Observation of Locked Phase Dynamics and Enhanced Frequency Stability in Synchronized Micromechanical Oscillators

We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization-given their high-quality factors, small footprint, and ease of cointegration with modern electronic signal processing technologies. Synchronization is a ubiquitous phenomenon both in the physical and biological sciences. It has been observed to occur over a wide range of scales-from the ecological [1], with oscillation periods of years, to the microscale [2], with oscillation periods of milliseconds. Although synchronization has been extensively studied theoretically [3][4][5], relatively few experimental systems have been realized that provide detailed insight into the underlying dynamics. Here we show that oscillators based on nanoelectromechanical systems (NEMS) can readily enable the resolution of such details, while providing many unique advantages for experimental studies of nonlinear dynamics [6][7][8]. In addition, nanomechanical systems might prove useful for exploring quantum synchronization [9,10].Nanomechanical oscillators also have been exploited for a variety of applications [11][12][13]. In particular, nanoscale mechanics exhibits enhanced nonlinearity [14,15] and tunability [16,17], which has been used to suppress feedback noise [18,19] and create new types of electromechanical oscillators [20][21][22]. These oscillators may find application as mass [23], gas [24,25], or force sensors [26], without the need of an external frequency source.Building frequency sources from arrays of NEMS may yield enhanced applicability, but is challenging. For example, statistical deviations in batch fabrication inevitably lead to undesirable array dispersion [24]. If an array has appreciable frequency dispersion, global sensor responsivity gets reduced. However, if the elements of the array are made into a self-sustained oscillators and synchronized with one another, then the array responsivity will recover due to a reduction in phase noise [3]. Since NEMS have numerous applications, and are useful in studying nonlinear dynamics, we set an important milestone by demonstrating synchronization in nanomechanical systems.There are previous reports of synchronization in microor nanomechanical systems. However, these do not, in fact, demonstrate the phenomenon as conventionally defined [3] -that is, the phase locking of weakly coupled selfsustained oscillators. Shim et al.[27] reported synchronization of the driven excitations in coupled resonat...

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“…We thank E. Kenig In the process of going through review, synchronization was explored in a similar system [36].…”

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confidence: 99%

Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

et al. 2014

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“…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.…”

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confidence: 99%

“…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.…”

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confidence: 99%

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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“…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].…”

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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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Observation of Locked Phase Dynamics and Enhanced Frequency Stability in Synchronized Micromechanical Oscillators

Cited by 93 publications

References 26 publications

Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

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

Light-Mediated Cascaded Locking of Multiple Nano-Optomechanical Oscillators

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