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Transition path reconstruction with a nanoparticle levitated in a bistable potential
During this project, the student will understand and improve an optical setup that
generates a double well potential, acquire position measurements of a nanoparticle
in the double well potential, analyse, understand and tune the transition paths of the
nanoparticle.
Transitions between metastable states are at the heart of many phenomena. This
includes chemical reactions, phase transitions or protein folding, just to name a few [1, 2].
Over the past decades, much effort has been invested into measuring and characterizing
the transition rate, i.e. the average time required for the system to transition between
the two metastable states [3]. Such measurement is typically performed by trapping a
levitated nanoparticle with two displaced laser beams. Each of the two foci acts as a
potential well, and the barrier between the two minima can be tuned by adjusting the
laser power and the distance between the two beams [3]. Measuring the position of a particle levitated in a double well potential allows us to step beyond the transition rate
estimation. We can in fact perform a characterization of the transition paths followed
by the particle, i.e. the trajectories followed by the particle in phase space during the
transitions [4].
During this project, the student will (1) understand and improve an optical setup that
generates a double well potential, (2) acquire position measurements of a nanoparticle
in the double well potential, (3) analyse, understand and tune the transition paths of the
nanoparticle.
Prerequisites: Experience or strong interest in data analysis and optics, basics of statistical
physics are a plus.
References:
[1] P. Hanggi, P. Talkner, M. Borkovec, Review of Modern Physics, (1990)
[2] H. Risken, The Fokker-Planck Equation, Springer
[3] L. Rondin et al., Nature Nanotechnology 12, 1130-1133 (2020)
[4] N. Zijlstra et al., Physical Review Letters 125, 146001 (2020)
Transitions between metastable states are at the heart of many phenomena. This includes chemical reactions, phase transitions or protein folding, just to name a few [1, 2]. Over the past decades, much effort has been invested into measuring and characterizing the transition rate, i.e. the average time required for the system to transition between the two metastable states [3]. Such measurement is typically performed by trapping a levitated nanoparticle with two displaced laser beams. Each of the two foci acts as a potential well, and the barrier between the two minima can be tuned by adjusting the laser power and the distance between the two beams [3]. Measuring the position of a particle levitated in a double well potential allows us to step beyond the transition rate estimation. We can in fact perform a characterization of the transition paths followed by the particle, i.e. the trajectories followed by the particle in phase space during the transitions [4]. During this project, the student will (1) understand and improve an optical setup that generates a double well potential, (2) acquire position measurements of a nanoparticle in the double well potential, (3) analyse, understand and tune the transition paths of the nanoparticle.
Prerequisites: Experience or strong interest in data analysis and optics, basics of statistical physics are a plus.
References: [1] P. Hanggi, P. Talkner, M. Borkovec, Review of Modern Physics, (1990) [2] H. Risken, The Fokker-Planck Equation, Springer [3] L. Rondin et al., Nature Nanotechnology 12, 1130-1133 (2020) [4] N. Zijlstra et al., Physical Review Letters 125, 146001 (2020)