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In the article the problem of output setpoint tracking for affine non-linear system is considered. Presented approach combines state feedback linearization and homotopy numerical continuation in subspaces of phase space where feedback…
We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
We introduce an efficient iterative method to prepare a target state in Hilbert spaces with high dimensionality using a combination of unitary evolution, measurements, and quantum Zeno dynamics. The latter confines the evolution within Zeno…
Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with…
We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.
We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection $X$ of $N$ one-dimensional manifolds and the corresponding set of boundary…
The evolution of a quantum state undergoing radiative decay depends on how the emission is detected. We employ phase-sensitive amplification to perform homodyne detection of the spontaneous emission from a superconducting artificial atom.…
The coupling between two or more objects can generally be categorized as strong or weak. In cavity quantum electrodynamics for example, when the coupling strength is larger than the loss rate the coupling is termed strong, and otherwise it…
Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…
The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
The successful application of Quantum Optimal Control (QOC) over the past decades unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular,…
Discrete-time quantum walks (DTQWs) provide a convenient platform for a realisation of many topological phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian. Nevertheless, researchers…