Cavity quantum electrodynamics

Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles, under conditions where the quantum nature of photons is significant. It could in principle be used to construct a quantum computer.

The case of a single 2-level atom in the cavity is mathematically described by the Jaynes–Cummings model, and undergoes vacuum Rabi oscillations ${\displaystyle |e\rangle |n-1\rangle \leftrightarrow |g\rangle |n\rangle }$, that is between an excited atom and ${\displaystyle n-1}$ photons, and a ground state atom and ${\displaystyle n}$ photons.

If the cavity is in resonance with the atomic transition, a half-cycle of oscillation starting with no photons coherently swaps the atom qubit's state onto the cavity field's, ${\displaystyle (\alpha |g\rangle +\beta |e\rangle )|0\rangle \leftrightarrow |g\rangle (\alpha |0\rangle +\beta |1\rangle )}$, and can be repeated to swap it back again; this could be used as a single photon source (starting with an excited atom), or as an interface between an atom or trapped ion quantum computer and optical quantum communication.

Other interaction durations create entanglement between the atom and cavity field; for example, a quarter-cycle on resonance starting from ${\displaystyle |e\rangle |0\rangle }$ gives the maximally entangled state (a Bell state) ${\displaystyle (|e\rangle |0\rangle +|g\rangle |1\rangle )/{\sqrt {2}}}$. This can in principle be used as a quantum computer, mathematically equivalent to a trapped ion quantum computer with cavity photons replacing phonons.