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Journal of Physics B Atomic Molecular and Optical Physics

Sub-half-wavelength localization of an atom via trichromatic phase control

Jun Xu, Xiangming Hu

Published Mar 15, 2007• 30 citations
Publisher

Abstract

We show that the trichromatic manipulation of the absorption spectrum leads to sub-half-wavelength atom localization. In particular, a three-level atom in the Λ 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.

DOI
10.1088/0953-4075/40/7/013

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We show that the trichromatic manipulation of the absorption spectrum leads to sub-half-wavelength atom localization. In particular, a three-level atom in the Λ 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.
We present a realistic and efficient scheme for sub-half-wavelength atom localization. This scheme is based on the phase-dependent electromagnetically induced transparency in a four-level system in the double-Λ configuration. We use a strong bichromatic field (one component of which is standing-wave field) as the driving components, and a weak bichromatic field as the probe components. By choosing the collective phase of the four applied components, the atom is localized in either of the two half-wavelength regions with 50% detecting probability when the absorption to the probe fields is detected.
We present a scheme for sub-half-wavelength localization based on phase-dependent coherent effects on resonance fluorescence. A three-level atom in the Λ configuration is considered. Two metastable states are so separated from each other that the fluorescence spectra from the different transitions do not overlap. Two dipole-allowed transitions and one dipole-forbidden transition are driven by a standing-wave laser field, a travelling-wave laser field and a microwave field, respectively. The spectrum of fluorescence from the standing-wave coupled transition is dependent not only on the position but also on the collective phase of all applied fields. When the phase is varied and fluorescence photons are detected, 50% probability is achieved in a half-wavelength region. This scheme is as efficient as previous ones based on coherence-controlled Autler–Townes spectra.
We propose a scheme of atom localization based on the interaction of the atom in the $\ensuremath{\Lambda}$ configuration with a strong bichromatic coupling field and a weak bichromatic probe field with equal frequency difference. One of the bichromatic coupling components is a standing-wave field, which imposes position information on the Rabi frequency. By varying the difference between the relative phases of the two bichromatic fields, the atom is localized in either of the two half-wavelength regions with 50% probability provided the population in the upper state is detected.
We propose a scheme for subwavelength localization of an atom conditioned upon the absorption of a weak probe field at a particular frequency. Manipulating atom-field interaction on a certain transition by applying drive fields on nearby coupled transitions leads to interesting effects in the absorption spectrum of the weak probe field. We exploit this fact and employ a four-level system with three driving fields and a weak probe field, where one of the drive fields is a standing-wave field of a cavity. We show that the position of an atom along this standing wave is determined when probe-field absorption is measured. We find that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. We term this result as sub-half-wavelength localization to contrast it with the usual atom localization result of four peaks spread over one wavelength of the standing wave. We observe two localization peaks in either of the two half-wavelength regions along the cavity axis.
We show that it is possible to localize an atom in a 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 (2002) 043819]. 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 travelling-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 one of the two half-wavelength regions with 50% detecting probability. The main advantage of the scheme is the experimental accessibility and controllability.
Coherent interaction of an atom with a position-dependent standing-wave cavity field can impart position information of a moving atom through the cavity leading to subwavelength atom localization. We show that the position of the atom along the standing-wave field is determined when the probe-field absorption is measured. We find out that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. In addition, we demonstrate that the position information of a three-level V-shaped moving atom strongly depends on the relative phase of applied fields. By appropriate choice of the relative phase, it is shown that the scheme can be used for localizing an atom flying through the standing-wave field to the sub-half-wavelength domain.