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Hopf and perioddoubling bifurcations in an electromechanical resonator
I. Mahboob, R. Dupuy, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, Appl. Phys. Lett. 109, 073101 (2016) 
An electromechanical resonator is developed in which the dissipation can be dynamically eliminated. The resultant motional dynamics captured by the Van der Pol equation of motion opens up the possibility of a Hopf bifurcation where the mechanical resonance loses stability when the dissipation is eliminated and perioddoubling bifurcations when the dissipation becomes negative. In this latter regime, the mechanical spectral response is characterised by multistability spanning a bandwidth that is more than an order of magnitude wider than the intrinsic linewidth and it sustains a peak structure that can be tuned by the input used to dynamically manipulate the dissipation. 
An electromechanical Ising Hamiltonian
I. Mahboob, H. Okamoto, and H. Yamaguchi , Sci. Adv. 2, e1600236 (2016) 
Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating twomode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling. 
Gatecontrolled electromechanical backaction induced by a quantum dot
Y. Okazaki, I. Mahboob, K. Onomitsu, S. Sasaki, and H. Yamaguchi, Nature Communications 7, 11132 (2016) 
Semiconductorbased quantum structures integrated into mechanical resonators have emerged as a unique platform for generating entanglement between macroscopic phononic and mesocopic electronic degrees of freedom. A key challenge to realizing this is the ability to create and control the coupling between two vastly dissimilar systems. Here, such coupling is demonstrated in a hybrid device composed of a gatedefined quantum dot integrated into a piezoelectricitybased mechanical resonator enabling milliKelvin phonon states to be detected via charge fluctuations in the quantum dot. Conversely, the single electron transport in the quantum dot can induce a backaction onto the mechanics where appropriate bias of the quantum dot can enable damping and even currentdriven amplification of the mechanical motion. Such electron transport induced control of the mechanical resonator dynamics paves the way towards a new class of hybrid semiconductor devices including a current injected phonon laser and an ondemand single phonon emitter. 
Dispersive and Dissipative Coupling in a Micromechanical Resonator Embedded with a Nanomechanical Resonator
I. Mahboob, N. Perrissin, K. Nishiguchi, D. Hatanaka, Y. Okazaki, A. Fujiwara, and H. Yamaguchi , Nano Lett. 15, 2312 (2015) 
A micromechanical resonator embedded with a nanomechanical resonator is developed whose dynamics can be captured by the coupledVan der Pol縫uffing equations. Activating the nanomechanical resonator can dispersively shift the micromechanical resonance by more than 100 times its bandwidth and concurrently increase its energy dissipation rate to the point where it can even be deactivated. The coupledVan der Pol縫uffing equations also suggest the possibility of selfoscillations. In the limit of strong excitation for the nanomechanical resonator, the dissipation in the micromechanical resonator can not only be reduced, resulting in a quality factor of >3ﾗ10^6, it can even be eliminated entirely resulting in the micromechanical resonator spontaneously vibrating. 
TwoMode ThermalNoise Squeezing in an Electromechanical Resonator
I. Mahboob, H. Okamoto, K. Onomitsu, and H. Yamaguchi , Phys. Rev. Lett. 113, 167203 (2014) 
An electromechanical resonator is developed in which mechanical nonlinearities can be dynamically engineered to emulate the nondegenerate parametric downconversion interaction. In this configuration, phonons are simultaneously generated in pairs in two macroscopic vibration modes, resulting in the amplification of their motion. In parallel, twomode thermal squeezed states are also created, which exhibit fluctuations below the thermal motion of their constituent modes as well as harboring correlations between the modes that become almost perfect as their amplification is increased. The existence of correlations between two massive phonon ensembles paves the way towards an entangled macroscopic mechanical system at the single phonon level. 
Rapid switching in highQ mechanical resonators
H. Okamoto, I. Mahboob, K. Onomitsu, and H. Yamaguchi , Appl. Phys. Lett. 105, 083114 (2014) 
Sharp resonance spectra of highQ micromechanical resonators are advantageous in their applications, such as highly precise sensors and narrow bandpass filters. However, the highQ characteristics hinder quick repetitive operations of mechanical resonators because of their long ringdown time due to their slow energy relaxation. Here, we demonstrate a scheme to solve this tradeoff problem in paired GaAs micromechanical resonators by using parametrically induced intermode coupling. The strong intermode coupling induced by the piezoelectric modulation of tension allows ondemand energy transfer between closely spaced mechanical modes of the resonator via coherent control of the coupling. This enables rapid switching of the vibration amplitude within the ringdown time, leading to quick repetitive operations in highQ mechanical resonators. 
A multimode electromechanical parametric resonator array
I. Mahboob, M. Mounaix, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi , Sci. Rep. 4, 4448 (2014) 
Electromechanical resonators have emerged as a versatile platform in which detectors with unprecedented sensitivities and quantum mechanics in a macroscopic context can be developed. These schemes invariably utilise a single resonator but increasingly the concept of an array of electromechanical resonators is promising a wealth of new possibilities. In spite of this, experimental realisations of such arrays have remained scarce due to the formidable challenges involved in their fabrication. In a variation to this approach, we identify 75 harmonic vibration modes in a single electromechanical resonator of which 7 can also be parametrically excited. The parametrically resonating modes exhibit vibrations with only 2 oscillation phases which are used to build a binary information array. We exploit this array to execute a mechanical byte memory, a shiftregister and a controlledNOT gate thus vividly illustrating the availability and functionality of an electromechanical resonator array by simply utilising higher order vibration modes. 
Quantum point contact displacement transducer for a mechanical resonator at subKelvin temperatures
Y. Okazaki, I. Mahboob, K. Onomitsu, S. Sasaki, and H. Yamaguchi , Appl. Phys. Lett. 103, 153105 (2013) 
Highly sensitive displacement transduction of a 1.67 MHz mechanical resonator with a quantum point contact (QPC) formed in a GaAs heterostructure is demonstrated. By positioning the QPC at the point of maximum mechanical strain on the resonator and operating at 80 mK, a displacement responsivity of 3.81 A/m is measured, which represents a two order of magnitude improvement on the previous QPC based devices. By further analyzing the QPC transport characteristics, a subPoissonnoiselimited displacement sensitivity of 25 fm/Hz^0.5 is determined which corresponds to a position resolution that is 23 times the standard quantum limit. 
Multimode parametric coupling in an electromechanical resonator
I. Mahboob, V. Nier, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi , Appl. Phys. Lett. 103, 192105 (2013) 
Parametric coupling between multiple vibration modes in an electromechanical resonator is demonstrated via a strain inducing piezoelectric pump which enables construction of a mechanicalvibration register. In particular, the coupling between the flexural and torsional vibration modes can exceed their intrinsic dissipation rates enabling operation deep into the strongcoupling regime. The dynamic nature of this parametric coupling also permits temporal manipulation of the mechanicalvibration register enabling both longlived modes to be rapidly switched off and phonon populations to be coherently exchanged between modes. 
Coherent phonon manipulation in coupled mechanical resonators
H. Okamoto, A. Gourgout, CY Chang, K. Onomitsu, I. Mahboob, E. Y. Chang, and H. Yamaguchi , Nature Physics 9, 480484 (2013) 
Coupled nanomechanical resonators have recently attracted great attention for both practical applications and fundamental studies owing to their sensitive sympathetic oscillation dynamics. A challenge to the further development of this architecture is the coherent manipulation of the coupled oscillations. Here, we demonstrate strong dynamic coupling between two GaAsbased mechanical resonators by periodically modulating (pumping) the stress using a piezoelectric transducer. This strong coupling enables coherent transfer of phonon populations between the resonators, namely phonon Rabi oscillations. The nature of the dynamic coupling can also be tuned from a linear firstorder interaction to a nonlinear higherorder process in which more than one pump phonon mediates the coherent oscillations (that is, multipump phonon mixing). This coherent manipulation is not only useful for controlling classical oscillations but can also be extended to the quantum regime, opening up the prospect of entangling two distinct macroscopic mechanical objects. 
Phonon Lasing in an Electromechanical Resonator
I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi , Phys. Rev. Lett. 110, 127202 (2013) 
An electromechanical resonator harboring an atomlike spectrum of discrete mechanical vibrations, namely, phonon modes, has been developed. A purely mechanical threemode system becomes available in the electromechanical atom in which the energy difference of the two higher modes is resonant with a longlived lower mode. Our measurements reveal that even an incoherent input into the higher mode results in coherent emission in the lower mode that exhibits all the hallmarks of phonon lasing in a process that is reminiscent of Brillouin lasing. 
Phononcavity electromechanics
I. Mahboob, K. Nishiguchi, H. Okamoto, and H. Yamaguchi , Nature Physics 8. 387392 (2012) 
Photonic cavities have emerged as an indispensable tool to control and manipulate harmonic motion in opto/electromechanical systems. Invariably, in these systems a highqualityfactor photonic mode is parametrically coupled to a highqualityfactor mechanical oscillation mode. This entails the demanding challenges of either combining two physically distinct systems, or else optimizing the same nanostructure for both mechanical and optical properties. In contrast to these approaches, here we show that the cavity can be realized by the second oscillation mode of the same mechanical oscillator. A piezoelectric pump generates straininduced parametric coupling between the first and the second mode at a rate that can exceed their intrinsic relaxation rate. This leads to a mechanically induced transparency in the second mode which plays the role of the phonon cavity, the emergence of parametric normalmode splitting and the ability to cool the first mode. Thus, the mechanical oscillator can now be completely manipulated by a phonon cavity. 
Motion detection of a micromechanical cantilever through magnetopiezovoltage in twodimensional electron systems
H. Yamaguchi, H. Okamoto, S. Ishihara , and Y. Hirayama , Appl. Phys. Lett. 100, 012106 (2012) 
We study the straininduced voltage generation, i.e., piezovoltage, in a twodimensional electron system under a magnetic field at low temperature. We find its strong magneticfield dependence, where the voltage increases up to several microvolts at the boundaries between localized and extended electronic states. The order of magnitude of the generated electrical power is comparable to that of the energy dissipation in mechanical vibration, indicating highefficiency mechanicaltoelectrical energy transduction. 
Interconnectfree parallel logic circuits in a single mechanical resonator
I. Mahboob, E. Flurin, K. Nishiguchi, A. Fujiwara,and H. Yamaguchi, Nature Communications 2 (2011) 198 
In conventional computers, wiring between transistors is required to enable the execution of Boolean logic functions. This has resulted in processors in which billions of transistors are physically interconnected, which limits integration densities, gives rise to huge power consumption and restricts processing speeds. A method to eliminate wiring amongst transistors by condensing Boolean logic into a single active element is thus highly desirable. Here, we demonstrate a novel logic architecture using only a single electromechanical parametric resonator into which multiple channels of binary information are encoded as mechanical oscillations at different frequencies. The parametric resonator can mix these channels, resulting in new mechanical oscillation states that enable the construction of AND, OR and XOR logic gates as well as multibit logic circuits. Moreover, the mechanical logic gates and circuits can be executed simultaneously, giving rise to the prospect of a parallel logic processor in just a single mechanical resonator. 
Highsensitivity charge detection using antisymmetric vibration in coupled micromechanical oscillators H. Okamoto, N. Kitajima, K. Onomitsu,1 R. Kometani, S. Warisawa, Sunao Ishihara, and H. Yamaguchi, Appl. Phys. Lett. 98 (2011) 014103 
Highsensitivity charge detection using antisymmetric vibration in two coupled GaAs oscillators is demonstrated. The antisymmetric mode under inphase simultaneous driving of the two oscillators disappears with perfect frequency tuning. The piezoelectric stress induced by a small gatevoltage modulation breaks the balance of the two oscillators, leading to the reemergence of the antisymmetric mode. Measurement of the amplitude change enables detection of the applied voltage or, equivalently, added charges. In contrast to the frequencyshift detection using a single oscillator, our method allows a large readout up to the strongly driven nonlinear response regime, providing the high roomtemperature sensitivity of 147 e/Hz0.5. 
Room temperature piezoelectric displacement detection via a silicon field
effect transistor I. Mahboob, K. Nishiguchi, A. Fujiwara, and H. Yamaguchi, Appl. Phys. Lett. 95, 233102 (2009) 
An electromechanical oscillator embedded with a two dimensional electron gas is capacitively coupled to a silicon field effect transistor SiFET. The piezovoltage induced by the mechanical motion modulates the current passing through the SiFET enabling the electromechanical oscillator’s position to be monitored. When the SiFET is biased at its optimal point, the motion induced piezovoltage can be amplified resulting in a displacement sensitivity of 6 10?12 mHz?1/2 for a 131 kHz GaAs resonator which is among the highest recorded for an allelectrical room temperature detection scheme. 
Bit storage and bit flip operations in an electromechanical oscillator I. Mahboob and H. Yamaguchi, Nature Nanotechnology 3, 275 (2008) 
The Parametron was first proposed as a logicprocessing system almost 50 years ago. In this approach the two stable phases of an excited harmonic oscillator provide the basis for logic operations. Computer architectures based on LC oscillators were developed for this approach, but high power consumption and difficulties with integration meant that the Parametron was rendered obsolete by the transistor. Here we propose an approach to mechanical logic based on nanoelectromechanical systems that is a variation on the Parametron architecture and, as a first step towards a possible nanomechanical computer, we demonstrate both bit storage and bit flip operations. 
Improved resonance characteristics of GaAs beam resonators by epitaxially induced strain Applied Physics Letters 92 (25), 251913 (2008) 
Micromechanicalbeam resonators were fabricated using a strained GaAs film grown on relaxed In_{0.1}Ga_{0.9}As/In_{0.1}Al_{0.9}As buffer layers. The natural frequency of the fundamental mode was increased 2.54 times by applying tensile strain, showing good agreement with the model calculation assuming strain of 0.35% along the beam. In addition, the Q factor of 19,000 was obtained for the best sample, which is one order of magnitude higher than that for the unstrained resonator. This technique can be widely applied for improving the performance of resonatorbased micro/nanoelectromechanical devices. 
Motion detection of a micromechanical resonator embedded in a d.c. SQUID S. Etaki, M. Poot, I. Mahboob, K. Onomitsu, H. Yamaguchi and H. S. J. Van Der Zant, Nature Physics 4, 785 (2008) 
Superconducting quantum interference devices (SQUIDs) are the most sensitive detectors of magnetic flux and are also used as quantum twolevel systems (qubits). Recent proposals have explored a novel class of devices that incorporate micromechanical resonators into SQUIDs to achieve controlled entanglement of the resonator ground state and a qubit as well as permitting cooling and squeezing of the resonator modes and enabling quantumlimited position detection. In spite of these intriguing possibilities, no experimental realization of an onchip, coupled mechanicalresonatorSQUID system has yet been achieved. Here, we demonstrate sensitive detection of the position of a 2MHz flexural resonator that is embedded into the loop of a d.c. SQUID. We measure the resonator's thermal motion at millikelvin temperatures, achieving an amplifierlimited displacement sensitivity of 10 fm/Hz^{0.5} and a position resolution that is 36 times the quantum limit. 