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arXiv:1006.3663 · Physical Review Letters

Noninvasive Vibrational Mode Spectroscopy of Ion Coulomb Crystals through Resonant Collective Coupling to an Optical Cavity Field

Aurélien Dantan, Joan P. Marler, Magnus Albert, D. Guénot, Michael Drewsen

Published Aug 31, 2010• 35 citations
arXivHTMLPDF

Abstract

We report on a novel noninvasive method to determine the normal mode frequencies of ion Coulomb crystals in traps based on the resonance enhanced collective coupling between the electronic states of the ions and an optical cavity field at the single photon level. Excitations of the normal modes are observed through a Doppler broadening of the resonance. An excellent agreement with the predictions of a zero-temperature uniformly charged liquid plasma model is found. The technique opens up for investigations of the heating and damping of cold plasma modes, as well as the coupling between them.

DOI
10.1103/physrevlett.105.103001

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We report on a novel noninvasive method to determine the normal mode frequencies of ion Coulomb crystals in traps based on the resonance enhanced collective coupling between the electronic states of the ions and an optical cavity field at the single photon level. Excitations of the normal modes are observed through a Doppler broadening of the resonance. An excellent agreement with the predictions of a zero-temperature uniformly charged liquid plasma model is found. The technique opens up for investigations of the heating and damping of cold plasma modes, as well as the coupling between them.
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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.
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We analyze the dynamics of a chain of singly charged ions confined in a linear Paul trap and which couple with the mode of a high-finesse optical resonator. In these settings the ions interact via the Coulomb repulsion and are subject to the mechanical forces due to scattering of cavity photons. We show that the interplay of these interactions can give rise to bistable equilibrium configurations, into which the chain can be cooled by cavity-enhanced photon scattering. We characterize the resulting equilibrium structures by determining the stationary state in the semiclassical limit for both cavity field and crystal motion. The mean occupation of the vibrational modes at steady state is evaluated, showing that the vibrational modes coupled to the cavity can be simultaneously cooled to low occupation numbers. It is also found that at steady state the vibrations are entangled with the cavity field fluctuations. The entanglement is quantified by means of the logarithmic negativity. The spectrum of the light at the cavity output is evaluated and the features signaling entanglement are identified.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
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.