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 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.
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.
Coulomb crystallisation of large ensembles of ions has in the past years been intensively studied experimentally with many spectacular results of relevance to infinite systems in one-, two-, and three-dimensions.While strings of a few ions have proven to be very attractive objects in quantum information processing, larger Coulomb crystals have very recently found applications within other aspects the dynamics of quantum systems. Smaller finite ensembles of cold identical charged particles confined by a harmonic potential furthermore constitute very special types of clusters due to the pure repulsive long-range inter-particle forces. Here, we report on the direct imaging of metastable structures of Coulomb clusters consisting of a few thousands confined and laser-cooled 40Ca+ ions. The observations are attributed to structural excitations due to finite temperatures, a feature likely to appear in clusters of short-range interacting particles, but yet not observed directly.
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.
We present long-time simulations of expanding ultracold neutral plasmas, including a full treatment of the strongly coupled ion dynamics. Thereby, the relaxation of the expanding laser-cooled plasma is studied, taking into account elastic as well as inelastic collisions. It is demonstrated that, depending on the initial conditions, the ionic component of the plasma may exhibit short-range order or even a superimposed long-range order resulting in concentric ion shells. In contrast to ionic plasmas confined in traps, the shell structures build up from the center of the plasma cloud rather than from the periphery.
We describe a simple and fast method for simulating observed images of ion Coulomb crystals. In doing so, cold elastic collisions between Coulomb crystals and virtual very light atoms are implemented in a molecular dynamics (MD) simulation code. Such an approach reproduces the observed images of Coulomb crystals by obtaining density plots of the statistics of existence of each ion. The simple method has the advantage of short computing time in comparison with previous calculation methods. As a demonstration of the simulation, the formation of a planar Coulomb crystal with a small number of ions has been investigated in detail in a linear ion trap both experimentally and by simulation. However, also large Coulomb crystals including up to 1400 ions have been photographed and simulated to extract the secular temperature and the number of ions. For medium-sized crystals, a comparison between experiments and calculations has been performed. Moreover, an MD simulation of the sympathetic cooling of small molecular ions was performed in order to test the possibility of extracting the temperature and the number of refrigerated molecular ions from crystal images of laser-cooled ions. Such information is basic to studying ultracold ion-molecule reactions using ion Coulomb crystals including sympathetically cooled molecular ions.
Ion Coulomb crystals form when trapped ions are cooled below a certain critical temperature. In radiofrequency (RF) traps, such crystals are usually stationary (i.e. non-rotating) with shapes similar to those of cold, homogeneously charged liquids when the number of ions is sufficient for three-dimensional structures to appear. ‘Dynamically stable’ structures can, however, also be created either by directly applying a torque to an initially stationary crystal or by choosing trap parameters just within the stability region where stationary crystals will melt due to parametric resonances between the RF trap field and ion plasma modes.