If a very slow moving, excited atom is sent into a resonant, empty cavity, these forces result in a kind of atomic beam splitter. The nonstationary initial state of the system consists of the sum of the repelling and attractive states-- a superposition of the two stationary atom-cavity wave functions. Half corresponds to an atom reflected back at the cavity entrance, and the other half corresponds to an atom passing through; either outcome occurs with equal probability.
To prepare a pure attractive or repelling state, one should detune the cavity slightly from the atomic transition. When the transition is a bit more energetic than the photon that the cavity can sustain, the state with an excited atom and no photon has a little more energy than the one with a de-excited atom and one photon. When the atom enters the cavity, the exchange coupling works to separate the two states, so that the state with an excited atom and no photon branches unambiguously into the higher-energy steady state, in which the atom is repelled. The same trick just as easily makes an attractive state if the cavity photon energy is slightly higher than the atomic transition.
This evolution of the atom-cavity system relies on the so-called adiabatic theorem, which says that if a quantum system's rate of change is slow enough, the system will continuously follow the state it is initially prepared in, provided the energy of that state does not coin- cide at any time with that of another state. This adiabaticity criterion is certainly met for the very slow atoms considered here.
These atom-cavity forces persist as long as the atom remains in its Rydberg state and the photon is not absorbed by the cavity walls. This state of affairs can typically last up to a fraction of a second, long enough for the atom to travel through the centimeter-size cavity.
The forces between atom and cavity are strange and ghostly indeed. The cavity is initially empty, and so in some way the force comes from the vacuum field, which suggests that it is obtained for nothing. Of course, that is not strictly true, because if the cavity is empty, the atom has to be initially excited, and some price is paid after all.
The force can also be attributed to the exchange of a photon between the atom and the cavity. Such a view is analogous to the way that electric forces between two charged particles are ascribed to the exchange of photons or the forces between two atoms in a molecule to the exchange of electrons.
Another interpretation of the atom-cavity vacuum attraction and repulsion, based on a microscopic analysis, shows that these phenomena are in fact not essentially different from the electrostatic forces whose demonstration was a society game in the 18th-century French court. If one charges a needle and brings small pieces of paper into its vicinity, the pieces stick to the metal. The strong electric field at the tip polarizes the pieces, pulling their electrons onto one side and leaving a net positive charge on the other, essentially making small electric dipoles. The attraction between the needle and the charges on the near side of the paper exceeds the repulsion be-tween the needle and those on the far side, creating a net attractive force.
The atom and the cavity contain the same ingredients, albeit at a quantum level. The vacuum field bounded by the cavity walls polarizes the Rydberg atom, and the spatial variations of the field produce a net force. The atomic dipole and the vacuum field are oscillating quantities, however, and their respective oscillations must maintain a constant relative phase if a net force is to continue for any length of time. As it turns out, the photon exchange process does in fact lock the atomic dipole and the vacuum fluctuations.
The tiny force experienced by the atom is enhanced by adding photons to the cavity. The atom-cavity exchange frequency increases with the field intensity, so that each photon adds a discrete quantum of height to the potential barrier in the repelling state and a discrete quantum of depth to the potential well in the attractive state. As a result, it should be possible to infer the number of photons inside the cavity by measuring the time an atom with a known velocity takes to cross it or, equivalently, by detecting the atom's position downstream of the cavity at a given time.