Macroscopic quantum tunneling in nanoelectromechanical systems

Sillanpää, Mika; Khan, Raphaël; Heikkilä, Tero T.; Hakonen, Pertti

doi:10.1103/physrevb.84.195433

Cited by 17 publications

(21 citation statements)

References 28 publications

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“…This will open up new directions owing to the large zero-point motion, large mechanical nonlinearity even at the few-quantum level [28][29][30], or along the interplay [31,32] of traditional graphene physics and mechanics.…”

Section: Prl 113 027404 (2014) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Graphene Optomechanics Realized at Microwave Frequencies

et al. 2014

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Cavity optomechanics has served as a platform for studying the interaction between light and micromechanical motion via radiation pressure. Here we observe such phenomena with a graphene mechanical resonator coupled to an electromagnetic mode. We measure thermal motion and backaction cooling in a bilayer graphene resonator coupled to a microwave on-chip cavity. We detect the lowest flexural mode at 24 MHz down to 50 mK, corresponding to roughly mechanical 40 quanta, representing nearly three orders of magnitude lower phonon occupation than recorded to date with graphene resonators.

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Section: Prl 113 027404 (2014) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Graphene Optomechanics Realized at Microwave Frequencies

et al. 2014

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“…n m determines the voltage dependence of the eigenfrequency as described in [11,12]. For V dc = 0, third-order terms Λ n mo vanish because of symmetry (u dc = 0), but for large V dc they grow as Λ hand is weak and in our analytical approximations [10] disregarded altogether.…”

mentioning

confidence: 99%

“…We arrive at the desired form (1) by writing the Hamiltonian in a basis which diagonalises Ω 2 n m and scaling the amplitude hy n of each mode by its zero point motion x zpn = 1 mωn [13]. Non-linearities are coming primarily from the induced tension, which is maximized for large deformations u(x) h. Therefore we concentrate on systems which allow large deformations, i.e., systems with d h. We truncate the expansion to the fourth order as in the model employed above the higher-order couplings are relevant only close to the point where the beam pulls into contact with the gate plane [12].…”

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confidence: 99%

Tension-induced nonlinearities of flexural modes in nanomechanical resonators

2013

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We consider the tension-induced non-linearities of mechanical resonators, and derive the Hamiltonian of the flexural modes up to the fourth order in the position operators. This tension can be controlled by a nearby gate voltage. We focus on systems which allow large deformations u(x) h compared to the thickness h of the resonator and show that in this case the third-order coupling can become non-zero due to the induced dc deformation and offers the possibility to realize radiationpressure-type equations of motion encountered in optomechanics. The fourth-order coupling is relevant especially for relatively low voltages. It can be detected by accessing the Duffing regime, and by measuring frequency shifts due to mode-mode coupling.PACS numbers: 85.85.+j Recent progress in fabricating nanomechanical resonators has shown how these systems can be used for ultrasensitive measurements of mass, force and charge [1][2][3][4]. Within the couple of past years these systems have also entered the quantum realm [5] as superpositions of vibration states and zero-point vibrations have been measured. Even though such measurements can be performed in a regime where the elastic properties of the resonators could essentially be considered as linear, the extension to non-linear conditions is well within reach of the current experimental techniques.In this paper we consider the generic non-linearities of the resonators, how these show up in measurements, and how they arise when the resonators are manipulated electronically. In general, the effect of non-linearites is twofold: on one hand they modify in an amplitudedependent way the resonant frequency of a given normal mode (Duffing self-non-linearity); on the other, they introduce a coupling between normal modes. Such nonlinearities show up in the presence of strong external driving, which allows to control the coupling of different modes or to detect their occupation numbers.Motivated by the recent advances in fabricating graphene and carbon nanotube resonators [4, 6], we concentrate especially on the regime of thin resonators where the mechanical deformation can be large compared to the resonator thickness. In this case, the major source of non-linearity is the tension induced by the deformation itself. Starting from the mechanical energy of the deformations, we derive the generic Hamiltonian of the flexural modes, including non-linearities up to the fourth order in the vibration amplitudes. In contrast to the results discussed in Refs. [7,8],where it is not taken into account, we explicitly consider the dc deformation of the resonator. This additional aspect creates an asymmetry in our system which leads to a cubic non-linearity. The dc deformation, dictating the strength of the non-linearity, is driven by a nearby gate voltage as in Fig. 1. Concentrating first on the Duffing self-non-linearity of the modes, this then allows us to derive the voltage depen- dence of the Duffing constant and show that it changes sign for a certain value of voltage that depends on mode index and the...

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“…Further evidence of the quantum nature of a mechanical resonator was provided by a measurement of the distinctively quantum asymmetry in the noise spectrum [45]. A few theoretical proposals for creating double-well potentials in which mechanical tunneling could be observed have also been put forward [48][49][50][51].…”

Section: Experimental Prospectsmentioning

confidence: 99%

Oscillator tunneling dynamics in the Rabi model

Irish

Gea‐Banacloche

2014

Phys. Rev. B

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The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, continues to produce rich and surprising physics when the coupling strength becomes comparable to the individual subsystem frequencies. We construct approximate solutions for the eigenstates and energies in the regime in which the oscillator frequency is small compared to that of the two-level system and the coupling strength matches or exceeds the oscillator frequency. The resulting oscillator dynamics closely resembles that of a particle tunneling in a classical double-well potential. Relating our calculation to an earlier semiclassical approximation in which coupling to the two-level system creates an effective potential for the oscillator, we examine the extent to which this picture is valid. We find that, for certain parameter regimes, the interpretation of the oscillator dynamics in terms of tunneling holds to a good approximation despite the fundamentally entangled nature of the joint system. We assess the prospects for observation of oscillator tunneling in the context of nano-or micromechanical experiments and find that it should be possible if suitably high coupling strengths can be engineered.

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Macroscopic quantum tunneling in nanoelectromechanical systems

Cited by 17 publications

References 28 publications

Graphene Optomechanics Realized at Microwave Frequencies

Graphene Optomechanics Realized at Microwave Frequencies

Tension-induced nonlinearities of flexural modes in nanomechanical resonators

Oscillator tunneling dynamics in the Rabi model

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