Aharonov-Bohm quantum rings in high-$Q$ microcavities

A single-mode microcavity with an embedded Aharonov-Bohm quantum ring, which is pierced by a magnetic flux and subjected to a lateral electric field, is studied theoretically. It is shown that external electric and magnetic fields provide additional means of control of the emission spectrum of the system. In particular, when the magnetic flux through the quantum ring is equal to a half-integer number of the magnetic flux quantum, a small change in the lateral electric field allows tuning of the energy levels of the quantum ring into resonance with the microcavity mode providing an efficient way to control the quantum ring-microcavity coupling strength. Emission spectra of the system are calculated for several combinations of the applied magnetic and electric fields.

Figure 1

An Aharonov-Bohm quantum ring embedded into a single-mode THz microcavity.

Figure 2

The normalized energy spectrum for the electron ground and the first excited states in the QR as a function of dimensionless parameter $\varphi$ for $\beta =0.1$.

Figure 3

Emission spectrum of the QR-microcavity system in the presence of a lateral electric field $E=20.00\mathrm{kV}{\mathrm{m}}^{-1}$ for $P_{\text{MC}}/\mathcal{G}=0.005$ and $P_{\text{MC}}/\mathcal{G}=0.095$. The microcavity mode is in resonance with the QR transition. The upper row (gold) corresponds to the microcavity emission and the lower row (red) corresponds to the direct QR emission. The magnetic flux piercing the QR is either $\Phi =0$ or $\Phi ={\Phi }_0/2$. The emission frequencies are normalized by the QR-microcavity coupling constant $\mathcal{G}/\hslash$ and centered around ${\omega }_{\text{MC}}$.

Figure 4

Anticrossing in the emission spectrum of the QR-microcavity system at various magnitudes of the external lateral electric field $E$ from $19.80$ to $20.20\mathrm{kV}{\mathrm{m}}^{-1}$ with the increment $50\mathrm{V}{\mathrm{m}}^{-1}$: (a) microcavity emission spectrum (gold) and (b) direct QR emission spectrum (red). The magnetic flux piercing the QR $\Phi =0$. The resonance case $\Delta =\hslash {\omega }_{\text{MC}}$ corresponds to $E=20.00\mathrm{kV}{\mathrm{m}}^{-1}$. The microcavity pumping rate $P_{\text{MC}}/\mathcal{G}=0.095$. The emission frequencies are normalized by the QR-microcavity coupling constant $\mathcal{G}/\hslash$ and centered around ${\omega }_{\text{MC}}$.

Figure 5

Anticrossing in the emission spectrum of the QR-microcavity system at various magnitudes of the external lateral electric field $E$ from $19.80$ to $20.20\mathrm{kV}{\mathrm{m}}^{-1}$ with the increment $50\mathrm{V}{\mathrm{m}}^{-1}$: (a) microcavity emission spectrum (gold) and (b) direct QR emission spectrum (red). The magnetic flux piercing the QR $\Phi ={\Phi }_0/2$. The resonance case $\Delta =\hslash {\omega }_{\text{MC}}$ corresponds to $E=20.00\mathrm{kV}{\mathrm{m}}^{-1}$. The microcavity pumping rate $P_{\text{MC}}/\mathcal{G}=0.095$. The emission frequencies are normalized by the QR-microcavity coupling constant $\mathcal{G}/\hslash$ and centered around ${\omega }_{\text{MC}}$.

Figure 6

Anticrossing in the emission spectrum of the QR-microcavity system at various magnitudes of the magnetic flux $\Phi$ piercing the QR from 0 to $0.004{\Phi }_0$ with the increment $5\times {10}^{-4}{\Phi }_0$ and in the presence of the lateral electric field $E=20.00\mathrm{kV}{\mathrm{m}}^{-1}$: (a) microcavity emission spectrum (gold) and (b) direct QR emission spectrum (red). The resonance case $\Delta =\hslash {\omega }_{\text{MC}}$ corresponds to $\Phi =0$. The emission frequencies are normalized by the value of the QR-microcavity coupling constant calculated for $\Phi =0$ (${\mathcal{G}}_0$) and centered around ${\omega }_{\text{MC}}$. The microcavity pumping rate $P_{\text{MC}}/{\mathcal{G}}_0=0.095$.

Figure 7

Emission spectrum of the QR-microcavity system when the lateral electric field $E=20.00\mathrm{kV}{\mathrm{m}}^{-1}$ is rotated. The angle $\theta$ is counted between $\mathbf{E}$ and the projection of the microcavity mode polarization vector onto the QR plane $\mathbf{p}$. The upper row (gold) corresponds to the microcavity emission and the lower row (red) correspond to the direct QR emission. The system is in resonance $\Delta =\hslash {\omega }_{\text{MC}}$. The emission frequencies are normalized by the value of the QR-microcavity coupling constant for $\theta =\pi /2$ (${\mathcal{G}}_{\pi /2}$) and centered around ${\omega }_{\text{MC}}$. The microcavity pumping rate $P_{\text{MC}}/{\mathcal{G}}_{\pi /2}=0.095$.