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Chinese Physics B

Conditions for formation and trapping of the two-ion Coulomb cluster in the dissipative optical superlattice

I. V. Krasnov

Published Jun 1, 2015• 4 citations
Publisher

Abstract

Conditions have been studied under which a polychromatic optical superlattice can form and trap the Coulomb cluster of two strongly interacting ions. In our previous work (Krasnov I V and Kamenshchikov L P 2014 Opt. Comm. 312 192) this new all-optical method of obtaining and confining the Coulomb clusters was demonstrated by numerical simulations for special values of the optical superlattice parameters and in the case of Yb ions. In the present paper the conditions are explicitly formulated, under which the long-lived two-ion cluster in the superlattice cell is formed. The peculiarity of these conditions is the renormalization of the ion–ion Coulomb interaction. Notably, the renormalized Coulomb force is determined by the effective charge which depends on the light field parameters and can strongly differ from the bare ion charge. This result can be accounted for by the combined manifestation of the quantum fluctuations of optical forces, nonlinear dependence of these forces on the velocity, and non-Maxwellian (Tsallis type) velocity distribution of the ions in the optical superlattice. Explicit analytical formulas are also obtained for the parameters of the optical two-ion cluster.

DOI
10.1088/1674-1056/24/6/063701

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Conditions have been studied under which a polychromatic optical superlattice can form and trap the Coulomb cluster of two strongly interacting ions. In our previous work (Krasnov I V and Kamenshchikov L P 2014 Opt. Comm. 312 192) this new all-optical method of obtaining and confining the Coulomb clusters was demonstrated by numerical simulations for special values of the optical superlattice parameters and in the case of Yb ions. In the present paper the conditions are explicitly formulated, under which the long-lived two-ion cluster in the superlattice cell is formed. The peculiarity of these conditions is the renormalization of the ion–ion Coulomb interaction. Notably, the renormalized Coulomb force is determined by the effective charge which depends on the light field parameters and can strongly differ from the bare ion charge. This result can be accounted for by the combined manifestation of the quantum fluctuations of optical forces, nonlinear dependence of these forces on the velocity, and non-Maxwellian (Tsallis type) velocity distribution of the ions in the optical superlattice. Explicit analytical formulas are also obtained for the parameters of the optical two-ion cluster.
Abstract We demonstrate that the earlier suggested new all-optical method of creating long-term small (containing two or three particles) ion clusters using the rectified optical forces (RFs) can be used to create cold trapped Coulomb crystals (consisting of several tens of resonant ions). The results of the supercomputer simulations of the dynamics of a mercury ion cloud in a polychromatic optical superlattice (induced by RFs) are presented and analysed. Such a cloud (including 49 ions) in the absence of the optical field expands rapidly (during the characteristic time of the order of ) as a result of the Coulomb explosion. It is shown that the polychromatic optical field can result in the ‘quenching’ of the Coulomb explosion and crystallisation of the ion cloud: creation of a quasi-2D array of ordered and strongly coupled cold ions (with the Coulomb coupling parameter and temperature ∼10 −3 K). The mean destruction time of the studied metastable crystal is of the order of 10 s. Moreover, the central core of the ion cloud can retain its crystalline configuration for a much longer time.
Abstract We propose and study a dissipative optical superlattice for manipulation of resonant particles (atoms, ions and similar ones) located in a transparent buffer gas. Its working principle is based on the simultaneous effect of a longitudinal rectified gradient force and a transverse thermophoretic force in the field of collinear superposition of bichromatic cosine-Gaussian laser beams. As a result, there occurs a strong periodic stratification of the gas manifested in the accumulation and sharp localization of the resonant particles at the nodes of the superlattice and their cooling. Moreover, in the case of linearly polarized light beams, there appear circulating currents of the resonant particles (the so-called Brownian vortices) in the gas. Unlike the traditional dissipative optical lattices, in the superlattice under consideration, transverse particle confinement is implemented only due to the light-induced thermophoretic force, associated with the finiteness of the effective radius of the light beams.
We have investigated the role played by inter-ion Coulomb interactions in a magneto-optical trap ion source (MOTIS). Using a Monte Carlo simulation accounting for all pair-wise ion-ion Coulomb interactions in the source, we have calculated the broadening of the transverse spatial and velocity distributions as well as the increase in emittance over a range of beam currents and extraction electric fields. Using a 7Li MOTIS, we have experimentally studied the broadening of the spatial distribution as a function of total beam current and extraction electric field by measuring the fraction of the beam current that passes through a 20 μm diameter aperture. The Monte Carlo simulations agree well with the experimental results, indicating that such simulations capture the essential physics of the source. Our results show that while Coulomb interactions can cause a significant increase in emittance in some situations, it is possible to keep the effects to an acceptable level by suitable choice of extraction field and beam current. These considerations are essential to the process of optimizing MOTIS geometry and operating conditions for use in high-resolution focused ion beam applications.
Abstract Isolating neutral and charged particles from the environment is essential in precision experiments. For decades, this has been achieved by trapping ions with radio-frequency (RF) fields and neutral particles with optical fields. Recently, the trapping of ions by interaction with light has been demonstrated. This might permit the advantages of optical trapping and ions to be combined. For example, we would benefit from superimposing optical traps to investigate ensembles of ions and atoms in the absence of any RF fields and from the versatile and scalable trapping geometries featured by optical lattices. In particular, ions provide individual addressability, and electronic and motional degrees of freedom that can be coherently controlled and detected via high-fidelity, state-dependent operations. Their long-range Coulomb interaction is significantly larger compared to those of neutral atoms and molecules. This enables ultra-cold interaction and the chemistry of trapped ions and atoms to be studied, as well as providing a novel platform for higher-dimensional experimental quantum simulations. The aim of this topical review is to present the current state of the art and to discuss the current challenges and prospects of the emerging field.
Abstract A novel mechanism of the formation of a deep optical superlattice (OSL) for three-dimensional (3D) trapping of resonant impurity atoms immersed in a transparent cold buffer gas is proposed and investigated theoretically. This mechanism is associated with the joint action of two factors of different physical nature: rectification effect of the gradient force of light pressure and effect of the light induced drift (LID) of atoms (a consequence of the difference in gas-kinetic cross sections of excited and unexcited atoms). Such a situation can be realised when a gas mixture is irradiated by a bichromatic combined light beam which is a special coaxial superposition of cosine-Gaussian optical beams. Here, the RcGF creates a periodic 1D array of deep potential wells (OSL) along the beam axes, and an effective force, causing LID, pulls resonant particles into the combined light beam and provides their transverse (with respect to the beam axes) confinement in OSL. As a result, there can occur a giant accumulation of impurity particles in the OSL cells, accompanied by a strong spatial particle localization far away from the walls of the reservoir, in which the gas mixture is located.
Superradiant lasers have emerged as a promising platform for optical frequency references due to their potential to achieve exceptionally narrow linewidths with reduced sensitivity to cavity noise. Trapped ion Coulomb crystals provide an attractive emitting medium due to their long coherence times, great environmental isolation and precise control over their motional dynamics. However, scaling trapped ion systems to the large ion numbers required for strong collective emission introduces new challenges, including crystal stability and position-dependent decoherence mechanisms. This work presents a numerical framework for modelling large Coulomb crystals confined within a linear Paul trap and assessing their suitability for superradiant lasing. A numerical simulation was developed to generate equilibrium crystal configurations, followed by a normal mode analysis to verify crystal’s dynamical stability and characterise the collective motional spectrum. The dependence of the crystal properties on the trapping parameters was examined, while the damping coefficient and integration timestep used in the numerical relaxation procedure were systematically optimised to obtain equilibrium configurations. The decoherence mechanisms expected to influence superradiant operation, including RF micromotion and electric quadrupole shifts, were also investigated as functions of ion number and trapping conditions. The simulations can produce accurate models of mechanically stable Coulomb crystals with up to 10,000 ions under appropriate relaxation conditions. They also show how the collective motional spectrum evolves across the trapping parameter space where they were also compared with the theoretical lasing threshold to assess the suitability of the trapping conditions for superradiant operation. Although the largest micromotion amplitudes increase with crystal size, a significant fraction of the ions remain confined close to the RF null, suggesting that large ion numbers may still be compatible with superradiant operation. The developed framework also provides a means of quantifying the quadrupole shift, indicating that the resulting frequency shifts are relatively small for the trapping parameters considered here, although further optimisation of the operating conditions is required to fully assess their influence on superradiant perfomance. Overall, the computational suite developed here establishes a versatile platform for studies of large Coulomb ion crystals and provides the tools to determine whether superradiant lasing thresholds can be reached with trapped ion crystals.