High-precision two-dimensional atom localization from four-wave mixing in a double-Λ four-level atomic system

We propose a scheme for high-precision two-dimensional (2D) atom localization via the four-wave mixing (FWM) in a four-level double-$\Lambda$ atomic system. Due to the position-dependent atom-field interaction, the 2D position information of the atoms can be directly determined by the measurement of the normalized light intensity of output FWM-generated field. We further show that, when the position-dependent generated FWM field has become sufficiently intense, efficient back-coupling to the FWM generating state becomes important. This back-coupling pathway leads to competitive multiphoton destructive interference of the FWM generating state by three supplied and one internally generated fields. We find that the precision of 2D atom localization can be improved significantly by the multiphoton destructive interference and depends sensitively on the frequency detunings and the pump field intensity. Interestingly enough, we show that adjusting the frequency detunings and the pump field intensity can modify significantly the FWM efficiency, and consequently lead to a redistribution of the atoms. As a result, the atom can be localized in one of four quadrants with holding the precision of atom localization. (paper)