Charge-current generation in atomic systems induced by optical vortices

We envisage the possibility of producing and tuning electronic orbital currents in atoms by weak, spatially inhomogeneous laser pulses with optical vortices. As already known, when interacting with such pulses an electronic system attains a definite amount of angular momentum. Here we explore this effect in the case when the system size is atomically small, i.e., much smaller than the scale of the inhomogeneity of the light pulses. We show that, nonetheless, angular momentum is transferred to the atomic system. The amount of the attained angular momentum depends on the position of the atom inside the field. Our numerical calculations and analytical analysis show that, indeed, light-induced orbital magnetism emerges in a dilute atomic gas when it is exposed to resonant or broadband optical vortices. This effect can be assessed, for instance, in a Faraday rotation experiment.

Figure 1

A schematic of the used notation. The vector $\mathbf{r}$ denotes the position of the electron with respect to the center of mass of the atom, while ${\mathbf{r}}^{\prime \prime }$ is the position of this electron with respect to the optical axis of the OAM carrying beam that propagates along the $z$ axis. ${\mathbf{r}}^{\prime }={\mathbf{r}}^{\prime \prime }-\mathbf{r}$ is the distance between the center of mass of the atom and the optical axis. The shaded circular area indicates schematically the region of high intensity.

Figure 2

The current density in a.u. as a function of $y=r\sin \theta$ and $z=r\cos \theta$ for different topological charges, for $\omega =0.375$ a.u., and for $x=0$. Other parameters are $\delta =0.03$ a.u., the beam waist is $1.0\times {10}^3$ a.u., and the amplitude of the electric field is $A_0\omega =0.03$ a.u.

Figure 3

The induced current as a function of the off-center shift parameter and of the frequency for a hydrogen atom. The light is circularly polarized with $m_a=0$. We choose $\delta =0.03$ a.u. and $t_f\to \infty$. The panels in (a) and (b) are obtained for different initial electronic states, as indicated upon each panel with the brackets $|k_0\rangle =|n_0{\ell }_0{m}_0\rangle$. The dominant contributions to the current stem from the transitions to the levels $|(n_0+1)\ell m\rangle \cdots |(n_0+5)\ell m\rangle$.

Figure 4

The induced current as a function of the off-center shift parameter and of the frequency for a hydrogen atom. The light is circularly polarized with $m_a=1$ and $\delta =0.03$ a.u. and $t_f\to \infty$. The panels in (a) and (b) are obtained for different initial electronic states, as indicated upon each panel with the brackets $|k_0\rangle =|n_0{\ell }_0{m}_0\rangle$. The dominant contributions to the current stem from the transitions to the levels $|(n_0+1)\ell m\rangle \cdots |(n_0+5)\ell m\rangle$.

Figure 5

The induced current as a function of the off-center shift parameter and of the frequency for a hydrogen atom. The light is circularly polarized with $m_a=2$. We choose $\delta =0.03$ a.u. and $t_f\to \infty$. The panels in (a) and (b) are obtained for different initial electronic states, as indicated upon each panel with the brackets $|k_0\rangle =|n_0{\ell }_0{m}_0\rangle$. The dominant contributions to the current stem from the transitions to the levels $|(n_0+1)\ell m\rangle \cdots |(n_0+5)\ell m\rangle$.

Figure 6

In the case of a circularly polarized laser beam, the contributions of the different transitions to the induced current as a function of the shifting parameter for (a) $m_a=0$, (b) $m_a=1$, and (c) $m_a=2$. The subscript $f$ indicates the final state. $n_0=1$ states are given by dashed lines, and $n_0>1$ states are shown by solid lines for ${\ell }_f=1;m_f=-1$. The symbols indicate the nondipolar transitions.

Figure 7

The induced current in a hydrogen atom as a function of the off-center shift parameter and the frequency of a linearly polarized light for $m_a=1$. No sizable current can be generated if $m_a=0$. The beam duration is quantified by $\delta =0.03$ a.u. and $t_f\to \infty$. (a) and (b) show the dependence on the initial states, as indicated on each panel with the brackets $|k_0\rangle =|n_0{\ell }_0{m}_0\rangle$. The magnitude of the current as depicted on the panels is measured in units of nA.

Figure 8

The induced current in a hydrogen atom as a function of the off-center shift parameter and the frequency of a linearly polarized light for $m_a=2$. The beam duration is quantified by $\delta =0.03$ a.u. and $t_f\to \infty$. (a) and (b) show the dependence on the initial states, which are indicated on each panel with the brackets $|k_0\rangle =|n_0{\ell }_0{m}_0\rangle$. The magnitude of the current as indicated on the panels is measured in units of nA.