Master-Slave Locking of Optomechanical Oscillators over a Long Distance

Shah, Shreyas Y.; Zhang, Mian; Rand, Richard H.; Lipson, Michal

doi:10.1103/physrevlett.114.113602

Cited by 47 publications

(48 citation statements)

References 29 publications

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“…We further demonstrate that the phase noise of the oscillation signal can be reduced by a factor of N below the thermomechanical phase noise limit of each individual oscillator as N oscillators are synchronized, in agreement with theoretical predictions [10,11]. The highly efficient, low loss and controllable nature of light mediated coupling could put large scale nano-and micromechanical oscillator networks in practice [12][13][14][15][16][17][18].…”

supporting

confidence: 84%

Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light

et al. 2015

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Synchronization of many coupled oscillators is widely found in nature and has the potential to revolutionize timing technologies. Here we demonstrate synchronization in arrays of silicon nitride micromechanical oscillators coupled in an all-to-all configuration purely through an optical radiation field. We show that the phase noise of the synchronized oscillators can be improved by almost 10 dB below the phase noise limit for each individual oscillator. These results open a practical route towards synchronized oscillator networks.Nano-and micromechanical oscillator arrays have the potential to enable high power and low noise integrated frequency sources that play a key role in sensing and the essential time keeping of modern technology [1][2][3][4][5]. The challenge with building scalable oscillator arrays is that micromechanical oscillators fabricated on a chip fundamentally have a spread of mechanical frequencies due to unavoidable statistical variations in the fabrication process [4,[6][7][8][9]. This dispersion in mechanical frequencies has a detrimental effect on the coherent operation in arrays of micromechanical oscillators. Here we show that arrays consisting of three, four and seven dissimilar microscale optomechanical oscillators can be synchronized to oscillate in unison coupled purely through a common optical cavity field using less than a milliwatt of optical power. We further demonstrate that the phase noise of the oscillation signal can be reduced by a factor of N below the thermomechanical phase noise limit of each individual oscillator as N oscillators are synchronized, in agreement with theoretical predictions [10,11]. The highly efficient, low loss and controllable nature of light mediated coupling could put large scale nano-and micromechanical oscillator networks in practice [12][13][14][15][16][17][18].Synchronization is a ubiquitous phenomenon found in coupled oscillator systems [10,19]. Heart beat is a result of synchronized motion of pace maker cells [20], circadian rhythm arises because of coordinated body physiology [21] and global positioning system relies on synchronized operation of clocks. On the nanoscale, synchronization has been experimentally demonstrated in nanomechanical systems coupled through mechanical connections [3], electrical capacitors [9], off-chip connections [6] and through an optical cavity [7,8]. However, these demonstrations were limited to only two oscillators. Achieving synchronization in large micromechanical oscillator networks requires scalable oscillator units and efficient and controllable coupling mechanisms [12,13,22].Here we experimentally demonstrate that arrays of free running micromechanical oscillators can be synchronized when coupled purely through a common electro- magnetic field as predicted by theories [12,13]. A conceptual view of an array of mechanical resonators coupled through light is illustrated in Figure 1a. Each optomechanical oscillator (OMO) possesses a slightly different frequency of mechanical oscillation (Ω i ) and is only connected...

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confidence: 84%

Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light

et al. 2015

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“…The total gain of the cascaded readout amplifier chain is 50dB. The effective forward scattering parameter achieved at resonance, S 21 , is ~25dB; depending upon 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 operating conditions; this yields output voltages ranging from ~1 to 1000mV. Low pass, high pass, and bandpass filters are incorporated within the amplifier chain to provide out-of-band signal suppression.…”

Section: X110mm (259 X 259 Dpi)mentioning

confidence: 99%

“…To our knowledge, independence between optomechanical nodes and inter-oscillator coupling has only been achieved with inter-nodal coupling mediated in the electrical, rather than the optical, domain 21 . In other recent optomechanical experiments that have purported to manifest synchronization, 22,23 the optical source used to drive the parametric nodal oscillations also provides common feedback to all resonators in the array.…”

Section: X110mm (259 X 259 Dpi)mentioning

confidence: 99%

Complex Dynamical Networks Constructed with Fully Controllable Nonlinear Nanomechanical Oscillators

Fon

Matheny

et al. 2017

Nano Lett.

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Control of the global parameters of complex networks has been explored experimentally in a variety of contexts. Yet, the more difficult prospect of realizing arbitrary network architectures, especially analog physical networks that provide dynamical control of individual nodes and edges, has remained elusive. Given the vast hierarchy of time scales involved, it also proves challenging to measure a complex network's full internal dynamics. These span from the fastest nodal dynamics to very slow epochs over which emergent global phenomena, including network synchronization and the manifestation of exotic steady states, eventually emerge. Here, we demonstrate an experimental system that satisfies these requirements. It is based upon modular, fully controllable, nonlinear radio frequency nanomechanical oscillators, designed to form the nodes of complex dynamical networks with edges of arbitrary topology. The dynamics of these oscillators and their surrounding network are analog and continuous-valued and can be fully interrogated in real time. They comprise a piezoelectric nanomechanical membrane resonator, which serves as the frequency-determining element within an electrical feedback circuit. This embodiment permits network interconnections entirely within the electrical domain and provides unprecedented node and edge control over a vast region of parameter space. Continuous measurement of the instantaneous amplitudes and phases of every constituent oscillator node are enabled, yielding full and detailed network data without reliance upon statistical quantities. We demonstrate the operation of this platform through the real-time capture of the dynamics of a three-node ring network as it evolves from the uncoupled state to full synchronization.

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“…When amplification overcomes mechanical dissipation, the system transits to a stable limit cycle, often referred to as optomechanical self-oscillation [26,27]. In the last years, several studies investigated the synchronization of such optomechanical oscillators [20][21][22]25]. The synchronization of two oscillators placed close to contact and sharing a common optical mode was reported in [20].…”

mentioning

confidence: 99%

“…Two spatially-separated oscillators integrated in a common optical racetrack cavity were also synchronized in [22]. The possibility of locking two optomechanical systems without sharing a common optical mode was implemented as well in [21], in two steps and with two lasers. The optical output of a first laser-driven optomechanical oscillator was transduced into an electrical signal, which was carried away to fed a distant electro-optic modulator.…”

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confidence: 99%

Light-Mediated Cascaded Locking of Multiple Nano-Optomechanical Oscillators

et al. 2017

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Collective phenomena emerging from non-linear interactions between multiple oscillators, such as synchronization and frequency locking, find applications in a wide variety of fields. Optomechanical resonators, which are intrinsically non-linear, combine the scientific assets of mechanical devices with the possibility of long distance controlled interactions enabled by travelling light. Here we demonstrate light-mediated frequency locking of three distant nano-optomechanical oscillators positioned in a cascaded configuration. The oscillators, integrated on a chip along a coupling waveguide, are optically driven with a single laser and oscillate at gigahertz frequency. Despite an initial frequency disorder of hundreds of kilohertz, the guided light locks them all with a clear transition in the optical output. The experimental results are described by Langevin equations, paving the way to scalable cascaded optomechanical configurations.Synchronization and frequency locking have been observed in a large variety of contexts ranging from physics to biology, e.g. in classical coupled pendula [1], in coupled lasers [2], and in the rhythmic beating of pacemaker cells [3]. These phenomena have found practical applications in RF communication [4], signal-processing [5], novel computing and memory concepts [6,7], clock synchronization and navigation [8], as well as in phased locked loop circuits [9]. For these applications, micro-and nano-mechanical devices are known to present opportunities of integration and scalability [10][11][12][13][14][15] but more recently, optomechanical systems further emerged as new appealing candidates. Indeed they support non-linearly coupled optical and mechanical modes [16,17], and add to the mechanics the assets of optical techniques in terms of precision and long-distance communications [18][19][20][21][22][23][24][25].Light injected in an optomechanical cavity can deform it under the action of optical forces, and in the dynamical backaction regime can amplify its mechanical motion. When amplification overcomes mechanical dissipation, the system transits to a stable limit cycle, often referred to as optomechanical self-oscillation [26,27]. In the last years, several studies investigated the synchronization of such optomechanical oscillators [20][21][22]25]. The synchronization of two oscillators placed close to contact and sharing a common optical mode was reported in [20]. Recently, the same configuration was pushed up to 7 resonators [25]. Two spatially-separated oscillators integrated in a common optical racetrack cavity were also synchronized in [22]. The possibility of locking two optomechanical systems without sharing a common optical mode was implemented as well in [21], in two steps and with two lasers. The optical output of a first laser-driven optomechanical oscillator was transduced into an electrical signal, which was carried away to fed a distant electro-optic modulator. The latter modulated a second laser driving a second optomechanical oscillator, ultimately insuring phase lo...

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Master-Slave Locking of Optomechanical Oscillators over a Long Distance

Cited by 47 publications

References 29 publications

Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light

Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light

Complex Dynamical Networks Constructed with Fully Controllable Nonlinear Nanomechanical Oscillators

Light-Mediated Cascaded Locking of Multiple Nano-Optomechanical Oscillators

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