Nonlinear damping in graphene resonators

Croy, Alexander; Midtvedt, Daniel; Isacsson, Andreas; Kinaret, Jari M.

doi:10.1103/physrevb.86.235435

Cited by 88 publications

(84 citation statements)

References 35 publications

(56 reference statements)

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“…S34 using typical parameters gives Γ i ∼ Γ mn . Since we have instead Q ω = Q f >> Q i , the fluctuations are sufficiently slow so that we find that Γ i << Γ mn and thus the static limit is the relevant one, since other energy damping mechanisms [14][15][16] such as clamping loss mentioned above are also expected to produce significantly larger Q values than Q i . Therefore we expect the effects of motional narrowing to be minimal and the measured quality factor should follow the relation given for Q i , eq.…”

Section: S19mentioning

confidence: 84%

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Graphene Nanoelectromechanical Systems as Stochastic-Frequency Oscillators

et al. 2014

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In this Supporting Information section, we present derivations of the equations used in the main text as well as derivations of background material. Sections S1-S2 derive basic equations for the mechanics of the graphene sheet. Section S3 presents calculations of the magnitude of the expected signal when using the frequency modulated (FM) method for excitation and detection described in the main text.The remainder of the supplement can be divided into sections concerning the linewidth in the linear damping regime (Sections S4-S5) and phenomena in the nonlinear regime (S6-S7). Specifically, section S4 first presents derivations of the non-dissipative line broadening due to stiffness fluctuations induced by the coupling between the fundamental and the rest of the thermally excited membrane modes. Section S4 then considers dissipative mechanisms. The energy loss rate from

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Section: S19mentioning

confidence: 84%

“…[14][15][16] Here, we also consider a mechanism of energy transfer from one vibrational mode to another. The tension fluctuations within the sheet give rise to spatially inhomogeneous wave velocity fluctuations.…”

Section: Fast Mode Behaviormentioning

confidence: 99%

Graphene Nanoelectromechanical Systems as Stochastic-Frequency Oscillators

et al. 2014

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“…4c. A general theory that incorporates nonlinearities in both the restoring force and damping 10,[23][24][25][26] as well as thermal vibrations is beyond the scope of this article. We note that our new technique to measure the motion of the equilibrium position allows one to study the response of the resonator over a broad parameter range in driving force.…”

Section: Discussionmentioning

confidence: 99%

Symmetry breaking in a mechanical resonator made from a carbon nanotube

et al. 2013

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Nanotubes behave as semi-flexible polymers in that they can bend by a sizeable amount. When integrating a nanotube in a mechanical resonator, the bending is expected to break the symmetry of the restoring potential. Here we report on a new detection method that allows us to demonstrate such symmetry breaking. The method probes the motion of the nanotube resonator at nearly zero-frequency; this motion is the low-frequency counterpart of the second overtone of resonantly excited vibrations. We find that symmetry breaking leads to the spectral broadening of mechanical resonances, and to an apparent quality factor that drops below 100 at room temperature. The low quality factor at room temperature is a striking feature of nanotube resonators whose origin has remained elusive for many years. Our results shed light on the role played by symmetry breaking in the mechanics of nanotube resonators.

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“…However, for some dissipation mechanisms, see for instance Ref. [28], symmetry can dictate that the lowest order coupling to the environment must be quadratic in the coordinates. Systems with such symmetries are thus strong candidates for studying NLD in the quantum regime.…”

Section: Discussionmentioning

confidence: 99%

“…Naturally occurring NLD has been reported in systems which possess strong intrinsic nonlinearities [26]. Among these are carbon-based nanomechanical systems like graphene and carbon nanotubes [25,27,28]. Additionally, there have been reports of inducing nonlinear dissipation in optome- * Electronic address: andreas.isacsson@chalmers.se chanical systems [29,30], and suggestions for possible emergence of NLD in solid state quantum devices [31].…”

Section: Introductionmentioning

confidence: 99%

Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments

Voje

Isacsson

2015

Phys. Rev. A

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We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that due to the parity conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a supression of information exchange between the oscillators via the bath in the common bath configuration at low temperatures.

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Nonlinear damping in graphene resonators

Cited by 88 publications

References 35 publications

Graphene Nanoelectromechanical Systems as Stochastic-Frequency Oscillators

Graphene Nanoelectromechanical Systems as Stochastic-Frequency Oscillators

Symmetry breaking in a mechanical resonator made from a carbon nanotube

Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments

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