Spectral properties and magneto-optical excitations in semiconductor double rings under Rashba spin-orbit interaction

Wen-Hsuan Kuan, Chi-Shung Tang, and Cheng-Hung Chang

Phys. Rev. B 75, 155326 – Published 23 April 2007

Abstract

We have numerically solved the Hamiltonian of an electron in a semiconductor double ring subjected to the magnetic flux and Rashba spin-orbit interaction. It is found that the Aharonov-Bohm energy spectrum reveals multizigzag periodic structures. The investigations of spin-dependent electron dynamics via Rabi oscillations in two-level and three-level systems demonstrate the possibility of manipulating quantum states. Our results show that the optimal control of photon-assisted inter-ring transitions can be achieved by employing cascade-type and $Λ$ -type transition mechanisms. Under chirped pulse impulsions, a robust and complete transfer of an electron to the final state is shown to coincide with the estimation of the Landau-Zener formula.

Received 13 September 2006

DOI:https://doi.org/10.1103/PhysRevB.75.155326

Authors & Affiliations

Wen-Hsuan Kuan¹, Chi-Shung Tang², and Cheng-Hung Chang^1,3

¹Physics Division, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan, Republic of China
²Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan, Republic of China
³Institute of Physics, National Chiao Tung University, Hsinchu 30013, Taiwan, Republic of China

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Issue

Vol. 75, Iss. 15 — 15 April 2007

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Images

Figure 1
(Color online) The diagram of part of the double-ring potential depicted in $0 ⩽ ϕ ⩽ 3 π ∕ 2$ . The radius of the ring is about $160 nm$ and effective range of the magnetic flux $r_{Φ}$ is about $7 nm$ .Reuse & Permissions
Figure 2
(Color online) (a) The Aharonov-Bohm oscillations in the energy spectrum of the double ring in the presence of the Rashba SOI with $α = 40 meV nm$ and a static magnetic flux. The spectrum of states with positive (negative) $m_{j}$ is depicted in solid (dashed) curves. The lowest five pairs of the states are specified by $∣ m_{j} ∣ = 2.5$ , 3.5, 1.5, 4.5, and 0.5. In each $1 ∕ 2 - Φ ∕ Φ_{0}$ region, up or down arrows denote net spin orientations of ground states. The zigzag curve shows the sixth lowest eigenenergy. (b) Energy levels within lowest four subbands, in which energies of subband bottoms line close by 30.6, 31.2, 52.1, and $53.6 meV$ , respectively. (c) Near the second subband bottom, anticrossing levels are depicted in thick curves. From left to right, these states are of $m_{j} = 0.5$ , 2.5, 1.5, and 3.5.Reuse & Permissions
Figure 3
(Color online) (a) The energy spectrum including two states: $∣ a ⟩ = {∣ - 2.5 ⟩}_{P_{↑}}$ and $∣ b ⟩ = {∣ - 1.5 ⟩}_{P_{↓}}$ . The sketch in the inset depicts inter-ring transitions under EM wave stimulations. (b) Population inversion as a function of time. When ignoring the spontaneous emission, $W (t)$ with large detuning is demonstrated by dotted symbol. If the spontaneous emission of an excited state is considered, then in small detuning regime, where we set $γ = 0.03$ and $δ = 0.02$ , $W (t)$ manifests an underdamped oscillation, as depicted by the solid curve, and the decay behavior is fitted by an exponential decay function, as shown by the dashed line.Reuse & Permissions
Figure 4
(Color online) (a) The energy spectrum including the chosen three levels, an up-spin state $∣ 1 ⟩ = {∣ - 1.5 ⟩}_{P_{↑}}$ and down-spin doublets $∣ 2 ⟩ = {∣ - 2.5 ⟩}_{P_{↓}}$ and $∣ 3 ⟩ = {∣ - 2.5 ⟩}_{P_{↓}}$ at $Φ = 1.7 Φ_{0}$ . Level repulsion occurs between the doublets, and the gap is about $0.17 meV$ for $α = 40 meV nm$ . (b) A sketch of a cascade-type model in the double ring population as a function of time for the cases of (c) $δ = 0.086$ and (d) $δ \to 0$ . Dash-dotted curve in (d) shows the ARP estimation of the transition from ∣2⟩ to ∣3⟩.Reuse & Permissions
Figure 5
(Color online) (a) A sketch of the $Λ$ -type scheme. States here are all with effective up-spin orientations. An electron initially occupies state $∣ 2 ⟩$ can be optically pumped to an outer-ring state $∣ 3 ⟩$ mediated by state $∣ 1 ⟩$ . (b) The population probabilities among three levels. The long-time occupation of an excited state is feasible by applying a short and intense pulse. In the inset, we show the optimal transfer is feasible provided that there is common Rabi frequency in the two paths. (c) An alternative output signal can be obtained under successive pulse stimulations.Reuse & Permissions

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