Related papers: Bloch space structure, the qutrit wave function an…
The cascade, lambda and vee type of three-level systems are shown to be described by three different Hamiltonians in the SU(3) basis. We investigate the Bloch space structure of each configuration by solving the corresponding Bloch equation…
We present a novel method to study the Bloch space of the qutrit system by examining the Bloch trajectories in it. Since such system is inherently a three-level quantum system, therefore we use the SU(3) group as the basis group to obtain…
The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The…
We present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using…
We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give…
We theoretically study the resonance fluorescence spectra of the lambda ($\Lambda$), vee ($V$) and cascade ($\Xi$) type three-level configurations. It is shown that each system with two detuning frequencies can be modelled using the $SU(3)$…
Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…
The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives…
We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially…
A two-sphere ("Bloch" or "Poincare") is familiar for describing the dynamics of a spin-1/2 particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs…
The two-qubit pure state is explicitly parameterized by three unit 2-spheres and a phase factor. For separable states, two of the three unit spheres are the Bloch spheres of each qubit. The third sphere parameterizes the degree and phase of…
Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system,…
We study an analogous Bloch sphere representation of higher-level quantum systems using the Heisenberg-Weyl operator basis. We introduce a parametrization method that will allow us to identify a real-valued Bloch vector for an arbitrary…
We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear…
We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$ ($\lambda$ odd) and we also study the large $SU(4)$ isospin-$\lambda$ limit. The model Hamiltonian…
Physical quantum systems are commonly composed of more than two levels and offer the capacity to encode information in higher-dimensional spaces beyond the qubit, starting with the three-level qutrit. Here, we encode neutral-atom qutrits in…
We map neutrinos to qubit and qutrit states of quantum information theory by constructing the Poincar\'e sphere using SU(2) Pauli matrices and SU(3) Gell-Mann matrices, respectively. The construction of the Poincar\'e sphere in the…
Visual methods are of great utility in understanding and interpreting quantum mechanics at all levels of understanding. The Bloch sphere, for example, is an invaluable and widely used tool for visualising quantum dynamics of a two level…
Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the…
In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…