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

Electric ring currents Iₙₗₘ and corresponding magnetic fields Bₙₗₘ exist in atomic orbitals ψₙₗₘ (m≠0). Simple expressions are derived for Iₙₗₘ and for Bₙₗₘ(r=0) at the nucleus. The magnitude of Iₙₗₘ depends only on n and decreases with increasing quantum number n. In contrast, Bₙₗₘ(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, Iₙₗₘ and Bₙₗₘ(r=0) increase with the nuclear charge Z as Z² and Z³, respectively. Simple circularly polarized π laser pulses are designed for complete population transfers from $1s$ to target 2p_±1 orbitals. The corresponding solutions of the time-dependent Schr\"odinger equation for the hydrogen atom H $(Z=1)$ imply equivalent solutions for arbitrary Z, by means of simple scaling laws for the time (1∕Z²), frequency (Z²), and field strength (Z³) or intensity (Z⁶). For example, the parameters of the π pulse for H (pulse duration τ=1150.3em0exfs, maximum intensity Iₘₐₓ=1.47×10¹⁰0.3em0exW0.2em0excm^-2) are scaled to values τ=679 as and Iₘₐₓ=7.09×10¹⁶0.3em0exW0.2em0excm^-2 for Al¹²⁺, inducing the giant magnetic field B_21±1(r=0)=11460.3em0exT. 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.