Beyond lowest order mean-field theory for light interacting with atom arrays
F. Robicheaux, Deepak A. Suresh
Abstract
Results from higher order mean-field calculations of light interacting with atom arrays are presented for calculations of one- and two-time expectation values. The atoms are approximated as two levels and are fixed in space. Calculations were performed for mean-field approximations that include the expectation value of one operator (mean field), two operators (mean field 2), and three operators (mean field 3). For the one-time expectation values, we examined three different situations to understand the convergence with increasing order of mean field and some limitations of higher order mean-field approximations. As a representation of a two-time expectation value, we calculated the ${g}^{(2)}(\ensuremath{\tau})$ for a line of atoms illuminated by a perpendicular plane wave at several emission angles and two different intensities. For many cases, the mean field 2 will be sufficiently accurate to quantitatively predict the response of the atoms as measured by one-time expectation values. However, the mean-field-3 approximation will often be needed for two-time expectation values.