AC Stark effect or time-dependent Aharonov-Bohm effect for particle on a ring

TL;DR

The paper analyzes a quantum ring threaded by a sinusoidally varying magnetic flux, yielding a time-dependent vector potential and nonzero electromagnetic fields. It shows the setup is not a strict Aharonov-Bohm effect but is mathematically akin to the ac Stark/Autler-Townes framework, with linear and quadratic terms tied through minimal coupling. By solving the TDSE in the low-frequency limit via Jacobi-Anger expansion, it demonstrates that the system exhibits Floquet quasi-energies E'_n + rħω with weighting C_r, producing observable energy sidebands at ±r_peak ħω that can be enhanced by suitable α and β, especially for n=1. The work also discusses persistent currents, extensions to discrete rings via the Hubbard model, and practical experimental parameter ranges, outlining how to realize and detect the predicted sidebands in spectroscopy.

Abstract

We study the effect of a time-varying solenoidal vector potential for a quantum particle confined to a ring. The setup appears to be a time-varying version of the Aharonov-Bohm effect, but since the particle moves in the presence of fields, it is not strictly an Aharonov-Bohm effect. The results are similar to the ac Stark effect, but with a time-varying electric field coming from the vector potential, rather than the scalar potential. We compare and contrast the present effect with the standard ac Stark effect. The signature of this setup is the generation of quasi-energy sidebands which are observable via spectroscopy.

Figures (5)

• Figure 1: For $n=0$, the weighting function $C_r (\beta)$ versus the index $r$ for $\beta = 10^3$.
• Figure 2: For $n=0$, the weighting function $C_r (\beta)$ versus the index $r$ for $\beta = 10^6$.
• Figure 3: Plot of the weighting coefficient $C_r$ from \ref{['Ck']} as a function of the index $r$ for $n=1$. For this plot, $\alpha =10^3$ and the flux ratio was chosen as $\frac{\Phi_0}{\Phi_{QM}} =1.1$ which gave $\beta = \frac{\Phi_0}{\Phi_{QM}} \frac{\alpha}{8n}= 137.5$.
• Figure 4: Plot of the weighting coefficient $C_r$ from \ref{['Ck']} as a function of the index $r$ for $n=1$. For this plot $\alpha = 10 ^6$, and we choose the flux ratio $\frac{\Phi_0}{\Phi_{QM}} =1.1$ which gave $\beta = \frac{\Phi_0}{\Phi_{QM}} \frac{\alpha}{8n} = 1.375 \times 10^5$.
• Figure 5: The energy level diagram for the $n=0$ and $n=1$ states for the static magnetic field (far left in diagram) and then the shifting of the energies into quasi-energy sidebands (far right in the diagram). Only the most prominent sidebands are shown.