Related papers: Classical and quantum controllability of a rotatin…
We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices.…
We prove approximate controllability of the bilinear Schr\"odinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and…
We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\"oermer problem within a sphere, with the dipole in its centre. We start from a…
We consider deflection of rotating symmetric molecules by inhomogeneous optical and static electric fields, compare results with the case of linear molecules, and find new singularities in the distribution of the scattering angle.…
Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to…
We study the translational motions of homonuclear diatomic molecules prepared in their ${}^3\Sigma$ electronic states, deeply bound vibrational states, and rotational states of well-defined parity. The trapping potential arises due to the…
A controlled quantum dense coding scheme is investigated with a four-particle non-maximal quantum channel. The amount of classical information is shown to be capable of being controlled by the controllers through adjustments of the local…
Coherent control experiments in molecules are often done with shaped laser fields. The electric field is described classically and control over the time evolution of the system is achieved by shaping the laser pulses in the time or…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
In this paper we study controllability of a $d$-level atom interacting with the electromagnetic field in a cavity. The system is modelled by an ordered graph $\Gamma$. The vertices of $\Gamma$ describe the energy levels and the edges…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
In solid materials, the parameters relevant to quantum effects, such as the spin quantum number, are basically determined and fixed at the chemical synthesis, which makes it challenging to control the amount of quantum correlations. We…
We investigate a hybrid electro-mechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg…
We use an optical centrifuge to align asymmetric top $\mathrm{SO_2}$ molecules by adiabatically spinning their most polarizable O-O axis. The effective centrifugal potential in the rotating frame confines sulfur atoms to the plane of the…
We experimentally study a system of quantum kicked rotors - an ensemble of diatomic molecules exposed to a periodic sequence of ultrashort laser pulses. In the regime, where the underlying classical dynamics is chaotic, we investigate the…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
We introduce a new approach to analyzing the interaction between classical and quantum systems that is based on a limiting procedure applied to multi-particle Schr\"{o}dinger equations. The limit equations obtained by this procedure, which…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…