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Nanomechanical oscillators in quartic and quadratic potentials
The goal of this project is to bridge the gap between the theory and the experiment. Your tasks will involve formulating theoretical predictions on what PSD we should expect at different experimental parameters and analyzing the experimental data in the context of these predictions.
In most optomechanics experiments, we assume that position and orientation degrees of freedom of optically levitated nanoparticles behave like harmonic oscillators. In other words, the potential is approximately quadratic; i.e. V=-m ω^2 x^2. However, this is only an approximation and normally a small anharmonic component is also present (such as a quartic term in the form V=α x^4), which becomes noticeable as we increase the motion amplitude.
In ETH Photonics Laboratory we have engineered a sophisticated system, in which a librational degree of freedom (orientation angle θ- see picture) of a levitated nanodumbbell follows a dynamical behavior with a completely tunable quartic nonlinearity.
However, it is not possible to directly measure the potential in order to verify this claim - all we have access to is the power spectral density (PSD) of the motion of the nanoparticle. Although the relation between PSD and potential shape is non-trivial, a recently published theoretical work ( https://doi.org/10.1103/PhysRevA.103.013110) describes the signatures of quartic nonlinearity we should observe in the PSD of the oscillator.
The goal of this project is to bridge the gap between the theory and the experiment. Your tasks will involve formulating theoretical predictions on what PSD we should expect at different experimental parameters and analyzing the experimental data in the context of these predictions.
This a predominantly theoretical project, but with a very close proximity to experiments (working with experimental data, and possibly involving a small experimental component).
In most optomechanics experiments, we assume that position and orientation degrees of freedom of optically levitated nanoparticles behave like harmonic oscillators. In other words, the potential is approximately quadratic; i.e. V=-m ω^2 x^2. However, this is only an approximation and normally a small anharmonic component is also present (such as a quartic term in the form V=α x^4), which becomes noticeable as we increase the motion amplitude.
In ETH Photonics Laboratory we have engineered a sophisticated system, in which a librational degree of freedom (orientation angle θ- see picture) of a levitated nanodumbbell follows a dynamical behavior with a completely tunable quartic nonlinearity.
However, it is not possible to directly measure the potential in order to verify this claim - all we have access to is the power spectral density (PSD) of the motion of the nanoparticle. Although the relation between PSD and potential shape is non-trivial, a recently published theoretical work ( https://doi.org/10.1103/PhysRevA.103.013110) describes the signatures of quartic nonlinearity we should observe in the PSD of the oscillator.
The goal of this project is to bridge the gap between the theory and the experiment. Your tasks will involve formulating theoretical predictions on what PSD we should expect at different experimental parameters and analyzing the experimental data in the context of these predictions.
This a predominantly theoretical project, but with a very close proximity to experiments (working with experimental data, and possibly involving a small experimental component).