Electric ring currents in atomic orbitals and magnetic fields induced by short intense circularly polarized π laser pulses

Electric ring currents I-nlm and corresponding magnetic fields B-nlm exist in atomic orbitals psi(nlm) (m not equal 0). Simple expressions are derived for I-nlm and for B-nlm(r=0) at the nucleus. The magnitude of I-nlm depends only on n and decreases with increasing quantum number n. In contrast, B-nlm(r=0) decreases with increasing quantum numbers n and l but increases with m. The largest magnitudes of the electric ring currents and induced magnetic fields are thus obtained for 2p(+/- 1) orbitals. Moreover, I-nlm and B-nlm(r=0) increase with the nuclear charge Z as Z(2) and Z(3), respectively. Simple circularly polarized pi laser pulses are designed for complete population transfers from 1s to target 2p(+/- 1) orbitals. The corresponding solutions of the time-dependent Schrodinger equation for the hydrogen atom H (Z=1) imply equivalent solutions for arbitrary Z, by means of simple scaling laws for the time (1/Z(2)), frequency (Z(2)), and field strength (Z(3)) or intensity (Z(6)). For example, the parameters of the pi pulse for H (pulse duration tau=115 fs, maximum intensity I-max=1.47x10(10) W cm(-2)) are scaled to values tau=679 as and I-max=7.09x10(16) W cm(-2) for Al12+, inducing the giant magnetic field parallel to B-21 +/- 1(r=0)parallel to=1146 T. The results for hydrogenlike atoms allow corresponding estimates of electric ring currents and magnetic fields in molecules, where molecular orbitals are expressed as linear combinations of atomic orbitals.