Related papers: Non-Integrability of the Trapped Ionic System II
Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review,…
In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try…
We present the design, fabrication, and experimental implementation of surface ion traps with Y-shaped junctions. The traps are designed to minimize the pseudopotential variations in the junction region at the symmetric intersection of…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the…
Radiofrequency multipole traps have been used for some decades in cold collision experiments, and are gaining interest for precision spectroscopy due to their low mi-cromotion contribution, and the predicted unusual cold-ion structures.…
Hybrid quantum systems integrate laser-cooled trapped ions and ultracold quantum gases within a single experimental configuration, offering vast potential for applications in quantum chemistry, polaron physics, quantum information…
We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields…
We study integrable and superintegrable systems with magnetic field possessing quadratic integrals of motion on the three-dimensional Euclidean space. In contrast with the case without vector potential, the corresponding integrals may no…
The subject of this review are atom traps based on optical dipole forces in laser fields, along with their unique features as storage devices at ultralow energies. The basic physics of the dipole interaction is discussed, and the…
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…
This paper presents the most complete framework to date for understanding the nonlinear optical trapping of highly absorbing nanoparticles within the dipole regime. Highly absorbing and plasmonic particles garner considerable interest due…
We demonstrate that the trapped magnetic resonance mode can be induced in an asymmetric double-bar structure for electromagnetic waves normally incident onto the double-bar plane, which mode otherwise cannot be excited if the double bars…
We consider a two-dimensional system of harmonically trapped particles with pseudo-spin-$\frac{1}{2}$ degree of freedom. This degree of freedom is coupled to the particle's momentum via the so-called Rashba spin-orbit interaction. We…
Multipole radiofrequency ion traps are a highly versatile tool to study molecular ions and their interactions in a well-controllable environment. In particular the cryogenic 22-pole ion trap configuration is used to study ion-molecule…
The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytical Hamiltonian systems via the differential Galoisian obstruction. In this paper we give a new Morales-Ramis type theorem on the…
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…
A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create…
The general integrability cases in the rigid-body dynamics are the solutions of Lagrange, Euler, Kovalevskaya, and Goryachev-Chaplygin. The first two can be included in Smale's scheme for studying the phase topology of natural systems with…
This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…