Orthogonality parameter associated with a magnetic field gradient for single-site addressing in a 1D optical lattice

We investigate the possibility of detecting atoms in a 1D optical lattice with the nearest-site resolution by using a magnetic resonance technique. A superimposed magnetic field gradient introduces a position-dependent Zeeman shift to label each site. Among the line-broadening mechanisms, we focus on sideband transitions between the motional states of the lower and the upper hyperfine levels. In addition to the sidebands of the axial motion induced by the field gradient itself, we consider those of the transverse motion induced by field misalignments with respect to the optical lattice. Parameters that determine the sideband strengths are identified in a manner analogous to the Lamb-Dicke parameter. The analysis shows that it is advantageous to use light and cold atoms in a deep optical potential well. An explicit expression for the lineshape of the hyperfine transition is obtained. We use it to calculate lineshapes for a cesium and a lithium atom in a typical optical lattice as well as those for the previously reported experiments using cesium atoms.