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arXiv:quant-ph/0611148 · Physical Review A

Localization of atomic ensembles via superfluorescence

Mihai Macovei, Jörg Evers, Christoph H. Keitel, Muhammad Suhail Zubairy

Published Mar 2, 2007• 50 citations
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Abstract

The subwavelength localization of an ensemble of atoms concentrated to a small volume in space is investigated. The localization relies on the interaction of the ensemble with a standing wave laser field. The light scattered in the interaction of the standing wave field and the atom ensemble depends on the position of the ensemble relative to the standing wave nodes. This relation can be described by a fluorescence intensity profile, which depends on the standing wave field parameters and the ensemble properties and which is modified due to collective effects in the ensemble of nearby particles. We demonstrate that the intensity profile can be tailored to suit different localization setups. Finally, we apply these results to two localization schemes. First, we show how to localize an ensemble fixed at a certain position in the standing wave field. Second, we discuss localization of an ensemble passing through the standing wave field.

DOI
10.1103/physreva.75.033801

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Journal of Physics B Atomic Molecular and Optical Physics•Sep 3, 2008•7 citations
The subwavelength localization of an ensemble of atoms concentrated to a small volume in space is investigated. The localization relies on the interaction of the ensemble with a standing wave laser field. The light scattered in the interaction of the standing wave field and the atom ensemble depends on the position of the ensemble relative to the standing wave nodes. This relation can be described by a fluorescence intensity profile, which depends on the standing wave field parameters and the ensemble properties and which is modified due to collective effects in the ensemble of nearby particles. We demonstrate that the intensity profile can be tailored to suit different localization setups. Finally, we apply these results to two localization schemes. First, we show how to localize an ensemble fixed at a certain position in the standing wave field. Second, we discuss localization of an ensemble passing through the standing wave field.
We describe a scheme capable of localizing an ensemble of interacting two-level atoms. The atoms are assumed to be bunched together in a volume much smaller than an emission wavelength, and they interact with a standing wave laser field. Due to the laser-pumping of the atomic sample, it collectively emits fluorescence light with properties depending on the ensemble position in the standing wave. This relation can be described by a fluorescence intensity profile, which depends on the standing wave field parameters, the ensemble properties, and which is modified due to collective effects in the ensemble of nearby particles. We demonstrate that the intensity profile can be tailored to suit different localization setups.
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.
Entanglement of the atom and field leads towards the measurement of the state of the atom or field depending on the kind of measurement made. Taking advantage of this fact, we propose spectroscopic methods for the single atom localization within the subwavelength domain of the optical standing wave field. \n \nWhen a two-level atom interacts with some intense radiation field the spectrum of the scattered light signal exhibits a three-peak Mollow spectrum. We propose a scheme of atom localization based on the resonance fluorescence from a two-level atom interacting with a standing wave field. The Rabi frequency is considered to be position dependent and therefore, the spontaneously emitted photon carries the information about the center-of-mass motion of the atom. This leads to the localization of the single atom by measuring the frequency of the spontaneously emitted photon even during the passage of the atom through the standing wave field. We predict a spatial resolution in position information of up to λ/60 where λ is the optical wavelength. \n \nDetuning of the coherent field with the atomic transition plays an important role in the characterization of the peaks present in the Autler- Townes spectrum of a three-level atom. Strong line narrowing is observed in one of the peaks of the Autler- Townes doublet depending on the choice of the detuning. We investigate how this detuning effects the position information of the atom inside the standing wave field in upper-level and lower-level coupling schemes of Autler- Townes microscopy. We show an enhancement in precision position measurement by factor of at least 4 in upper-level coupling scheme due to the quantum interference phenomenon. This enhancement is not observed in lower-level coupling scheme where the quantum interference is not taking place. \n \nWe also consider a system where a three-level atom is interacting with a monochromatic radiation field in such a way that the decay takes place from upper level to the intermediate level with a rate T and from intermediate level to lower level at a rate γ. This type of system exhibits a non stationary scattered light signal. We report the results of the spontaneous emission spectrum for non stationary scattered light signal by using the definition of time-dependent physical spectrum. This is a rare example of problems where time-dependent physical spectrum can be calculated exactly. We study the characteristics of the spontaneous spectrum for a resonant and off-resonant case and show that this physical spectrum recovers the results of earlier work quite successfully. We also show that the decay rate r disturbs the atomic coherence and finally eliminates the dark line from the center of the spontaneous spectrum. Here we only consider upper-level coupling case for the time-dependent spontaneous spectrum because in lower-level coupling case the system automatically evolved a pumping mechanism due to the coupling of ground level to the upper level via radiation field. Thus a steady-state limit exists in lower-level coupling scheme. \n \nWe investigate the phenomenon of atom localization by using the non stationary Autler-Townes microscopy. The decay rate T reduces the precision in position measurement which is consistent with the results of the non stationary spontaneous emission spectrum. This is due to the fact that for the upper-level coupling case, the standing wave field is coupled to atomic transition and it induces a coherence in the upper-level atomic transition but the spontaneous decay from the upper level to the intermediate level disturbs this coherence. When the effect of the spontaneous decay dominates the coherence effect the quantum interference phenomenon vanishes and thus the precision in localization reduces.
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.