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Nonlinear position calibration of an optically trapped nanoparticle

The light field scattered by an optically levitated nanoparticle encodes in its phase
information about the position of the particle. An interferometric measurement allows us
to retrieve the position of the particle.

The light field scattered by an optically levitated nanoparticle encodes in its phase information about the position of the particle. An interferometric measurement allows us to retrieve the position of the particle. Large displacements, however, present a degree of inevitable distortion due to the nonlinear nature of the interferometric measurement [1].
The degree of distortion cannot be a priori estimated as it depends on the equilibrium
position of the particle and on the aberrations introduced by optical elements along the light’s path.
A promising approach to correct the nonlinear distortions has been recently investigated in the Photonics Laboratory. The method does not assume any specific functional form of the detection or of the optical potential. The idea relies on the fact that the thermal fluctuations that affect the particle are additive, i.e. the strength of the stochastic forces should not depend on the position of the particle. An additive fluctuation appears however as a state-dependent fluctuation if the measurement has nonlinear components. By studying how the fluctuations depend on the recorded position, it is possible to estimate the nonlinearity induced by the detector and correct for it.
The student will 1) familiarize him- of herself with the nonlinear calibration protocol for the over-damped regime, 2) estimate its performance for different scenarios and study its limits, 3) extend the protocol to the underdamped regime, where inertial effects change significantly the picture.
References:
[1] L. Rondin et al., Direct measurement of the Kramers turnover, Nat. Nanotech. (2017)
Prerequisites:
Experience or strong interest in data analysis (nonlinear fitting, uncertainty estimation, Fourier analysis, post-processing filtering), experience with simulation of differential equations is a plus.

The light field scattered by an optically levitated nanoparticle encodes in its phase information about the position of the particle. An interferometric measurement allows us to retrieve the position of the particle. Large displacements, however, present a degree of inevitable distortion due to the nonlinear nature of the interferometric measurement [1].
The degree of distortion cannot be a priori estimated as it depends on the equilibrium
position of the particle and on the aberrations introduced by optical elements along the light’s path.
A promising approach to correct the nonlinear distortions has been recently investigated in the Photonics Laboratory. The method does not assume any specific functional form of the detection or of the optical potential. The idea relies on the fact that the thermal fluctuations that affect the particle are additive, i.e. the strength of the stochastic forces should not depend on the position of the particle. An additive fluctuation appears however as a state-dependent fluctuation if the measurement has nonlinear components. By studying how the fluctuations depend on the recorded position, it is possible to estimate the nonlinearity induced by the detector and correct for it.
The student will 1) familiarize him- of herself with the nonlinear calibration protocol for the over-damped regime, 2) estimate its performance for different scenarios and study its limits, 3) extend the protocol to the underdamped regime, where inertial effects change significantly the picture.

References:
[1] L. Rondin et al., Direct measurement of the Kramers turnover, Nat. Nanotech. (2017)

Prerequisites:
Experience or strong interest in data analysis (nonlinear fitting, uncertainty estimation, Fourier analysis, post-processing filtering), experience with simulation of differential equations is a plus.

Not specified

Supervisor:
Andrei Militaru (andreimi@ethz.ch), Martin Frimmer (mfrimmer@ethz.ch)

Supervisor:
Andrei Militaru (andreimi@ethz.ch), Martin Frimmer (mfrimmer@ethz.ch)