## Quantum information storage in atoms

February 9, 2017 Leave a comment

In a previous post I explained a little about why Seth Lloyd said that anything can be a quantum computer if you shine the right kind of light on it. Quantum information can be stored in electronic states of atoms. Those states might in principle be used for quantum computation. And those states can be manipulated by shining light on the atom. A more complete account can be found in these lecture notes. This post will be a very short summary in which I indicate some of the physical effects taking place in atoms. The subject overall is very complicated and mathematical so I can’t do much more than summarise it in a blog post.

A stable state for an electron around an atom is one in which its expectation values for measurable quantities don’t change over time. These states are states of constant energy and they form a discrete set that can be labelled by integers starting at zero, typically labelled by the letter *n*. The electron’s state isn’t fully described by how much energy it has, its orbital angular momentum also plays a role. The total amount of orbital angular momentum is labelled by another quantum number *l*. The orbital angular momentum in the *z* direction is also relevant and is labelled by another number *m*. Finally, an electron also has a type of intrinsic angular momentum called spin. The spin can only have two states and those a labelled by the letter *s* that can only take values -1,1. States of electrons around atoms are then described in terms of those values (*n,l,m,s*) that are called quantum numbers. Now, the amount of angular momentum an electron can have is related to its energy. Having angular momentum gives the electron energy. So an electron with a particular energy can’t have too much angular momentum or it will have more than is compatible with the amount of energy it has.

The electron’s stable states give probabilities for the electron to be in a given region. Those probabilities can be plotted in various ways, e.g. – drawing surfaces inside which the electron has some high probability of being found. There are websites full of such plots so I won’t reproduce them here.

Since the states I described are stable, and they are labelled by a discrete set of quantum numbers they an be used to store qubits. There are restrictions on how those values can be manipulated. If you want to change the values of the quantum numbers of an electron then are trying to change its energy and angular momentum, which are conserved quantities. So if you want to increase the energy and angular momentum, you have to shine light on the atom that is carrying the relevant amount of energy and angular momentum. And if you want the atom to drop to a lower energy and angular momentum state, the light has to be able to carry away that energy and angular momentum.

Manipulating atoms with light requires using coherent light: light where different versions of a photon are related to one another in controlled ways. This allows you to control the whether they arrive at different places at the same time or different times at the same place and that sort of thing. This requires using lasers. So researchers making quantum computers will try to pick atoms with transitions where the energy matches those available in relatively inexpensive commercially available lasers. It is also possible to arrange for photons to have a particular amount of orbital angular momentum with the right equipment.