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Quantum Localization of Vibrational Mirror in Cavity Optomechanics

Authors: Madiha Tariq, Hena Rabbani

Abstract:

Recently, cavity-optomechanics becomes an extensive research field that has manipulated the mechanical effects of light for coupling of the optical field with other physical objects specifically with regards to dynamical localization. We investigate the dynamical localization (both in momentum and position space) for a vibrational mirror in a Fabry-Pérot cavity driven by a single mode optical field and a transverse probe field. The weak probe field phenomenon results in classical chaos in phase space and spatio temporal dynamics in position |ψ(x)²| and momentum space |ψ(p)²| versus time show quantum localization in both momentum and position space. Also, we discuss the parametric dependencies of dynamical localization for a designated set of parameters to be experimentally feasible. Our work opens an avenue to manipulate the other optical phenomena and applicability of proposed work can be prolonged to turn-able laser sources in the future.

Keywords: Dynamical localization, cavity optomechanics, hamiltonian chaos, probe field.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2643980

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References:


[1] Kippenberg, Tobias J., and Kerry J. Vahala. "Cavity optomechanics: back-action at the mesoscale." science 321, no. 5893 (2008): 1172-1176.
[2] Liu, Ke, Lei Tan, Chun-Hai Lv, and Wu-Ming Liu. "Quantum phase transition in an array of coupled dissipative cavities." Physical Review A 83, no. 6 (2011): 063840.
[3] Sun, Qing, Xing-Hua Hu, An-Chun Ji, and W. M. Liu. "Dynamics of a degenerate Fermi gas in a one-dimensional optical lattice coupled to a cavity." Physical Review A 83, no. 4 (2011): 043606.
[4] Yixiang, Yu, Yu Chen, Jinwu Ye, and Wuming Liu. "Goldstone and Higgs modes of photons inside an cavity and their detections." In APS Meeting Abstracts. 2013.
[5] Arcizet, Olivier, P-F. Cohadon, Tristan Briant, Michel Pinard, and Antoine Heidmann. "Radiation-pressure cooling and optomechanical instability of a micromirror." Nature 444, no. 7115 (2006): 71.
[6] Thompson, J. D., B. M. Zwickl, A. M. Jayich, Florian Marquardt, S. M. Girvin, and J. G. E. Harris. "Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane." Nature 452, no. 7183 (2008): 72.
[7] Lin, Qiang, Jessie Rosenberg, Darrick Chang, Ryan Camacho, Matt Eichenfield, Kerry J. Vahala, and Oskar Painter. "Coherent mixing of mechanical excitations in nano-optomechanical structures." Nature Photonics 4, no. 4 (2010): 236.
[8] Eichenfield, Matt, Jasper Chan, Ryan M. Camacho, Kerry J. Vahala, and Oskar Painter. "Optomechanical crystals." Nature462, no. 7269 (2009): 78.
[9] Zotos, Euaggelos E. "Escapes in Hamiltonian systems with multiple exit channels: part I." Nonlinear Dynamics 78, no. 2 (2014): 1389-1420.
[10] Braginsky, V. B., and S. P. Vyatchanin. "Low quantum noise tranquilizer for Fabry–Perot interferometer." Physics Letters A293, no. 5-6 (2002): 228-234.
[11] Yasir, Kashif Ammar, Muhammad Ayub, and Farhan Saif. "Exponential localization of moving end mirror in optomechanics." Journal of Modern Optics 61, no. 16 (2014): 1318-1323.
[12] Khorasani, Sina. "Higher‐Order Interactions in Quantum Optomechanics: Revisiting Theoretical Foundations." Applied Sciences 7, no. 7 (2017): 656.
[13] Zhang, Kuang, W. Chen, M. Bhattacharya, and P. Meystre. "Hamiltonian chaos in a coupled BEC–optomechanical-cavity system." Physical Review A 81, no. 1 (2010): 013802.
[14] Wang, Ying-Dan. "Y.-D. Wang and AA Clerk, Phys. Rev. Lett. 108, 153603 (2012)." Phys. Rev. Lett. 108 (2012): 153603.
[15] Singh, S., H. Jing, E. M. Wright, and P. Meystre. "Quantum-state transfer between a Bose-Einstein condensate and an optomechanical mirror." Physical Review A 86, no. 2 (2012): 021801.
[16] Buchmann, L. F. "LF Buchmann, L. Zhang, A. Chiruvelli, and P. Meystre, Phys. Rev. Lett. 108, 210403 (2012)." Phys. Rev. Lett. 108 (2012): 210403.
[17] Meystre, Pierre. "A short walk through quantum optomechanics." Annalen der Physik 525, no. 3 (2013): 215-233.
[18] Moore, M., and R. Blümel. "Quantum manifestations of order and chaos in the Paul trap." Physical Review A 48, no. 4 (1993): 3082.
[19] Frahm, Klaus M., and Dima L. Shepelyansky. "Quantum localization in rough billiards." Physical review letters 78, no. 8 (1997): 1440.
[20] Saif, Farhan. "Classical and quantum chaos in atom optics." Physics Reports 419, no. 6 (2005): 207-258.
[21] Pillet, Pierre. "Special issue on Optics and Interferometry with Atoms." J. Phys. II 4 (1994): 1877.
[22] Saif, Farhan. "Dynamical localization and signatures of classical phase space." Physics Letters A 274, no. 3-4 (2000): 98-103.
[23] Blümel, Reinhold, Andreas Buchleitner, Robert Graham, Leszek Sirko, Uzy Smilansky, and Herbert Walther. "Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise." Physical Review A44, no. 7 (1991): 4521.
[24] Moore, F. L., J. C. Robinson, C. Bharucha, P. E. Williams, and M. G. Raizen. "Observation of dynamical localization in atomic momentum transfer: A new testing ground for quantum chaos." Physical review letters 73, no. 22 (1994): 2974.
[25] Borgonovi, Fausto, Paolo Conti, Daniela Rebuzzi, Bambi Hu, and Baowen Li. "Cantori and dynamical localization in the Bunimovich stadium." Physica D: Nonlinear Phenomena 131, no. 1-4 (1999): 317-326.
[26] Saif, Farhan. "Dynamical localization and signatures of classical phase space." Physics Letters A 274, no. 3-4 (2000): 98-103.
[27] Gong, Jiangbin, Hans Jakob Wörner, and Paul Brumer. "Control of dynamical localization." Physical Review E 68, no. 5 (2003): 056202.
[28] Ayub, Muhammad, Kashif Ammar Yasir, and Farhan Saif. "Dynamical localization of matter waves in optomechanics." Laser Physics 24, no. 11 (2014): 115503.
[29] Yasir, Kashif Ammar, Muhammad Ayub, and Farhan Saif. "Exponential localization of moving end mirror in optomechanics." Journal of Modern Optics 61, no. 16 (2014): 1318-1323.
[30] Liu, Yu-Long, and Yu-xi Liu. "Energy-localization-enhanced ground-state cooling of a mechanical resonator from room temperature in optomechanics using a gain cavity." Physical Review A 96, no. 2 (2017): 023812.
[31] Fu, Hao, Zhi-cheng Gong, Li-ping Yang, Tian-hua Mao, Chang-pu Sun, Su Yi, Yong Li, and Geng-yu Cao. "Classical dynamical localization in a strongly driven two-mode mechanical system." arXiv preprint arXiv:1706.06254 (2017).
[32] Fu, Hao, Zhi-cheng Gong, Li-ping Yang, Tian-hua Mao, Chang-pu Sun, Su Yi, Yong Li, and Geng-yu Cao. "Coherent Optomechanical Switch for Motion Transduction Based on Dynamically Localized Mechanical Modes." Physical Review Applied 9, no. 5 (2018): 054024.
[33] Major, Jan, Giovanna Morigi, and Jakub Zakrzewski. "Single-particle localization in dynamical potentials." arXiv preprint arXiv:1808.07509 (2018).
[34] Wan, Liang-Liang, Xin-You Lü, Jin-Hua Gao, and Ying Wu. "Controllable photon and phonon localization in optomechanical Lieb lattices." Optics express 25, no. 15 (2017): 17364-17374.