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A quantum harmonic oscillator (spring subsystem) is stabilized towards a target Fock state by reservoir engineering. This passive and open-loop stabilization works by consecutive and identical Hamiltonian interactions with auxiliary…
For the Hill equation describing one-dimensional periodic systems, a constructive formulation is developed for generating Floquet-Bloch states directly from arbitrary pairs of linearly independent solutions. One-dimensional photonic…
Semiconductor quantum dots coherently driven by pulsed laser are fundamental physical systems which allow studying the dynamical properties of confined quantum states. These systems are attractive candidates for a solid-state qubit, which…
Nonlinear coherent states are an interesting resource for quantum technologies. Here we investigate some critical features of the single-boson nonlinear coherent states, which are theoretically constructed as eigenstates of the annihilation…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…
The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models.…
We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…
The type III Hermite $X_m$ exceptional orthogonal polynomial family is generalized to a double-indexed one $X_{m_1,m_2}$ (with $m_1$ even and $m_2$ odd such that $m_2 > m_1$) and the corresponding rational extensions of the harmonic…
Phase transition in quantum many-body systems inevitably causes changes in certain physical properties which then serve as potential indicators of critical phenomena. Besides the traditional order parameters, characterization of quantum…
Factorization method is developed for a family of discretely spiked harmonic oscillators. Two sets of intertwining and ladder operators are presented to algebraically generate eigenstates with energies isomorphic to those of the ordinary…
We present a comprehensive study of the rational extension of the quantum anisotropic harmonic oscillator (QAHO) potentials with linear and/or quadratic perturbations. For the one-dimensional harmonic oscillator plus imaginary linear…
Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate…
We report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without…
One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets)…
The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is in principle capable of obtaining excitations, the extension to a block Lanczos routine can…
We studied quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain andvtwo-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden…
Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie…
The generally deformed oscillator (GDO) and its multiphoton realization as well as the coherent and squeezed vacuum states are studied. We discuss, in particular, the GDO depending on a complex parameter q (therefore we call it q-GDO)…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method…