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Physical Review A

Free-space read-out and control of single-ion dispersion using quantum interference

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

Published Oct 18, 2013• 12 citations
Publisher

Abstract

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 $V$ 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 ($98\ifmmode\pm\else\textpm\fi{}1$)%.

DOI
10.1103/physreva.88.041804

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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 \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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±\else\textpm\fi198\ifmmode\pm\else\textpm\fi{}198\ifmmode±\else\textpm\fi1)%.
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.
A scheme for entangling distant atoms is realized, as proposed in the seminal paper by [C. Cabrillo et al., Phys. Rev. A 59, 1025 (1999)]. The protocol is based on quantum interference and detection of a single photon scattered from two effectively one meter distant laser cooled and trapped atomic ions. The detection of a single photon heralds entanglement of two internal states of the trapped ions with high rate and with a fidelity limited mostly by atomic motion. Control of the entangled state phase is demonstrated by changing the path length of the single-photon interferometer.
The properties of an optically probed atomic medium can be changed dramatically by coherent interaction with a near-resonant control light field. The authors present experimental results on the elementary case of electromagnetically induced transparency (EIT) with a single neutral atom inside an optical cavity probed by a weak field. The modification of the dispersive and absorptive properties of a single atom by changing the frequency of the control light field in the off-resonant regime is observed.
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.
We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, and we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over the 157 μm range along the trap axis at accuracies of better than 6 nm.