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arXiv:1108.0528 · Physical Review A

Collective strong coupling between ion Coulomb crystals and an optical cavity field: Theory and experiment

Magnus Albert, Joan P. Marler, Peter F. Herskind, Aurélien Dantan, Michael Drewsen

Published Feb 15, 2012• 22 citations
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Abstract

A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single-field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of P. F. Herskind et al.[Nature Phys. 5, 494 (2009)] and of complementary new measurements. Generally, a very good agreement between theory and experiments is obtained.

DOI
10.1103/physreva.85.023818

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A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single-field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of P. F. Herskind et al.[Nature Phys. 5, 494 (2009)] and of complementary new measurements. Generally, a very good agreement between theory and experiments is obtained.
We present an investigation of the coherent coupling of various transverse field modes of an optical cavity to ion Coulomb crystals. The obtained experimental results, which include the demonstration of identical collective coupling rates for different transverse modes of a cavity field to ions in the same large Coulomb crystal, are in excellent agreement with theoretical predictions. The results furthermore suggest that Coulomb crystals in the future may serve as near-ideal media for high-fidelity multimode quantum information processing and communication purposes, including the generation and storage of single-photon qubits encoded in different transverse modes.
The authors report on CQED experiments where solid state features of ion Coulomb crystals are exploited for detailed studies of the coherent collective coupling of ions of such crystals to different transverse modes of the cavity. By using extremely prolate ion Coulomb crystals oriented along the cavity axis with a radial extension of only a few tens of microns, the spatial profiles of different cavity modes are mapped out by measuring the effective coherent coupling as the crystal is moved radially across the cavity modes. From the resulting profile of the coupling strength, the cavity mode transverse profile can be reconstructed.
We experimentally investigate the transient dynamics of an optical cavity field interacting with large ion Coulomb crystals in a situation of electromagnetically induced transparency (EIT). EIT is achieved by injecting a probe field at the single photon level and a more intense control field with opposite circular polarization into the same mode of an optical cavity to couple Zeeman substates of a metastable level in 40Ca+ ions. The EIT interaction dynamics are investigated both in the frequency-domain – by measuring the probe field steady state reflectivity spectrum – and in the time-domain – by measuring the progressive buildup of transparency. The experimental results are observed to be in excellent agreement with theoretical predictions taking into account the inhomogeneity of the control field in the interaction volume, and confirm the high degree of control on light-matter interaction that can be achieved with ion Coulomb crystals in optical cavities.
Cavity Quantum Electrodynamics (CQED) is an attractive platform for the realization of efficient light-matter quantum interfaces at the single photon level. Such interfaces are key elements for the development of quantum information and communication science due to the need for swapping information between flying and stationary qubits. Here, we report on the first CQED demonstration of collective strong coupling between atomic ions in a solid in the form of an ion Coulomb crystal and an optical field [1].
Recent technological advances in cavity quantum electrodynamics (CQED) are paving the way to utilize multiple quantum emitters confined in a single optical cavity. In such systems, it is crucially important to control the quantum mechanical coupling of individual emitters to the cavity mode. In this regard, combining ion trap technologies with CQED provides a particularly promising approach due to the well-established motional control over trapped ions. Here, we experimentally demonstrate coupling of up to five trapped ions in a string to a high-finesse optical cavity. By changing the axial position and spacing of the ions in a fully deterministic manner, we systematically characterize their coupling to the cavity mode through visibility measurements of the cavity emission. In good agreement with the theoretical model, the results demonstrate that the geometrical configuration of multiple trapped ions can be manipulated to obtain optimal cavity coupling. Our system presents a new ground for exploring CQED with multiple quantum emitters, enabled by the highly controllable collective light-matter interaction.