1. College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China 2. State Key Laboratory of Metastable Materials Science and Technology & Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China
The absorption of single-cavity and double-cavity optomechanical systems and periodic optomechanical lattices has previously been investigated extensively. In this paper, we present the absorption of a nonperiodic cavity chain, where the absorption value on the resonance point shows switchable dips or peaks, according to whether the optomechanical interaction is at an odd or even-numbered position in the chain. Meanwhile, the value of absorption due to the optomechanical interaction varies with the number of the bare cavities. The calculated results may have some novel applications, such as detecting the position of the movable mirror in a long cavity chain, which would be useful in quantum information processing based on optomechanical systems.
J. Q. Liao and C. K. Law, Cooling of a mirror in cavity optomechanics with a chirped pulse, Phys. Rev. A 84(5), 053838 (2011) https://doi.org/10.1103/PhysRevA.84.053838
3
S. Huang and G. S. Agarwal, Electromagnetically induced transparency from two-phonon processes in quadratically coupled membranes, Phys. Rev. A 83(2), 023823 (2011) https://doi.org/10.1103/PhysRevA.83.023823
J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, Sideband cooling of micromechanical motion to the quantum ground state, Nature 475(7356), 359 (2011) https://doi.org/10.1038/nature10261
6
S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, Pulsed laser cooling for cavity optomechanical resonators, Phys. Rev. Lett. 108(15), 153601 (2012) https://doi.org/10.1103/PhysRevLett.108.153601
7
J. Chan, T. P. M. Alegre, A. H. Safavi Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature 478(7367), 89 (2011) https://doi.org/10.1038/nature10461
8
M. Bhattacharya and P. Meystre, Trapping and cooling a mirror to its quantum mechanical ground state, Phys. Rev. Lett. 99(7), 073601 (2007) https://doi.org/10.1103/PhysRevLett.99.073601
M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, Enhanced quantum nonlinearities in a two-mode optomechanical system, Phys. Rev. Lett. 109(6), 063601 (2012) https://doi.org/10.1103/PhysRevLett.109.063601
11
X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems, Sci. Rep. 3(1), 2943 (2013) https://doi.org/10.1038/srep02943
12
Y. W. Hu, Y. F. Xiao, Y. C. Liu, and Q. H. Gong, Optomechanical sensing with on-chip microcavities, Front.Phys. 8(5), 475 (2013) https://doi.org/10.1007/s11467-013-0384-y
13
S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Entangling macroscopic oscillators exploiting radiation pressure, Phys. Rev. Lett. 88(12), 120401 (2002) https://doi.org/10.1103/PhysRevLett.88.120401
14
M. J. Hartmann and M. B. Plenio, Steady state entanglement in the mechanical vibrations of two dielectric membranes, Phys. Rev. Lett. 101(20), 200503 (2008) https://doi.org/10.1103/PhysRevLett.101.200503
15
D. Vitali, S. Gigan, A. Ferreira, H. R. Bohm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Optomechanical entanglement between a movable mirror and a cavity field, Phys. Rev. Lett. 98(3), 030405 (2007) https://doi.org/10.1103/PhysRevLett.98.030405
X. G. Zhan, L. G. Si, A. S. Zheng, and X. Yang, Tunable slow light in a quadratically coupled optomechanical system, J. Phys. At. Mol. Opt. Phys. 46(2), 025501 (2013) https://doi.org/10.1088/0953-4075/46/2/025501
18
A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, Electromagnetically induced transparency and slow light with optomechanics, Nature 472(7341), 69 (2011) https://doi.org/10.1038/nature09933
19
K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, Optomechanical quantum information processing with photons and phonons, Phys. Rev. Lett. 109(1), 013603 (2012) https://doi.org/10.1103/PhysRevLett.109.013603
20
A. Safavi-Naeini and O. Painter, Proposal for an optomechanical traveling wave phonon–photon translator, New J. Phys. 13(1), 013017 (2011) https://doi.org/10.1088/1367-2630/13/1/013017
21
M. Schmidt, M. Ludwig, and F. Marquardt, Optomechanical circuits for nanomechanical continuous variable quantum state processing, New J. Phys. 14(12), 125005 (2012) https://doi.org/10.1088/1367-2630/14/12/125005
22
M. Pang, W. He, X. Jiang, and P. Russell, All-optical bit storage in a fibre laser by optomechanically bound states of solitons, Nat. Photonics 10(7), 454 (2016) https://doi.org/10.1038/nphoton.2016.102
23
S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, A. Szorkovszky, W. P. Bowen, and H. Rubinsztein-Dunlop, Cavity optomechanical magnetometer, Phys. Rev. Lett. 108(12), 120801 (2012) https://doi.org/10.1103/PhysRevLett.108.120801
24
M. Li, W. Pernice, and H. X. Tang, Ultrahigh-frequency nano-optomechanical resonators in slot waveguide ring cavities, Appl. Phys. Lett. 97(18), 183110 (2010) https://doi.org/10.1063/1.3513213
25
C. Jiang, H. Liu, Y. Cui, X. Li, G. Chen, and B. Chen, Electromagnetically induced transparency and slow light in two-mode optomechanics, Opt. Express 21(10), 12165 (2013) https://doi.org/10.1364/OE.21.012165
26
K. H. Qu and G. S. Agarwal, Phonon-mediated electromagnetically induced absorption in hybrid optoelectromechanical systems, Phys. Rev. A 87, 031802(R) (2013)
27
B. P. Hou, L. F. Wei, and S. J. Wang, Optomechanically induced transparency and absorption in hybridized optomechanical systems, Phys. Rev. A 92(3), 033829 (2015) https://doi.org/10.1103/PhysRevA.92.033829
28
Z. Qian, M. M. Zhao, B. P. Hou, and Y. H. Zhao, Tunable double optomechanically induced transparency in photonically and phononically coupled optomechanical systems, Opt. Express 25(26), 33097 (2017) https://doi.org/10.1364/OE.25.033097
29
A. B. Shkarin, N. E. Flowers-Jacobs, S. W. Hoch, A. D. Kashkanova, C. Deutsch, J. Reichel, and J. G. E. Harris, Optically mediated hybridization between two mechanical modes, Phys. Rev. Lett. 112(1), 013602 (2014) https://doi.org/10.1103/PhysRevLett.112.013602
30
C. Bai, B. P. Hou, D. G. Lai, and D. Wu, Tunable optomechanically induced transparency in double quadratically coupled optomechanical cavities within a common reservoir, Phys. Rev. A 93(4), 043804 (2016) https://doi.org/10.1103/PhysRevA.93.043804
31
A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, Reservoir engineering and dynamical phase transitions in optomechanical arrays, Phys. Rev. A 86(3), 033821 (2012) https://doi.org/10.1103/PhysRevA.86.033821
G. D. de Moraes Neto, F. M. Andrade, V. Montenegro, and S. Bose, Quantum state transfer in optomechanical arrays, Phys. Rev. A 93(6), 062339 (2016) https://doi.org/10.1103/PhysRevA.93.062339
34
Z. Duan and B. Fan, Coherently slowing light with a coupled optomechanical crystal array, Europhys. Lett. 99(4), 44005 (2012) https://doi.org/10.1209/0295-5075/99/44005
35
OMPY is programmed by python combined with fortran, devoted to solve an optomechanical system consisted of multiple cavities by the standard linearization method. OMPY starts with an optomechanical Hamiltonian and then generates the Heisenberg–Langevin equations, which are solved by the standard linearization procedure, automatically.