In order to realize a quantum computer, it is necessary to have a system with long coherence times and qubits (quantum bits) that are able to interact strongly to perform gate operations. Often, the hyperfine levels of atoms or ions are used to meet these requirements. Atoms are particularly attractice because of the extremely long coherence times of their hyperfine ground states, however, it is difficult to realize a strong, controllable two-body interaction. One way to overcome this is to use the strong interactions of the permanent dipole moments of Rydberg atoms in an applied electric field. This was proposed by Dieter Jaksch in 2000 (Phys. Rev. Lett. 85, 2208 (2000)).
For 87Rb, the atomic states that could be used for a quantum gate are the F=1 and F=2 hyperfine levels of the 5S1/2 ground state. These levels are separated by 6GHz. By exciting atoms momentarily into a Rydberg state in order to achieve strong interactions, a fast gate can be realized. Rydberg atoms have a dipole-dipole interaction potential which scales as Vint = m1m2 /r3, where m is the the dipole moment of the atoms, and r is the distance between the atoms. This strong interaction makes it possible to generate a gate operation in a time scale of 100ns.
The phase gate uses three atom levels. The |0> and |1> states are the hyperfine ground states of the atom, and the |r> state is a Rydberg state. The two atoms used for the gate are assumed to be individually addressable, and the excitation laser is resonant with the |0> -> |r> transition. A first p pulse addresses atom one, which excites the atom into the Rydberg state if it was in the qubit |0> state. A two-p pulse then addresses atom two. If the first atom is in the Rydberg state, then the second atom cannot be excited due to the Rydberg excitation blockade. Lastly, another p pulse addresses atom one. The truth table for the gate is shown below. All qubit configurations obtain a phase shift except for the state where both atoms were in the |1> state. This phase gate is a universal quantum logic gate.