Master-slave locking of optomechanical oscillators over a long distance

We show that two independent mechanical oscillators, placed ~3.2km apart, and separated in frequency by ~80kHz, can be locked in a master-slave configuration, using light. This scheme can be generalised for an arbitrary network configuration.

[1]  October I.  Physical Review Letters , 2022 .

[2]  I. Mahboob,et al.  Bit storage and bit flip operations in an electromechanical oscillator. , 2008, Nature nanotechnology.

[3]  K. Vahala,et al.  Observation of injection locking in an optomechanical RF oscillator , 2008, LEOS 2008 - 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society.

[4]  Florian Marquardt,et al.  Collective dynamics in optomechanical arrays , 2010, 2013 Conference on Lasers & Electro-Optics Europe & International Quantum Electronics Conference CLEO EUROPE/IQEC.

[5]  R. Adler.  A Study of Locking Phenomena in Oscillators , 1946, Proceedings of the IRE.

[6]  Franco Maloberti,et al.  Circuits for Systems , 2011 .

[7]  H. Haus.  Waves and fields in optoelectronics , 1983 .

[8]  Richard H. Rand,et al.  Lecture Notes on Nonlinear Vibrations , 2012 .

[9]  Xudong Cao,et al.  Phase noise in coupled oscillators: theory and experiment , 1997 .

[10]  Brian H. Houston,et al.  Frequency entrainment for micromechanical oscillator , 2003 .

[11]  N. MacDonald.  Nonlinear dynamics , 1980, Nature.

[12]  K. Vahala,et al.  Brownian noise in radiation-pressure-driven micromechanical oscillators , 2005 .

[13]  Andrew G. Glen,et al.  APPL , 2001 .

[14]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[15]  K. Kurokawa,et al.  Noise in Synchronized Oscillators , 1968 .

[16]  Quantum many-body dynamics in optomechanical arrays. , 2012, Physical review letters.

[17]  W. Pernice,et al.  Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation. , 2011, Nature nanotechnology.

[18]  S. Girvin,et al.  Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities. , 2005, Physical review letters.

[19]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[20]  Chaitanya Joshi,et al.  Entanglement of distant optomechanical systems , 2011, 1111.2571.

[21]  J. Pierce.  The Proceedings of the IRE , 1954, Proceedings of the IRE.

[22]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[23]  K. Vahala,et al.  Modal coupling in traveling-wave resonators. , 2002, Optics letters.

[24]  M. Roukes,et al.  Phase synchronization of two anharmonic nanomechanical oscillators. , 2013, Physical review letters.

[25]  Tamás Roska,et al.  IEEE Transactions on Circuits and Systems I - Fundamental Theory and Applications: Editorial , 2003 .

[26]  Franziska Abend,et al.  Sync The Emerging Science Of Spontaneous Order , 2016 .

[27]  P. McEuen,et al.  Synchronization of micromechanical oscillators using light , 2011, IEEE Photonic Society 24th Annual Meeting.

[28]  H. Tang,et al.  Photonic cavity synchronization of nanomechanical oscillators. , 2013, Physical review letters.

[29]  V. E. Wood.  Table errata: Handbook of mathematical functions with formulas, graphs, and mathematical tables (Nat. Bur. Standards, Washington, D.C., 1964) edited by M. Abramowitz and I. A. Stegun , 1969 .

[30]  Robert A. York,et al.  Phase noise in externally injection-locked oscillator arrays , 1997 .

[31]  P. Zoller,et al.  Reservoir engineering and dynamical phase transitions in optomechanical arrays , 2012, 1206.6321.

[32]  Frank C. Hoppensteadt,et al.  Synchronization of MEMS resonators and mechanical neurocomputing , 2001 .

[33]  B. Razavi.  A study of injection locking and pulling in oscillators , 2004, IEEE Journal of Solid-State Circuits.

[34]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[35]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[36]  C. C. Wang,et al.  Nonlinear optics. , 1966, Applied optics.

[37]  K. D. Stephan,et al.  Inter-Injection-Locked Oscillators for Power Combining and Phased Arrays , 1986 .

[38]  Stefano Bregni,et al.  Synchronization of Digital Telecommunications Networks , 2002 .

[39]  Kerry Vahala,et al.  Cavity opto-mechanics. , 2007, Optics express.

[40]  K. J. Dean,et al.  Waves and Fields in Optoelectronics: Prentice-Hall Series in Solid State Physical Electronics , 1984 .

[41]  Chris Arney.  Sync: The Emerging Science of Spontaneous Order , 2007 .

[42]  David D. Wentzloff,et al.  IEEE Transactions on Microwave Theory and Techniques and Antennas and Propagation Announce a Joint Special Issue on Ultra-Wideband (UWB) Technology , 2010 .

[43]  M. Pandey,et al.  Frequency locking in a forced Mathieu–van der Pol–Duffing system , 2008 .

[44]  Abira Sengupta.  IEEE Journal of Solid-State Circuits Best Paper Award Through the Years , 2016, IEEE Solid-State Circuits Magazine.

[45]  M. Imboden,et al.  Synchronized Oscillation in Coupled Nanomechanical Oscillators , 2007, Science.

[46]  Sen,et al.  Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators , 1998, Physical review letters.