Orbital angular momentum of an arbitrary axisymmetric light field after passing through an off-axis spiral phase plate

We obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude passed through a spiral phase plate (SPP) whose center is shifted from the optical axis. The formula shows that the OAM equals zero if the incident beam is bounded by an aperture and the SPP center is outside this aperture. For the incident beam bounded by an annular aperture, there is another interesting consequence of the obtained expression. The total OAM of such a beam is the same regardless of the position of the SPP center within the shaded circle of the aperture. Thus, it would be appropriate to illuminate the SPP by beams with an annular intensity distribution, since in this case an inaccurate alignment of the SPP center and the center of the annular intensity distribution does not affect the total OAM of the beam. We also obtain an expression for the OAM density of such a beam in the initial plane.

FEW-ELECTRON DOUBLE-LAYER QUANTUM DOTS IN MAGNETIC FIELDS: ENERGY SPECTRUM OF AN ARTIFICIAL MOLECULE

An exact method is proposed to diagonalize the Hamiltonian of a double-layer quantum dot containing N electrons in arbitrary magnetic fields. For N = 3 and 4, energy spectra of the dot are calculated as a function of the applied magnetic field. As a result of the electron–electron interaction, complete sets of "magic numbers" are found to characterize the total orbital angular momentum of the N-electron dot in the ground state for both the polarized and unpolarized spins. It is shown that discrete transitions of the ground state between magic numbers takes place when the external magnetic field changes. The origin of the magic numbers is completely explained in terms of the underlying symmetry.

Decoupling of measured spherical tensor components of resolved J states of collisionally excited (Ar)+

We measured Stoke's parameters P1, P2, P3, and P4 of excited Ar+ in coincidence with the scattered He for the two-electron process[Formula: see text]From the measured Stoke's parameters of the 4610 Å (1 Å = 10−10 m) radiation of the 2F(J = 7/2) to the 2D(J = 5/2) transition and the 4590 Å radiation of the 2F(J = 5/2) to 2D(J = 3/2) transition we determined the alignment and orientation parameters of the upper states using the Fano–Macek formalism. These parameters were then converted to the appropriate spherical tensor components in the J representation to obtain, in general eight values of [Formula: see text]. Since these states are best described by LS coupling, we decoupled the spherical tensor components of the density matrix of each J state in terms of the spherical components of the density matrices of the total orbital angular momentum L and total spin 5. The unknowns in the expansion are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], with [Formula: see text] because of reflection symmetry. We used Mathematica to calculate the decoupling coefficients and solve these nonlinear equations. The decoupling also allows us to optically determine the octopole moments of the total orbital momentum provided that [Formula: see text] is nonzero. When [Formula: see text], the two sets of equations are linearly dependent. In this case, the determination of a single set of [Formula: see text] specifies [Formula: see text].

Orbital angular momentum eigenfunctions for many-particle systems

Methods are presented for constructing eigenfunctions of the total orbital angular momentum operator of a many-particle system without the use of the Clebsch–Gordan coefficients. One of the equations derived in this paper is analogous to Dirac's identity for total spin; and through this equation, a connection is established between eigenfunctions of L2 and irreducible representations of the symmetric group Sn.

Basis states for equivalent electrons. II. States for the Lie group Sp(4l + 2)

The Slater basis states for N equivalent electrons form the basis for the irreducible representation (1N) of the Lie group U(4l + 2). States which are eigenfunctions of the total spin and total orbital angular momentum form the basis for irreducible representations of SO(3) × SU(2). In this paper the intermediate group Sp(4l + 2) is studied. The basis states for irreducible representations of Sp(4l + 2) are expressed in terms of the Slater basis states.