In this exercise, students are asked to explore parametric excitation. That is, what happens when you shake or squeeze a state in a harmonic potential? This is an interesting problem from the point of view of atomic physics, where it is commonly used to characterize harmonic atom traps; this technique is known as modulation spectroscopy. Excitation in harmonic and anharmonic potentials is an interesting problem from the point of view of quantum control and state transfer. This is explored in more detail in the Shake Up challenge found in this subfolder.

This problem can be tackled and understood using time-dependent perturbation theory and Fermi's golden rule.

There are two flow files used in this exercise: one for shaking, and one for squeezing.

Key words and phrases: quantum harmonic oscillator, parametric heating, time-dependent perturbation theory, Fermi's golden rule, potential modulation