A group-theoretical approach to study atomic motion in a laser field

Abstract

Group-theoretical approach is applied to study behavior of lossless twolevel atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is described quantum mechanically in terms of the SU (2) group parameters. The evolution operator is found in an explicit way after solving a single ODE for one of the group parameters. The translational motion in a standing wave is governed by the classical Hamilton equations which are coupled to the SU (2) group equations. It is shown that the full set of equations may be chaotic in some ranges of the control parameters and initial conditions. It means physically that there are regimes of motion with chaotic center-ofmass motion and irregular internal dynamics. It is established that the chaotic regime is specified by the character of oscillations of the group parameter characterizing the mean interaction energy between the atom and the laser field. It is shown that the effect of chaotic walking can be observed in a real experiment with cold atoms crossing a standing-wave laser field.

Exactly Solvable One-Qubit Driving Fields Generated via Nonlinear Equations

“…The aim of the present paper is to propose a method to obtain new families of analitically solvable driving fields by requiring that the corresponding time-evolution operator exactly factorizes as a product of exponentials whose arguments are proportional to the generators of the su(2) algebra. This procedure is related to the well-known Wei-Norman theorem [13] which has been used to study the dynamics of systems with SU (2) and SU (1, 1) symmetries [14][15][16][17], e.g., the interaction of two-level atoms with electromagnetic radiation [18], field modulation in nuclear magnetic resonance [19], propagation and perfect transmission in three-waveguide axially varying structures [20], the time-evolution of harmonic oscillators with time-dependent both mass and frequency [21,22] among others. We are interested in the dynamics of systems whose Hamiltonians can be written in the form…”

Impact of Spontaneous Emission on the form and Dynamics of Atomic Wave Packets in an Optical Lattice

“…From the theoretical point of view, atoms in optical lattices and high-quality cavities are ideal objects to study a variety of processes of atom-field interaction, including dynamic symmetries [9][10][11][12][13][14][15] and dynamic chaos [16][17][18][19]. A single atom in a standing-wave laser field may be semiclassically treated as a nonlinear dynamic system with coupled internal (electronic) and external (mechanical) degrees of freedom.…”

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

“…In spite of their structural simplicity, these models have been shown to demonstrate rich dynamics from full controllability to dynamic chaos with sensitive dependence of outputs on small variations in the initial conditions and control parameters. Atoms in optical lattices and high-quality cavities are ideal objects to study a variety of phenomena in the atom-field interaction, including dynamic symmetries [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and dynamic chaos [13,[18][19][20][21][22][23][24][25][26][27][28].…”