Visualizing Quantum Dynamics:

Bloch Spheres and Q-Functions

Jared Ostmeyer and Julio Gea-Banacloche

University of Arkansas

With support from the National Science Foundation

This is the gateway to a collection of applets developed in order to help visualize the evolution of some quantum mechanical systems of interest in quantum optics, atomic physics, and quantum information theory. The basic tools used are the Bloch Sphere, for two-level systems (such as a two-level atom, a spin 1/2 system or a Cooper-pair box), and the Q-function (sometimes called the Husimi function) for a quantum harmonic oscillator, such as a single mode of the electromagnetic field, or a nanoresonator.

The applets are highly interactive: they can be resized and the viewpoint can be rotated in real time, and a wide range of initial conditions and parameters may be chosen.

The applets currently available are:

An interesting feature of these applets is a "math reader" java class that allows the user to enter any mathematical expression in a text field. A separate demo with links to the code is available here.


The applets were developed by Jared Ostmeyer (jostmey AT uark DOT edu) under the supervision of Julio Gea-Banacloche (jgeabana AT uark DOT edu) during the summer of 2006 as part of an NSF-sponsored REU program in the Physics Department at the University of Arkansas. The code is freely available; please contact any of us for it.

In order to run these applets properly it is generally best to have the most recent version of the Java virtual machine installed in your computer. This seems to be especially true for Mac OS computers.


This page has been accessed times since September 12, 2006.