Exciton absorption properties of coherently coupled exciton-biexciton systems in quantum dots

Exciton-biexciton coherent coupling effects are examined in semiconductor quantum dots. The exciton absorption spectrum is measured with the microphotoluminescence excitation technique in a single InGaAs quantum dot. The spectrum changes from a Lorenztian-type line shape to an unusual dip-shaped line shape with increasing excitation intensities in a higher exciton state where there is a large oscillator strength between the exciton and biexciton states. The intensity dependence of the dip energy width clearly indicates that coherent Rabi oscillation occurs between the exciton and biexciton states. The absorption properties with excitation light of different polarizations show that the dip-shaped spectra only appear when there is a large biexciton state population with linear polarization. A theoretical analysis undertaken with the density matrix method agrees well with experimental results. This agreement reveals that exciton-biexciton coherent interactions lead to unusual absorption spectra and contribute crucially to the optical properties of quantum dots. The exciton-biexciton coherent effects provide a scheme for controlling four distinguishable states, which can be applied to a demonstration of quantum gate operations.

Figure 1

PL and broadband PLE spectra of the exciton (X) and biexciton (XX). The excitation intensity is about $250\mathrm{W}∕{\mathrm{cm}}^2$. The energy level structures for levels A and B are shown in right hand side. The suffix “$i$” represents “A” or “B.”

Figure 2

PLE spectra of X and XX for three excitation powers for levels A and B. In the results for level B, the PLE spectrum of X changes from a Lorentzian-shaped to a dip-shaped structure with increasing excitation. All spectra are obtained with high energy resolution compared with the results in Fig. 1.

Figure 3

Power dependence of dip-shaped structure shown in Fig. 2. The energy splitting is the width of the dip-shaped structure. The solid line shows a fitted curve which is proportional to a square root of the power density. The dotted curve is linear dependence for a comparison. The inset shows a schematic dip-shaped spectrum and energy splitting.

Figure 4

Energy level structures in the ${\mathrm{XX}}_{\mathrm{B}}\text{−}{\mathrm{X}}_{\mathrm{B}}\text{−}g$ system for a linearly polarized excitation light (a) and a circularly polarized light (b). PLE spectra for a linearly polarized excitation light (c) and a circularly polarized light (d). The linearly polarized light, which is expressed as a linear combination of two opposite circularly polarized lights, can create the ${\mathrm{X}}_{\mathrm{B}}$ states of spin-up $({\mathrm{X}}_{\mathrm{B}}\uparrow )$ and spin down $({\mathrm{X}}_{\mathrm{B}}\downarrow )$.

Figure 5

Energy level structure and physical parameters used in the theoretical analysis. Coherent effects are included only in ${\mathrm{XX}}_i\text{−}{\mathrm{X}}_i$ and ${\mathrm{X}}_i\text{−}g$ with dipole moments of ${\mu }_{\mathrm{XX}\text{−}\mathrm{X}}$ and ${\mu }_{\mathrm{X}\text{−}g}$. The relaxation processes from ${\mathrm{XX}}_i$ and ${\mathrm{X}}_i$ to ${\mathrm{XX}}_0$ and ${\mathrm{X}}_0$ are incoherent processes characterized by $T_1^{\mathrm{XX}}$ and $T_1^{\mathrm{X}}$. The PL signals correspond to relaxations in ${\mathrm{XX}}_0\text{−}{\mathrm{X}}_0$ with $T_1^{\mathrm{XX}0}$ and ${\mathrm{X}}_0\text{−}g$ with $T_1^{\mathrm{X}0}$ for biexciton and exciton PLs, respectively.

Figure 6

Exciton population ${\rho }_{\mathrm{X}0\text{−}\mathrm{X}0}$ as a function of detuning energy for different excitation powers and different ${\mu }_{\mathrm{XX}\text{−}\mathrm{X}}$. (a) ${\mu }_{\mathrm{XX}\text{−}\mathrm{X}}={\mu }_{\mathrm{X}\text{−}g}$ and (b) ${\mu }_{\mathrm{XX}\text{−}\mathrm{X}}=20{\mu }_{\mathrm{X}\text{−}g}$. The ${\rho }_{\mathrm{X}0\text{−}\mathrm{X}0}$ plots from $0.2\text{to}2\mathrm{kW}∕{\mathrm{cm}}^2$ in $0.3\mathrm{kW}∕{\mathrm{cm}}^2$ steps. The detuning energy of zero is for an excitation light with resonant energy to exciton energy. (c) The energy splitting in (b) as a function of power density.

Figure 7

Energy diagram for accessing and observing four distinguishable states. Circularly polarized light can distinctively create ${\mathrm{X}}_i\uparrow$ or ${\mathrm{X}}_i\downarrow$ excitons. These excitons emit PL whose polarizations are the same as the excitation. Linearly polarized light can excite a ${\mathrm{XX}}_i$ biexciton. The biexciton emits PL whose energy is lower than the exciton PL by the biexciton binding energy.