SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 45, Issue 4: 44201(2015) https://doi.org/10.1360/SSPMA2014-00422

## The cavity modes and the adiabatic theory in coupled cavity optomechanical systems

• AcceptedFeb 2, 2015
• PublishedMar 13, 2015
Share
Rating

### Abstract

Following a direct physical picture, this paper presents a simple but general study on the coupled cavity optomechanical system as well as some other similar systems based on the adiabatic approximation theory. The basic theoretical model and the relevant mathematical method are provided in this paper. The cavity optomechanics is a very quickly developing field and its basic theoretical model is an essential starting point to study the physical properties of the system. The traditional theoretical method to derive the model is based on the Maxwell equations with a moving cavity boundary condition. This method involves a complicated calculation procedure which lacks clear physical picture and misses general connections to other similar systems. This paper adopts the adiabatic theory and the transfer matrix method instead to investigate the coupled Fabry-Pérot cavities with the membrane-in-the-middle scheme, and gives a universal calculation on the cavity- mode frequency and the transmission rate modulating by the collective motion of the membranes. The method not only leads to the same model as that derived from Maxwell equations, but also presents a more general physical background to the study of cavity-coupled mechanical systems.

### References

[1] Walther H, Varcoe B T H, Englert B G, et al. Cavity quantum electrodynamics. Rep Prog Phys, 2006, 69: 1325-1382

[2] Maldovan M. Sound and heat revolutions in phononics. Nature, 2013, 503: 209-217

[3] Midtvedt D, Isacsson A, Croy A, et al. Nonlinear phononics using atomically thin membranes. Nat Commun, 2014, 5: 4838

[4] Juska G, Dimastrodonato V, Mereni L O, et al. Towards quantum dot arrays of entangled photon emitters. Nat Photon, 2013, 7: 527-531

[5] Wacker A. Semiconductor superlattices: A model system for nonlinear transport. Phys Rep, 2002, 357: 1-111

[6] Lapine M, Shadrivov I V, Kivshar Y S. Colloquium: Nonlinear metamaterials. Rev Mod Phys, 2014, 86: 1093-1123

[7] Ritsch H, Domokos P, Brennecke F, et al. Cold atoms in cavity-generated dynamical optical potentials. Rev Mod Phys, 2013, 85: 553-601

[8] Soljacic M, Joannopoulos J D. Enhancement of nonlinear effects using photonic crystals. Nat Mater, 2004, 3: 211-219

[9] Joannopoulos J D, Villeneuve P R, Fan S H. Photonic crystals: Putting a new twist on light. Nature, 1997, 386: 143-149

[10] Eichenfield M, Chan J, Camacho R M, et al. Optomechanical crystals. Nature, 2009, 462: 78-82

[11] Kauranen M, Zayats A V. Nonlinear plasmonics. Nat Photon, 2012, 6: 737-748

[12] Ren M X, Plum E, Xu J J, et al. Giant nonlinear optical activity in a plasmonic metamaterial. Nat Commun, 2012, 3: 833

[13] Christodoulides D N, Lederer F, Silberberg Y, et al. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature, 2003, 424:817-823

[14] Cho A. To physicists' surprise, a light touch sets tiny objects aquiver. Science, 2005, 309: 366

[15] Chan J, Alegre T P M, Safavi-Naeini A H, et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature, 2011, 478:89-92

[16] Aspelmeyer M, Kippenberg T J, Marquardt F. Cavity Optomechanics: Nano- and Micromechanical Resonators Interacting with Light. Berlin: Springer, 2014

[17] Aspelmeyer M, Kippenberg T J, Marquardt F. Cavity optomechanics. Rev Mod Phys, 2014, 86: 1391-1452

[18] Metcalfe M. Applications of cavity optomechanics. Appl Phys Rev, 2014, 1: 031105

[19] Thompson J D, Zwickl B M, Jayich A M, et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature, 2008,452: 72-75

[20] Sankey J C, Yang C, Zwickl B M, et al. Strong and tunable nonlinear optomechanical coupling in a low-loss system. Nat Phys, 2010, 6: 707-712

[21] Holmes C A, Meaney C P, Milburn G J. Synchronization of many nanomechanical resonators coupled via a common cavity field. Phys Rev E,2012, 85: 066203

[22] Griffiths D J. Introduction to Quantum Mechanics. 2nd ed. Upper Saddle River: Prentice Hall, 2004

[23] Bhattacharya M, Shi H, Preble S. Coupled second-quantized oscillators. Am J Phys, 2013, 81: 267-273

[24] Walls D F, Milburn G J. Quantum Optics. 2nd ed. Berlin: Spring-Verlag, 2008

[25] Law C K. Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation. Phys Rev A, 1995, 51: 2537-2541

[26] Milburn J, Walls D F. Quantum nondemolition measurements via quadratic coupling. Phys Rev A, 1983, 28: 2065-2070

[27] Nunnenkamp A, Børkje K, Harris J G E, et al. Cooling and squeezing via quadratic optomechanical coupling. Phys Rev A, 2010, 82: 021806

[28] Vanner M R. Selective linear or quadratic optomechanical coupling via measurement. Phys Rev X, 2011, 1: 021011

[29] Zhang L, Song Z D. Modification on static responses of a nano-oscillator by quadratic opto-mechanical couplings. Sci China-Phys Mech Astron,2014, 57: 880-886

[30] Zhang L, Kong H Y. Self-sustained oscillation and harmonic generation in optomechanical systems with quadratic couplings. Phys Rev A, 2014,89: 023847

[31] Wilson D J, Regal C A, Papp S B, et al. Cavity optomechanics with stoichiometric SiN films. Phys Rev Lett, 2009, 103: 207204

[32] Wiederhecker G S, Chen L, Gondarenko A, et al. Controlling photonic structures using optical forces. Nature, 2009, 462: 633-636

[33] Zou C L, Dong C H, Cui J M, et al. Whispering gallery mode optical microresonators: Fundamentals and applications (in Chinese). Sci Sin-Phys Mech Astron, 2012, 42: 1155-1175 [邹长铃, 董春华, 崔金明, 等. 回音壁模式光学微腔: 基础和应用. 中国科学: 物理学力学天文 学, 2012, 42: 1155-1175]

[34] Fader W J. Theory of two coupled lasers. IEEE J Quantum Electron, 1985, 21: 1838-1844

[35] Bhattacharya M, Uys H, Meystre P. Optomechanical trapping and cooling of partially reflective mirrors. Phys Rev A, 2008, 77: 033819

[36] Massel F, Chow S U, Pirkkalainen J-M, et al. Multimode circuit optomechanics near the quantum limit. Nat Commun, 2012, 3: 987

[37] Zhu W, Wang Z H, Zhou D L. Multimode effects in cavity QED based on a one-dimensional cavity array. Phys Rev A, 2014, 90: 043828

[38] Landau L D. Theory of energy transfer II. Phys Z Sowjetunion, 1932, 2: 19

[39] Zener C. Non-adiabatic crossing of energy levels. Proc R Soc Lond A, 1932, 137: 696-702

[40] Liao J Q, Nori F. Photon blockade in quadratically coupled optomechanical systems. Phys Rev A, 2013, 88: 023853

[41] Huang S Y, Tsang M K . Electromagnetically induced transparency and optical memories in an optomechanical system with N membranes. arXiv:1403.1340

[42] Xu X W, Zhao Y J, Liu Y X. Entangled-state engineering of vibrational modes in a multimembrane optomechanical system. Phys Rev A, 2013,88: 022325

[43] Xuereb A, Genes C, Dantan A. Strong coupling and long-range collective interactions in optomechanical arrays. Phys Rev Lett, 2012, 109: 223601

[44] Asbóth J K, Ritsch H, Domokos P. Optomechanical coupling in a one-dimensional optical lattice. Phys Rev A, 2008, 77: 063424

[45] Poot M, van der Zant H S J. Mechanical systems in the quantum regime. Phys Rep, 2012, 511: 273-335

[46] Teufel J D, Harlow J W, Regal C A, et al. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys Rev Lett, 2008, 101:197203

[47] Barzanjeh S, Abdi M, Milburn G J, et al. Reversible optical to microwave quantum interface. Phys Rev Lett, 2012, 109: 130503

Citations

• #### 0

Altmetric

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有