Optical injection of charge current in quantum wires: Oscillations induced by excitonic effects

We investigate the charge current that is optically injected by interference between one- and two-photon excitation in the presence of excitonic effects. We consider a realistic V-shaped quantum wire excited slightly below the band gap by two simultaneous femtosecond laser pulses of frequency $2\omega$ and $\omega$ that interact, respectively, with the lowest $B_1$ and $A_1$ excitons. Using effective multiband Bloch equations for two-photon transitions, including the Coulomb interaction within the Hartree-Fock approximation, we show that, because of the different symmetry properties of the involved excitons, the generated charge current displays oscillations due to the quantum interference between the excitonic coherences.

Figure 1

Band structure of a V-shaped $\mathrm{Al}\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum wire. Two bands that are degenerate at zone center are mutually conjugate by time reversal and belong to the irreps ${}^{1}E_{1∕2}$ (solid line) and ${}^{2}E_{1∕2}$ (dashed line) of the group ${\mathbf{C}}_s$ (the little group of $k$). The QWR is excited by two optical pulses of frequency $\omega$ and $2\omega$ with $2\omega$ slightly below the band gap. The inset shows a TEM picture of the quantum wire considered in this study.

Figure 2

Lowest $B_1$ and $A_1$ excitonic resonances in the one-photon absorption (1PA) and two-photon absorption (2PA), respectively. The absorption spectra are calculated for thermalized carrier distributions that correspond approximatively to the carrier densities excited in the configuration for current injection used in this paper. Decoherence time, $\tau =1\mathrm{ps}$. $E_g$, energy gap of the QWR.

Figure 3

(Color online) Charge current along the V-shaped quantum wire for two different optical phases, $\varphi =0$ (solid line) and $\varphi =\pi ∕2$ (dashed line). Thick lines, the Coulomb interaction is taken into account within the Hartree-Fock approximation. Thin lines, the Coulomb interaction is neglected. Relaxation time $\tau =1\mathrm{ps}$. The shaded curve on the bottom of the figure shows the time dependence of the optical pulses in the QWR.

Figure 4

Power spectrum of the far-field THz emission for two different optical phases, $\varphi =0$ (solid line) and $\varphi =\pi ∕2$ (dashed line). Relaxation time $\tau =1\mathrm{ps}$.

Figure 5

Charge current along the V-shaped quantum wire for different optical phases $\varphi$. Relaxation time $\tau =1\mathrm{ps}$.

Figure 6

Charge current in the different subbands. Relaxation time, $\tau =1\mathrm{ps}$. Optical phase, $\varphi =\pi ∕2$.

Figure 7

Carrier distribution in the lowest pair of conduction subbands $c_1$ at different times (0.7, 0.8, and $0.9\mathrm{ps}$). The distribution is shown for the subband belonging to ${}^{1}E_{1∕2}$. The distribution in the conjugate subband belonging to ${}^{2}E_{1∕2}$ is similar. Optical phase, $\varphi =\pi ∕2$.

Figure 8

(Color online) Charge current along the V-shaped quantum wire for different relaxation times $\tau$ ($1\mathrm{ps}$, $0.5\mathrm{ps}$, and $0.2\mathrm{ps}$). Optical phase, $\varphi =\pi ∕2$. The shaded curve on the bottom of the figure shows the time dependence of the optical pulses in the QWR.

Figure 9

Power spectrum of the far-field THz emission for different relaxation times $\tau$ ($1\mathrm{ps}$, $0.5\mathrm{ps}$, and $0.2\mathrm{ps}$). Optical phase, $\varphi =\pi ∕2$.