Abstract
The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are incommensurate. The dynamics are frustrated and in specific limiting cases can be cast in terms of the Frenkel-Kontorova model, which reproduces features of friction in one dimension. We numerically recover the sliding and pinned phases. For strong cavity nonlinearities, they are in general separated by bistable regions where superlubric and stick-slip dynamics coexist. The cavity, moreover, acts as a thermal reservoir and can cool the chain vibrations to temperatures controlled by the cavity parameters and by the ions' phase. These features are imprinted in the radiation emitted by the cavity, which is readily measurable in state-of-the-art setups of cavity quantum electrodynamics.
Highlights
Cavity quantum electrodynamics (CQED) with cold atomic ensembles provides exciting settings in which to study the physics of long-range interacting systems [1, 2]
When the interactions are short-ranged, at ultra-low temperatures their interplay with the cavity potential can give rise to exotic phases, which tend to maximize photon scattering into the resonator and the strength of the long-range intracavity potential [1, 7, 9,10,11]. It is to a large extent unknown, how these dynamics are modified as the range of the competing interacting potential is increased
The ions are confined by an external trap inside a standing-wave resonator of wavelength λ, in the geometry illustrated in Fig. 1(a), where their motion is assumed to be one-dimensional along the xaxis. This setup is expected to simulate the FrenkelKontorova (FK) model [19,20,21] which describes a chain of elastically-bound particles subjected to an external periodic potential in one dimension [12, 13, 22,23,24,25] and reproduces the salient features of stick-slip motion between two surfaces
Summary
Cavity quantum electrodynamics (CQED) with cold atomic ensembles provides exciting settings in which to study the physics of long-range interacting systems [1, 2]. In the FK model the sliding and pinned phases are separated by the Aubry transition, whose control field is the relative amplitude of the periodic potential [26,27,28], and whose hallmark is the abrupt growth of the lowest phonon frequency (phonon gap) [29].
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