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Chinese Physics Letters

Sub-Half-Wavelength Atom Localization Based on Phase-Dependent Electromagnetically Induced Transparency

Gong Cheng, Xiangming Hu, Yandong Peng

Published Feb 1, 2008• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/25/2/042

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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 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 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 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 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 propose a scheme for two-dimensional atom localization based on the coherent controlled absorption and gain of a weak probe field in a four-level double-\ensuremath{\Lambda} system, in which the atom interacts with two orthogonal standing-wave fields. Owing to the space-dependent atom-field interaction, the position probability distribution of the atom passing through the standing waves can be directly determined by measuring the resulting absorption and gain spectra. The phase-sensitive property of the atomic system significantly reduces the uncertainty in the position measurement of the atom. It is found that, by properly varying the parameters of the system, we can achieve sub-half-wavelength atom localization with high precision. Especially the probability of finding the atom at a particular position can be 100% when a photon with certain frequency is absorbed or amplified. Numerical calculations and qualitative analyses show that the enhancement of precision in the position measurement of the atom is attributed to the interference between the one-photon excitation and the phase-dependent three-photon excitation from the closed interacting contour in the laser-driven atomic system.
Interaction of the internal states of an atom with spatially dependent standing-wave cavity field can impart position information of the atom passing through it leading to subwavelength atom localization. We recently demonstrated a different regime of atom localization [Phys. Rev. A 72, 013820 (2005)], namely sub-half-wavelength localization through phase control of electromagnetically induced transparency. This regime corresponds to extreme localization of atoms within a chosen half-wavelength region of the standing-wave cavity field. Here we present further investigation of the simplified model considered earlier and show interesting features of the proposal. We show how the model can be used to simulate a variety of energy-level schemes. Furthermore, the dressed-state analysis is employed to explain the emergence and suppression of the localization peaks, and the peak positions and widths. The range of parameters for obtaining clean sub-half-wavelength localization is identified.