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

Abstract

We report on a novel non-invasive 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.PACS numbers: 37.30.+i,52.27.Gr,37.10. Vz,52.27.Jt,42.50.Pq Cold one-component plasma physics [1] has in the past two decades led to a series of interesting results due to the availability of fast computers [2][3][4][5] as well as the possibility to experiment with ensembles of trapped, lasercooled atomic ions [6][7][8][9][10][11][12][13][14][15][16]. Prominent examples are the understanding of structural properties of crystallized cold plasmas in both Penning [6,7] and Paul [8-10, 15, 16] traps, and the investigation of the normal mode dynamics of cold magnetized plasmas in Penning traps [11][12][13][14]. While there exist many similarities between experiments in Penning and Paul traps, the unmagnetized plasmas in Paul traps are e.g. known to heat up much faster than the magnetized plasmas in Penning traps due to the presence of the rf fields [3,17]. The lack of a rotational symmetry axis in Paul traps has as well been found to be responsible for the observation of specific crystalline structures [16]. Exploration of the normal mode dynamics of unmagnetized ion Coulomb crystals in e.g. linear Paul traps will hence add to our understanding of the influence of the trapping environment on the physics of such crystals. Furthermore, since large Coulomb crystals are excellent candidates for the realization of high-fidelity quantum memories for light [18], such studies can shed light on the influence of the excitation of these modes on the fidelity as well as on the prospect of storing several photonic quantum bits through deliberate excitations of specific vibrational modes. Larger Coulomb crystals have as well recently been considered as a system for performing quantum simulations, in which respect knowledge of normal mode dynamics is needed [19]. Finally, ion Coulomb crystals represent extremely interesting systems to study cavity optomechanics phenomena [20,21], since, in spite of their solid nature, they possess free atomic resonance properties and can hence be made very sensitive to the radiation pressure force exerted by optical fields.In this Letter, we report on the study of normal mode vibrations of Coulomb crystals of 40 Ca + ions in a linear Paul trap by a novel non-invasive technique. The technique is based on monitoring the coherent collective resonant response of the atomic ions constituting the crystal to a single photon optical cavity field [18]. By having a standing wave optical cavity incorporated in the tr...

Spectroscopy and Thermometry of Drumhead Modes in a Mesoscopic Trapped-Ion Crystal Using Entanglement

“…Previous global mode studies on 2D planar ion arrays were restricted to modes with wavelengths on the order of the cloud size [18][19][20][21][22]. By contrast, the shortwavelength modes studied here are of particular interest due to their increased sensitivity to strong-correlation corrections [23,24] compared to those with long wavelength, which are well-described by fluid theory.…”

Entanglement detection by Bragg scattering

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Buckling Transitions and Clock Order of Two-Dimensional Coulomb Crystals

“…The discussion of this section is centered on determining the signatures of the phase diagram by direct measurement of the crystal planes and by a Bragg diffraction experiment. Bragg scattering could be performed at the asymptotics of laser cooling, when the ions have reached the stationary state and the emitted photons carry the information about the crystal structure and excitations [35,66]. In addition, it is worth mentioning that the transverse shift of the crystal planes could also be measured by mapping the crystal structure into the electronic degrees of freedom of the ions [37,[67][68][69].…”