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arXiv:1212.0810

Faraday rotation of a tightly focussed beam from a single trapped atom

Gabriel Hetet, L. Slodička, N. Röck, R. Blatt

Published Dec 4, 2012• 1 citation
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Abstract

Faraday rotation of a laser field induced by a single atom is demonstrated by tightly focussing a linearly polarized laser beam onto a laser-cooled ion held in a harmonic Paul trap. The polarization rotation signal is further used to measure the phase-shift associated with electromagnetically-induced-transparency and to demonstrate read-out of the internal state on the qubit transition with a detection fidelity of 98 $\pm$ 1%. These results have direct implications for single atom magnetometery and dispersive read-out of atomic superpositions.

DOI
10.48550/arxiv.1212.0810

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Faraday rotation of a laser field induced by a single atom is demonstrated by tightly focussing a linearly polarized laser beam onto a laser-cooled ion held in a harmonic Paul trap. The polarization rotation signal is further used to measure the phase-shift associated with electromagnetically-induced-transparency and to demonstrate read-out of the internal state on the qubit transition with a detection fidelity of 98 ±\pm± 1%. These results have direct implications for single atom magnetometery and dispersive read-out of atomic superpositions.
We perform a free-space measurement and control of the refractive index of a single trapped ion in the presence of quantum interference effects. The single atom refractive index is characterized by the Faraday rotation of a laser field tightly focused onto a trapped and laser-cooled barium ion. It is tuned using the internal ion state that is optically controlled via a VVV or a $\ensuremath{\Lambda}$ scheme. Measurements of the phase shift associated with an electromagnetically induced transparency are then performed and the internal state on the qubit transition is read-out with a detection fidelity of ($98\ifmmode\pm\else\textpm\fi{}1$)%.
We report on experimental and theoretical study of the nonlinear Faraday effect under conditions of electromagnetically induced transparency at the $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{5/2}$ two-photon transition in rubidium vapor. These transitions realize the inverted YYY model which combines the $\ensuremath{\Lambda}$ and ladder systems. Strong nonlinearity allowing for large rotation angles of a probe beam tuned to the $S\ensuremath{\rightarrow}P$ transition was obtained by creation of quantum superpositions of magnetic sublevels (Zeeman coherences) in the rubidium ground state ($\ensuremath{\Lambda}$ scheme). Additionally, electromagnetically induced transparency was accomplished in a ladder scheme by acting with a second strong coupling laser on the $P\ensuremath{\rightarrow}D$ transition. Under conditions of a two-photon resonance the rotation was significantly reduced, which is interpreted as a competition between the coherent processes. The effect was observed in sub-Gauss magnetic fields and could be used for efficient coherent control of generation of the ground-state coherences, e.g., for controlling the polarization state of the probe light.
Polarization rotation of weak probe light induced by circularly polarized strong coupling light in a $\ensuremath{\Lambda}$ configuration is studied. We use spin-polarized cold cesium atoms trapped in a magneto-optical trap to remove complications from Zeeman distribution, Doppler broadening, and collisional decoherence. By using a very low probe intensity and short illumination period we work in a strictly linear regime. The probe and the coupling fields are optically phase locked to eliminate phase fluctuation and consequent atomic decoherence. Using this idealized situation we clarify the roles of optically induced Faraday rotation, circular dichroism, and electromagnetically induced transparency (EIT) in determining the final state of the probe light. In particular, we identify an experimental situation where the roles of atomic coherence and EIT are important.
A Faraday-rotation atomic magnetometer typically employs a resonant, circularly polarized pump beam and an off-resonant, linearly polarized probe beam. Using two light beams is an obstacle to miniaturization, though. This study develops a single-beam scheme that converts a linearly polarized three-color beam into a circularly polarized carrier with orthogonally linearly polarized side bands. In a magnetic field, the carrier prepares anisotropic atoms, which then symmetrically rotate the polarizations of the side bands in opposite directions. This approach should enable miniature devices, and the sensing technologies that depend on them.
We present the experimental observation of photon-photon interactions at the single-particle level. The linearly polarized signal beam undergoes Faraday rotation by a nonlinear effective magnetic field induced by a very weak circularly polarized control beam due to the giant Kerr-like interactions between exciton-polaritons in our quantum well-based 0D microcavity structures. We measure a phase shift with a slope of 3.5×10^-3 radians per particle for low cavity occupancies between 0.1 and 3 excited by the control beam. These experimental findings are in agreement with theoretical models and pave the way towards the development of scalable photonic quantum gates.
In this Letter, we report an absorption spectroscopy experiment and the observation of electromagnetically induced transparency from a single trapped atom. We focus a weak and narrow band Gaussian light beam onto an optically cooled 138Ba+ ion using a high numerical aperture lens. Extinction of this beam is observed with measured values of up to 1.35%. We demonstrate electromagnetically induced transparency of the ion by tuning a strong control beam over a two-photon resonance in a three-level Λ-type system. The probe beam extinction is inhibited by more than 75% due to population trapping.