Related papers: Investigations on Dynamical Stability in 3D Quadru…
In this paper we develop a unified framework to study the coherent control of trapped ions subject to state-dependent forces. Taking different limits in our theory, we can reproduce two different designs of a two-qubit quantum gate --the…
Our work analyzes the potential of ion traps for the experimental simulation of non-equilibrium phase transitions observed in certain spin-chain models which can be mapped to free-fermion systems. In order to make the dynamics more…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
We complete the stability study of general relativistic spherically symmetric polytropic perfect fluid spheres, concentrating attention to the newly discovered polytropes containing region of trapped null geodesics. We compare the methods…
We explore the classical dynamics of atoms in an optical dipole trap formed by two identical Gaussian beams propagating in perpendicular directions. The phase space is a mixture of regular and chaotic orbits, the later becoming dominant as…
We consider a beam model representing the transverse deflections of a one dimensional elastic structure immersed in an axial fluid flow. The model includes a nonlinear elastic restoring force, with damping and non-conservative terms…
We study a quasi-two-dimensional electrostatic drift kinetic system as a model for near-marginal ion temperature gradient (ITG) driven turbulence. A proof is given of the nonlinear stability of this system under conditions of linear…
Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining…
We consider a basic model of the lossless interaction between a moving two-level atom and a standing-wave single-mode laser field. Classical treatment of the translational atomic motion provides the semiclassical Hamilton-Schrodinger…
The measurement process is taken into account in the dynamics of trapped ions prepared in nonclassical motional states. The induced decoherence is shown to manifest itself both in the inhibition of the internal population dynamics and in a…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…
Quantum mechanics dominates various effects in modern research from miniaturizing electronics, up to potentially ruling solid-state physics, quantum chemistry and biology. To study these effects experimental quantum systems may provide the…
We investigate the dynamics of ion crystals in zigzag configuration in transverse magnetic field gradients. A surface-electrode Paul trap is employed to trap $^{40}$Ca$^+$ ions and features submerged wires to generate magnetic field…
We investigate the structural properties and melting behavior of two-dimensional ion crystals in an RF trap, focusing on the effects of ion temperature and trap potential symmetry. We identify distinct crystal structures that form under…
The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical…
Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we have…
We derive the exact nonequilibrium steady state of a run-and-tumble particle (RTP) in $d$ dimensions confined in an isotropic harmonic trap $V(\mathbf r)=\mu r^{2}/2$, with $r=\|\mathbf r\|$. Rotational invariance reduces the problem to the…