In future transistors at the sub-micron scale, matter no longer behaves like the classical particles we are used to. Rather, it acts like a wave, and physicists use a quantity called a wavefunction to describe it.

My work at Harvard connects the wave-like properties of quantum matter back to the classical world by processing the wavefunction using a tiny object called a Husimi state, which exhibits both wave-like and particle-like properties.

Above, I show the quantum wavefunction for an electron trapped by an extremely strong magnetic field. Normally, all that is available to us are the wavefunction and the flux, which tells us, at each point, how the electron is moving.

However, the flux looks nothing like the actual classical orbits that correspond to the wavefunction. I can retrieve the correspondence using Husimi states and automatically extract the classical orbits out of the wavefunction.

The secret lies in the fact that Husimi states give us a richer set of information than the flux. I have magnified the information in the red circles below. At right, the wavefunction is shown, with the classical trajectories in white. The Husimi states give us a range of trajectories at a point (grey). While the flux (blue) averages over all the vectors at a point, I can extract the most meaningful vectors straight from the Husimi states (red).

Thanks to my work, developments in super-tiny transistors can march forward with a much deeper understanding of the quantum states that arise inside of them.