Emergence of classical behavior from the quantum spin

Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system

Gaussian-Induced Rotation in Triangular Photonic Lattices

Time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices is numerically investigated. Rotation occurs for some values of control parameters. For parameters of such rotation, the solitonic solutions are found using modified Petviashvili's method. It is shown that they correspond to the lowest values of propagation constant in the power diagrams and relation between observed rotation and less confined discrete solitonic solutions are demonstrated

Gaussian-Induced Rotation in Triangular Photonic Lattices

Time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices is numerically investigated. Rotation occurs for some values of control parameters. For parameters of such rotation, the solitonic solutions are found using modified Petviashvili's method. It is shown that they correspond to the lowest values of propagation constant in the power diagrams and relation between observed rotation and less confined discrete solitonic solutions are demonstrated

Geometric Phase for Analytically Solvable Driven Time-Dependent Two-Level Quantum Systems

Geometric phase for novel analytical solutions (Barnes and Das Sarma) of time-dependent two-level quantum systems is discussed, specifically for a general single-axis driving term, which is represented by a function J(t) in the Hamiltonian, and its corresponding evolution operator. It is demonstrated how general results for corresponding phases (total, dynamic and geometric) can be obtained. Using a specific case, it was found that over time in which the driving field is appreciably different from zero, the corresponding geometric phase changes (in the specific example by Δ β ≈ 0.8 radians) thus enabling detection. The results are relevant to qubit control and to quantum computing applications

Counterpropagating Matter Waves in Optical Lattices

An investigation of Bose-Einstein condensate in two-dimensional optical lattice potentials, formed by laser beams, is carried out. We are interested in the dynamics of Bose-Einstein condensate in a square optical lattice, where the periodic potential can lead to the stabilization of an otherwise unstable Bose-Einstein condensate. The behavior of Bose-Einstein condensate in optical lattices is described by the nonlinear Gross-Pitaevskii equation, which we treat numerically. By applying the Petviashvili iteration method, we demonstrate the existence of solitonic solutions in the case of counterpropagating matter waves, and analyze their stability