Related papers: Confining rigid balls by mimicking quadrupole ion …
We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to…
Planar rotors can be realized by confining molecular ions or charged nanoparticles together with atomic ions in a Paul trap. We study the case of molecular ions or charged nanoparticles that have an electric dipole moment which couples to…
We study a discrete-time asynchronous midpoint dynamics on the circle in which, at each step, a uniformly chosen neighboring pair moves to the midpoint along the shortest arc. Although the update rule is locally contractive, we show that…
We examine the properties of cold ions confined by a Paul trap in a linear crystal configuration, a system of considerable current interest due to its application to practical quantum computation. Using a combination of theoretical and…
We theoretically investigate the motional excitation of a single ion caused by spring-constant and position uctuations of a harmonic trap during trap shuttling processes. A detailed study of the sensitivity on noise for several transport…
For the closed string carrying 2 or 3 point-like masses the stability problem for central and linear rotational states is considered. This problem is important for applications of these model to describing baryons, glueballs or other exotic…
We investigate the behavior of trajectories of a $(3,2)$-rational $p$-adic dynamical system in the complex $p$-adic filed ${\mathbb C}_p$, when there exists a unique fixed point $x_0$. We study this $p$-adic dynamical system by dynamics of…
Cooling of ions or other charged particles in electromagnetic traps is an essential tool to achieve control over their degrees of freedom on the quantum level. For many objects, there is no viable route for direct cooling, such as an…
The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy,…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime ($\eta^2(2n+1) \ll 1$). Outside the…
Ball and hoop system is a well-known model for the education of linear control systems. In this paper, we have a look at this system from another perspective and show that it is also suitable for demonstration of more advanced control…
The electromagnetic trapping of ion chains can be regarded as a process of non-trivial entangled quantum state preparation within Hilbert spaces of the local axial motional modes. To begin uncovering properties of this entanglement resource…
A feedback stabilization scheme to stabilize a classical reacting Hamiltonian system is proposed. It is based on transforming a saddle-type equilibrium to an asymptotically stable one, and is given in a simple and algorithmic way. The…
First conceived as a topological construction, Wada basins abound in dynamical systems. Basins of attraction showing the Wada property possess the particular feature that any small perturbation of an initial condition lying on the boundary…
It is shown that in an anisotropic harmonic trap that rotates with the properly chosen rotation rate, the force of gravity leads to a resonant behavior. Full analysis of the dynamics in an anisotropic, rotating trap in 3D is presented and…
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in…
Ultranarrow-linewidth atoms coupled to a lossy optical cavity mode synchronize, i.e. develop correlations, and exhibit steady-state superradiance when continuously repumped. This type of system displays rich collective physics and promises…
We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the…
The motion of a test particle in the gravitational field of a non-spherical source endowed with both mass and mass quadrupole moment is investigated when a test radiation field is also present. The background is described by the Erez-Rosen…