Magnetoelectric response of quantum structures driven by optical vector beams

Key advances in the generation and shaping of spatially structured photonic fields in both the near and far fields render possible the control of the duration, the phase, and the polarization state of the field distributions. For instance, optical vortices having a structured phase are nowadays routinely generated and exploited for a range of applications. While the light-matter interaction with optical vortices have been well studied, the distinctive features of the interaction of quantum matter with vector beams, meaning fields with spatially inhomogeneous polarization states, have yet to be explored in full detail, which is done here. We analyze the response of atomic and low-dimensional quantum structures to irradiation with radially or azimuthally polarized cylindrical vector beams. Striking differences from vortex beams are found: Radially polarized vector beams drive radially breathing charge-density oscillations via electric-type quantum transitions. Azimuthally polarized vector beams do not affect the charge at all but trigger, via a magnetic vector potential, a dynamic Aharonov-Bohm effect, meaning a vector-potential-driven oscillating magnetic moment. In contrast to vortex beams, no unidirectional currents are generated. Atoms driven by a radially polarized vector beam exhibit angular-momentum-conserving quadrupole transitions tunable by a static magnetic field, while when excited with an azimuthally polarized beam, different final-state magnetic sublevels can be accessed.

Figure 1

Quantum ring (charge density is marked in blue) irradiated by a cylindrical vector beam (red rings at two different times). (a) The radially polarized vector beam initiates electric-type transitions leading to uniform radially breathing charge density (nondipolar collective charge excitations). (b) The azimuthally polarized vector beam drives homogeneously oscillating transient currents (orange arrows), giving rise to an oscillating magnetic dipole moment (green arrow). The frequency is set by the driving field. In both cases no unidirectional charge currents are generated.

Figure 2

Dynamics from full numerical quantum simulation: (a) time-dependent averaged value $\langle \rho \rangle \left(t\right)$ of a quantum ring driven by RVB with a six-optical-cycle duration, causing a radial dipole excitation. The oscillation frequency can be identified by $(E_{n=1}-E_{n=0})/\hslash$. (b) The time-dependent magnetic moment in the $z$ direction of a quantum ring driven by AVB. The white curves represent the normalized electric field amplitude of the incident light pulses with an intensity $I\sim {10}^4\mathrm{W}/{\mathrm{cm}}^2$ in the area of the ring, and $\hslash \omega =8$ meV.

Figure 3

Quadrupole transitions initiated by a vector laser pulse with a radial polarization. A comparison between the longitudinal and the transverse field contributions is shown. The inset in (a) illustrates the angle $\beta$ between the optical axis of the incident vector beam (blue) and the quantization $\left(z\right)$ axis of the atom (red sphere) as set by an external static magnetic field. Top row: The ratio between the quadrupole excitation probability, labeled by $Q_{\perp }$ and $Q_{\parallel }$, for the $p\text{−}p$ and $p\text{−}f$ transitions. Bottom row: Explicit quadrupole excitation probabilities for the $p\text{−}p$ and $p\text{−}f$ transitions. The field has a peak intensity of $3.51\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$. The atom is on the optical axis and experiences a much lower intensity. The photon energy is tuned to $\hslash \omega =4.37$ eV (for $p\text{−}p$ transitions) or $\hslash \omega =5.31$ eV $(p\text{−}f$ transitions); all fields have a duration corresponding to 30 optical cycles. The static magnetic field is set to 10 T.

Figure 4

Dipole transitions initiated by an azimuthally polarized vector laser pulse. The population of different magnetic sublevels dependent on the rotation angle $\beta$ between the beam optical axis and the direction of an external static magnetic field. Two initial states, $4p_{m_i=0}$ and $4p_{m_i=1}$, are shown. Inset: The ratio between the dipole transition probabilities originating from the longitudinal and the transverse field contributions, labeled by $D_{\perp }$ and $D_{\parallel }$. Field parameters similar to those in Fig. 3 were used.