Sub-half-wavelength Localization Of Moving Atom

In recent years, many studies on the optical methods to measure the position of the atom are the important works in laser physics. The optical methods provide better spatial resolution and have their potential applications to many areas of optical manipulations of atomic degrees of freedom. Among other things, there are laser cooling, Bose-Einstein condensation, atom localization in lattices, atom lithography and measurement of the center-of-mass wave function of moving atoms. Earlier schemes for the localization include the measurement of the phase shift of either the standing wave or the atomic dipole due to the interaction of the atom with the standing wave field, the entanglement between the atom's position and its internal states, and the resonance imaging methods. In this article, we present the sub-half wavelength localization schemes. The schemes are based on the dependence of the comblike spectra on the phase due to the interaction of a polychromatic field with the atom. The key points are presented as follows.1. Localization of a two-level atom via the absorption spectrum. A two-level atom is driven by a classical standing-wave field, the weak probe field absorption spectrum carries the position information of the atom. When the probe field is tuned resonant with the atomic transition, the absorption spectrum displays its peaks at the nodes of the standing-wave field. The atom is localized with the detecting probability 50% in the subwavelength. This is independent of whether or not the driving field is resonant with the atomic transition. On the other hand, when the probe is detuned from the atomic transition, the localization is achievable in a limited range of the detuning between the standing-wave field and the atomic transition. The essential feature is that the atom localization occurs when both the driving field and the probe field are resonant with the atomic transition.2. Sub-half-wavelength atom localization via phase control of a pair of bichro- matic fields. We propose a sub-half-wavelength atom localization scheme in which a pair of bichromatic fields with the common frequency difference are applied to the two dipole-allowed transitions of a three-level A atom. One bichromatic field is strong and serves as a coupling field, one component of which is the standing wave field in a cavity, while the other bichromatic field is weak and acts as a probe field. The measurement of the population in the excited state leads to the localization as the atom passes through the standing wave field. By varying the difference between the relative phases of the pair of bichromatic fields, it is possible to localize the atom within either of two half-wavelength domains with the detecting probability 50%.3. Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission. The scheme is the same with that in 2, the unique difference is the method of the measurement. When the spontaneous emitted photons are detected, the atom is localized in either of the two half-wavelength regions with 50% probability by the variation of the difference between the relative phases of the two bichromatic fields.4. Sub-half-wavelength localization of an atom via trichromatic phase control. We show that the trichromatic manipulation of the absorption spectrum leads to the sub-half-wavelength atom localization. In particular, a three-level atom in the A configuration is considered, in which one transition is coupled by a trichromatic field with one sideband component being a standing-wave field while the other transition is probed by a weak monochromatic field. By varying the sum of relative phases of the sideband components of the trichromatic field to the central component, the atom is localized in either of the two half-wavelength regions with 50% detecting probability when the absorption spectrum is measured.5. We show that it is possible to localize an atom in an half-wavelength region by relaxing the strict condition that the atom is prepared in a specific excited state as in the recently proposed scheme [Phys. Rev. A 65, 043819 (2002)]. In particular, we consider a four-level atom, for which a weak exciting field transfers population from the ground state to the excited state and three control fields (one standing-wave field while two traveling-wave fields) couple the excited state and two auxiliary states. By tuning the exciting field and by varying the collective phase of the control fields, the atom is localized in either of the two half-wavelength regions with 50% detecting probability. The main advantage of the scheme is the experimental accessibility and controllability.