4 - The Quantum Harmonic Oscillator
A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and Steven Chu
TL;DR Summary
Learn how to build a trap from scratch, starting with fundamental laser alignment, Gaussian beam opticals, and the balance of gradient and scattering forces.
Chapter 4 - The Quantum Harmonic Oscillator
In Chapter 2, we treated the trapped nanoparticle as a classical object bouncing around in a parabolic potential well, driven by the thermal energy of the room. However, if we evacuate the chamber to an ultra-high vacuum and use active feedback to “cool” the particle’s center-of-mass motion, something extraordinary happens. The classical equations of motion break down, and the particle enters the quantum regime.
Quantized Energy Levels In classical physics, a particle sitting at the bottom of the trap can have exactly zero energy.
In quantum mechanics, the Heisenberg Uncertainty Principle forbids this; if the particle had zero energy, its position and momentum would both be perfectly known simultaneously.
Instead, the energy of the trapped particle is quantized into discrete steps defined by the trapping frequency (