Quantum Sensing and Measurement

The course will begin with an introduction and review of the (classical) concepts of sensitivity, noise, and power spectral density.

The basics of the harmonic oscillator will be reviewed, including the example of the Harmonic oscillator coherent state and its properties, along with the quadrature representation of classical and quantum coherent fields, and wigner functoins

A first example of quantum noise will be introduced using the harmonic oscillator: in particular the concept of quantum (photon) shot noise in coherent states.

The paradigm of continuous measurement will be covered intuitively starting from the generalised statistical interpretation, and then using the Monte Carlo wavefunction technique

These concepts be used to understand the shot noise limit for imprecision noise, and intuitively explore the radiation pressure shot noise limit of optomechanics, a prototypical example of quantum backaction noise. Combining these, we will explore the standard quantum limit (SQL) of sensing and measurement.

The density matrix will be introduced as a tool for combining concepts of quantum and classical noise in qubits and in quantum optics

The mathematics of quantum noise will be formalized using the density matrix and the Lindblad master equation

The QuTiP software package for simulating dynamics of open and monitored quantum systems will be introduced

Basic examples of quantum dynamics will be illustrated using QuTiP

In the last component of the course, the students will simulate a physical process of quantum dynamics combining noise and quantum measurement in a quantum system of their choice, with support from the staff