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Fortschritte der Physik

Single trapped ions interacting with low‐ and high‐finesse optical cavities

Jürgen Eschner, Ch. Raab, A.B. Mundt, Axel Kreuter, Christoph Becher, Ferdinand Schmidt‐Kaler, R. Blatt

Published Apr 24, 2003• 4 citations
Publisher

Abstract

Abstract The presence of mirrors modifies both the coherent coupling of an atom to a light mode and its spontaneous emission into the mode [1]. We study such cavity QED effects experimentally with single ions and optical cavities. We focus on two examples which are equally interesting as fundamental systems and for application in quantum information processing. (i) By retroreflecting the fluorescence of a single trapped Ba+ ion with a mirror 25 cm away, we observe inhibition and enhancement of the atom's spontaneous emission. When two ions are trapped, the distant mirror creates super‐ and subradiance. (ii) With a single trapped Ca+ ion we demonstrate coherent coupling of its narrow S1/2 – D5/2 “qubit” transition to a mode of a high‐finesse optical cavity. We also achieve deterministic coupling of the cavity standing wave to the ion's vibrational state by controlling the ion's position with nanometer‐precision and selectively exciting vibrational state‐changing transitions.

DOI
10.1002/prop.200310049

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Journal of Physics B Atomic Molecular and Optical Physics•Jan 24, 2003•28 citations
Abstract The presence of mirrors modifies both the coherent coupling of an atom to a light mode and its spontaneous emission into the mode [1]. We study such cavity QED effects experimentally with single ions and optical cavities. We focus on two examples which are equally interesting as fundamental systems and for application in quantum information processing. (i) By retroreflecting the fluorescence of a single trapped Ba+ ion with a mirror 25 cm away, we observe inhibition and enhancement of the atom's spontaneous emission. When two ions are trapped, the distant mirror creates super‐ and subradiance. (ii) With a single trapped Ca+ ion we demonstrate coherent coupling of its narrow S1/2 – D5/2 “qubit” transition to a mode of a high‐finesse optical cavity. We also achieve deterministic coupling of the cavity standing wave to the ion's vibrational state by controlling the ion's position with nanometer‐precision and selectively exciting vibrational state‐changing transitions.
The quadrupole S(1/2)-D(5/2) optical transition of a single trapped Ca+ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ion's response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ion's vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer precision.
We describe a series of experiments showing how a single trapped ion, which interacts with its own resonance fluorescence via a distant mirror, exhibits cavity-QED effects such as modified spontaneous emission, level shifts, and even mechanical forces. The same interaction is used to establish feedback on the ion's quantum motion, providing additional cooling and phase stabilisation of its vibration in the trap. Based on these methods and results we present an experiment dedicated at creating entanglement between two distant ions by projective measurements.
The research undertaken unites two distinct areas of quantum information processing: single ions stored in radio-frequency traps and single photons in optical fibres. Strings of ions are presently the most successful implementation of quantum computing, with elementary quantum algorithm and quantum simulations realised. The principal challenge in the field is to enhance the quantum processing power by scaling up current devices to larger systems. We pursue one of the most promising strategies: distributed quantum computation in which multiple small-scale ion processors are interlinked by exchanging photonic quantum bits via optical fibres. This requires a coherent quantum interface between ions and photons, mapping ionic to photonic quantum states and vice versa. To maximise fidelity and the success rate of the scheme, the interaction of ions and photons must take place in a microscopic optical cavity with high finesse. To this end, single 40Ca+ were trapped in a radio-frequency ion trap whose trapping electrodes are hollow cylinders. Optical fibres with mirrors machined on the facets are inserted into the electrodes to form a Fabry-Pérot cavity. Because the fibres are shielded by the electrodes the detrimental distortion of the trapping field due to their presence is suppressed and ions can be trapped for several hours. 40Ca+ has a -type energy level scheme wherein the ion is cooled on the 42P1/2 ? 42S1/2 transition and the cavity is tuned to the 42P1/2 ? 32D3/2 transition. This thesis reports the successful coupling of single ions to a high finesse optical fibre based cavity, with coupling strength g = 2p · 4:6 MHz. The cavity has length 367 µm, finesse of 40,000 and linewidth 2k = 2p · 9:4 MHz. In this coupling regime, the enhancement of the ion's emission rate through the Purcell effect was observed. Further, anti-correlation was observed in the emission rates between the P1/2 ? D3/2 and P1/2 ? S1/2 transitions with an effective emission rate suppression of up to 60% in the latter transition. The built system offers greater promises. Once the position in the cavity mode has been optimised we expect to reach the long-sought after strong coupling regime with (g, k, y) = 2p · (12:2; 4:7; 11:2) MHz.
We have employed radio-frequency trapping to localize a single 40 Ca + -ion in a high-finesse optical cavity. By means of laser Doppler cooling, the position spread of the ion's wavefunction along the cavity axis was reduced to 42 nm, a fraction of the resonance wavelength of ionized calcium (λ = 397 nm). By controlling the position of the ion in the optical field, continuous and completely deterministic coupling of ion and field was realized. The precise three-dimensional location of the ion in the cavity was measured by observing the fluorescent light emitted upon excitation in the cavity field. The single-ion system is ideally suited to implement cavity quantum electrodynamics under cw conditions. To this end we operate the cavity on the D 3/2 –P 1/2 transition of 40 Ca + (λ = 866 nm). Applications include the controlled generation of single-photon pulses with high efficiency and two-ion quantum gates.