous-state mean phonon number of the oscillator cooled to the ground state under the resolved sideband regime. Furthermore, the steady-state cooling limit is also studied and the results show that the final mean phonon number splits into two minimum values when the detunings of the two cavity modes are different. Moreover, the minimal value of the final mean phonon number is much less than the case of equal driving detuning. By regulating the detunings of the optical modes from the corresponding driving fields and increasing the coupling strengths, the cooling effect will be optimized obviously.
Similar content being viewed by others
References
Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)
Meystre, P.: A short walk through quantum optomechanics. Ann. Phys. (Berlin) 525, 215 (2013)
Regal, C.A., Teufel, J.D., Lehnert, K.W.: Frequency and Q factor control of nanomechanical resonators. Nat. Phys. 4, 974 (2008)
Peng, H.B., Chang, C.W., Aloni, S., Yuzvinsky, T.D., Zettl, A.: Ultrahigh frequency nanotube resonators. Phys. Rev. Lett. 97, 087203 (2006)
Naik, A.K., Hanay, M.S., Hiebert, W.K., Feng, X.L., Roukes, M.L.: Towards single-molecule nanomechanical mass spectrometry. Nat. Nanotechnol. 4, 445 (2009)
Suh, J., Weinstein, A.J., Lei, C.U., et al.: Mechanically detecting and avoiding the quantum fluctuations of a microwave field. Science 344, 1262 (2014)
Hertzberg, J.B., Rocheleau, T., Ndukum, T., et al.: Back-action-evading measurements of nanomechanical motion. Nat. Phys. 10, 213 (2010)
Palomaki, T.A., Teufel, J.D., Simmonds, R.W., Lehnert, K.W.: Entangling mechanical motion with microwave fields. Science 342, 710 (2013)
Wang, Y.D., Clerk, A.A.: Reservoir-engineered entanglement in optomechanical systems. Phys. Rev. Lett. 110, 253601 (2013)
Mari, A., Eisert, J.: Opto- and electro-mechanical entanglement improved by modulation. New J. Phys. 14, 1 (2012)
Hofer, S.G., Wieczorek, W., Aspelmeyer, M., Hammerer, K.: Quantum entanglement and teleportation in pulsed cavity optomechanics. Phys. Rev. A 84, 052327 (2011)
Qin, W., Miranowicz, A., Li, P.B., Lü, X.Y., You, J.Q., Nori, F.: Exponentially enhanced light-matter interaction, cooperativities, and steady-state entanglement using parametric amplification. Phys. Rev. Lett. 120, 093601 (2018)
Brooks, D.W.C., Botter, T., Schreppler, S., et al.: Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476 (2012)
Purdy, T.P., Yu, P.L., Peterson, R.W., Kampel, N.S., Regal, C.A.: Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013)
Safavi-Naeini, A.H., Gröblacher, S., Hill, J.T., et al.: Squeezed light from a silicon micromechanical resonator. Nature 500, 185 (2013)
Szorkovszky, A., Brawley, G.A., Doherty, A.C., Bowen, W.P.: Strong thermomechanical squeezing via weak measurement. Phys. Rev. Lett. 110, 184301 (2013)
Asjad, M., Agarwal, G.S., Kim, M.S., Tombesi, P., Di Giuseppe, G., Vitali, D.: Robust stationary mechanical squeezing in a kicked quadratic optomechanical system. Phys. Rev. A 89, 023849 (2014)
Pontin, A., Bonaldi, M., Borrielli, A., Cataliotti, F.S., Marino, F., Prodi, G.A., Serra, E., Marin, F.: Squeezing a thermal mechanical oscillator by stabilized parametric effect on the optical spring. Phys. Rev. Lett. 112, 023601 (2014)
Gigan, S., Bhm, H.R., Paternostro, M., Blaser, F., Langer, G., Hertzberg, J.B., Schwab, K.C., Bauerle, D., Aspelmeyer, M., Zeilinger, A.: Self-cooling of a micromirror by radiation pressure. Nature 444, 67 (2006)
Kippenberg, T.J., Vahala, K.J.: Cavity optomechanics: Back-action at the mesoscale. Science 321, 1172 (2008)
Wang, Y., Li, C., Sampuli, E.M., Song, J., Jiang, Y.Y., Xia, Y.: Enhancement of coherent dipole coupling between two atoms via squeezing a cavity mode. Phys. Rev. A 99, 023833 (2019)
Genes, C., Vitali, D., Tombesi, P., Gigan, S., Aspelmeyer, M.: Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes. Phys. Rev. A 77, 033804 (2008)
Li, Y., Wu, L.A., Wang, Z.D.: Fast ground-state cooling of mechanical resonators with time-dependent optical cavities. Phys. Rev. A 83, 043804 (2011)
Karuza, M., Molinelli, C., Galassi, M., Biancofiore, C., Natali, R., Tombesi, P., Di, Giuseppe, Di Giuseppe, G., Vitali, D.: Optomechanical sideband cooling of a thin membrane within a cavity. New J. Physics 14, 095015 (2012)
Triana, J.F., Estrada, A.F., Pachón, L.A.: Ultrafast optimal sideband cooling under non-Markovian evolution. Phys. Rev. Lett. 116, 183602 (2016)
Kleckner, D., Bouwmeester, D.: Sub-kelvin optical cooling of a micromechanical resonator. Nature 444, 75 (2006)
Corbitt, T., Wipf, C., Bodiya, T., Ottaway, D., Sigg, D., Smith, N., Whitcomb, S., Mavalvala, N.: Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK. Phys. Rev. Lett. 99, 160801 (2007)
Poggio, M., Degen, C.L., Mamin, H.J., Rugar, D.: Role of spin noise in the detection of nanoscale ensembles of nuclear spins. Phys. Rev. Lett. 99, 250601 (2007)
Barzanjeh, S., Naderi, M.H., Soltanolkotabi, M.: Back-action ground-state cooling of a micromechanical membrane via intensity-dependent interaction. Phys. Rev. A 84, 023803 (2011)
Restrepo, J., Gabelli, J., Ciuti, C., Favero, I.: Classical and quantum theory of photothermal cavity cooling of a mechanical oscillator. Comptes Rendus Physique 12, 860 (2011)
Yasir, K.A., Zhuang, L., Liu, W.M.: Spin-orbit-coupling-induced backaction cooling in cavity optomechanics with a Bose-Einstein condensate. Phys. Rev. A 95, 013810 (2017)
Xu, M., Jäger, S.B., Schütz, S., Cooper, J., Morigi, G., Holland, M.J.: Supercooling of atoms in an optical resonator. Phys. Rev. Lett. 116, 153002 (2016)
Liu, Y.C., Xiao, Y.F., Luan, X., Wong, C.W.: Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics. Phys. Rev. Lett. 110, 153606 (2013)
Lai, D.G., Zou, F., Hou, B.P., Xiao, Y.F., Liao, J.Q.: Simultaneous cooling of coupled mechanical resonators in cavity optomechanics. Phys. Rev. A 98, 023860 (2018)
Huan, T.T., Zhou, R.G., Lan, H.: Dynamic entanglement transfer in a double-cavity optomechanical system. Phys. Rev. A 92, 022301 (2015)
Liu, Y.L., Liu, Y.X.: Energy-localization-enhanced ground-state cooling of a mechanical resonator from room temperature in optomechanics using a gain cavity. Phys. Rev. A 96, 023812 (2017)
Acknowledgments
Qingxia Mu thanks Xinyu Zhao for valuable discussions. This work was supported by the Fundamental Research Funds for the Central Universities (2018MS056) and National Natural Science Foundation of China (NSFC) (11605055, 11574082).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mu, Q., Lang, C. & Lin, P. Dynamic Cooling of a Micromechanical Membrane in a Double-cavity Optomechanical System. Int J Theor Phys 59, 454–464 (2020). https://doi.org/10.1007/s10773-019-04339-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-019-04339-6