# Thoughts from reading “Creation of a quantum oscillator by classical control”

Published on: Sun Jan 09 2011

The LIGO gravitational wave observatory uses mirrors as a method to detect gravitational waves. The mirrors are very sensitive to even the slightest disturbance, so reducing exposure to noise is critical for detecting gravitational waves.

SQL: Standard Quantum Limit (not Structured Query Language)

The mirrors are hanging like pendulums and oscillating with a resonant frequency and a damping rate. Electronic feedback control is used to shift the resonant mode upwards and then to damp it. This changed the occupation number. (What is an Occupation Number?)

Occupation Number: The occupation number is used in second quantization: field theory, which is used to describe systems where particles can be created or destroyed.

While reading this paper the capital omega symbol I was unsure of in a previous post (here) is defined. It is the eigenfrequency of the controlled oscillator.

The reason for observing the occupation number is to calculate the “quantum-ness’ of the system. In this case though I think the system is a 10 kg mirror, which is not what I think of when I hear ‘quantum system’. I’m not sure why, but this time occupation number is not an ideal measure of quantum-ness (Is it because the system is non-standard?). Instead they look at the purity, which is composed of the uncertainties of the oscillators position, momentum and the interrelation between the two. The purity is used to calculate a minimum occupation number and determine a value for an arbitrary eigenfrequency.

To rephrase the last sentence, “The eigenfrequency is a function of the minimum occupation number”. Depending on where or not the eigenfrequency is greater or less than lower case omega (I think it’s angular frequency here) the quantum state is either position squeezed or momentum squeezed. (Squeezed?)

The remainder of the paper (pages 2 -  4) are about how to use the calculated eigenfrequency to devise an optimal controller to be used for frequency of the oscillator.

There are several references to Markovian measurements, what makes a measurement Markovian?