We present a review of the neutral atom optical lattice quantum computer [Brennen et al., Phys. Rev. Lett. 82, 1060 (1999)] , which uses a laser mediated dipole-dipole coupling between the nearby atoms in an optical lattice to effect a quantum logic gate. Effectively the model creates a periodic array of two qubit (diatomic) systems, and should be considered as a kind of ensemble quantum computer operating at very low temperature.
Laser cooling and trapping [1] of neutral atoms, particularly alkali atoms, is the most important enabling technology in modern atom physics. Perhaps the most extraordinary achievement in this field is the ability to make an atomic Bose-Einstein condensate [2]. Many other important applications and fundamental physical investigations could be listed, including atom optics [3], atom interferometors [4] and quantum chaos [5]. In laser cooling dissipative mechanisms are used to control the centre of mass motion of atoms. In many other applications it is necessary to use conservative optical forces. This can be achieved using far off resonant laser light to induce an oscillating atomic dipole which is then attracted to regions of high intensity (red-detuning) or repelled from regions of high intensity (blue detuning). Such off-resonant interactions shift' the energy levels connected by the interaction by an amount proportional to the intensity of the laser and are thus called light shift' interactions. The interaction is a two photon process involving the absorption and emission of a photon, returning the atom to the same electronic state. The intensity of the trapping lasers vary in space and so the light shift also depends on position. The two photons need not come from the same laser, as for example a Raman process involving two lasers.
Of course even for very large detunings there is small but finite chance that the atom will be excited and undergo an incoherent spontaneous decay. This results in a momentum kick to the atom that is independent of the conservative light forces acting on the atom and thus represents a source of decoherence. However as the effective optical potential scales as inverse of the detuning while the probability of spontaneous emission scales as the inverse detuning squared, we can make the decoherence due to spontaneous emission negligible. Off-resonant optical lattices offer the ability to trap many atoms in conservative periodic potentials formed by optical standing waves [6]. With laser cooling techniques (adiabatic transfer, side-band cooling, etc.) it is possible for each trapped atom to be prepared in the ground state of the approximately harmonic potential at each node of the standing wave. Given this degree of control it is not surprising that such systems have been suggested for quantum information processing by two groups, Brennen et al. [7] and Jaksch et al. [8]. In this paper I will present a review of the first of these proposals, which uses a laser mediated dipole-dipole coupling between the atoms. The second uses cold collisions to couple the atoms. Both schemes assume that the relative position of atoms can be changed by controlling the standing waves forming the optical lattice.