Ion traps and quantum information

Thus far, we have focused our attention on neutral atoms, and their interactions with the electromagnetic field. Charged atoms are an important physical system which are also important to study, for a variety of reasons. They can be confined in with much deeper potential wells, using electric fields, than is possible with light forces alone. Ions can also be readily trapped in small numbers, allowing single atoms or small, discrete numbers of atoms to be individually manipulated. This capability has made trapped ions an excellent physical system for creation of exotic quantum states, such as Schr\"odinger cat superpositions, and highly entangled multi-atom states. Trapped ions have also proven to be an excellent platform for implementation of many quantum information protocols, including teleportation, superdense coding, and quantum error correction; simple quantum algorithms such as the Deutsch-Jozsa and Grover quantum search algorithms have also been demonstrated. Efforts are underway in the community to realize trapped ion systems with not just handfuls, but rather, hundreds to thousands of individually controlled ion qubits, in highly integrated trapped ion chips.

This chapter begins with a description of laser cooling in the trapped ion physical system. We then describe how arbitrary motional states of ions can be engineered, in the second section. The third section describes quantum computation with trapped ions, and the fourth section covers concepts in quantum simulation with ions.