Related papers: Lie-type transformations and effective Hamiltonian…
We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear,…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the…
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…
We study and exactly solve the two-photon and k-photon Jaynes-Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the $SU(2)$ group and let…
We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation,…
The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate…
The Lie-Hamilton approach for $t$-dependent Hamiltonians is extended to cover the so-called nonlinear Lie-Hamilton systems, which are no longer related to a linear $t$-dependent combination of a basis of a finite-dimensional Lie algebra of…
We perform the exact numerical diagonalization of the Hamiltonians that describe both degenerate and nondegenerate parametric amplifiers, by exploiting the conservation laws pertaining each device. We clarify the conditions under which the…
The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
We show how recent state-reconstruction techniques can be used to determine the Hamiltonian of an optical device that evolves the quantum state of radiation. A simple experimental setup is proposed for measuring the Liouvillian of…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
We propose a scheme to realize cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second harmonic fields propagating in a $\chi^{(2)}$ nonlinear medium…
We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based on the effective…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
With an increasing coupling between light and mechanics, nonlinearities begin to play an important role in optomechanics. We solve the quantum dynamics of an optomechanical system in the multi-photon strong coupling regime retaining…
At the heart of quantum technology development is the control of quantum systems at the level of individual quanta. Mathematically, this is realised through the study of Hamiltonians and the use of methods to solve the dynamics of quantum…