Coherent nonlinear optical spectroscopy of fluctuation quantum dots: Evidence for coupling between quantum dots

We report nonlinear spectroscopy spectra of GaAs quantum dots showing an induced absorption-like feature. Although similar to the nonlinear signature of the bound biexciton state, this feature is distinct from the former and taken together with the photoluminescence spectra is explained within the context of a model describing the coherent coupling of distinct quantum dots.

Figure 1

(a) Sixteen optically allowed levels in a two quantum dot system that can potentially be resonantly excited through either one or two photon excitation. (b) Simplified notation describing two QD system states of interest: the single QD exciton states and the 2-QD two-exciton state. Note that in this diagram, QD A and QD B can be exchanged to give four different 4-level systems.

Figure 2

Degenerate spectra. The data are taken with (a) $\mathrm{co}\text{−}{\sigma }_{+}$ and (b) $\mathrm{co}\text{−}{\sigma }_{-}$ polarized fields. The two resonances are at $1621.13\mathrm{meV}$ (∣01⟩) and $1622.59\mathrm{meV}$ (∣10⟩) for the case of $\mathrm{co}\text{−}{\sigma }_{-}$ polarized fields. The ${\sigma }_{+}$ Zeeman doublet states are slightly higher in energy $(\sim 50\mu \mathrm{eV})$. Each of the resonances has a narrow $(\hslash \gamma \sim 20\mu \mathrm{eV})$ linewidth indicating confinement to QDs.

Figure 3

Degenerate and nondegenerate spectra taken in a $0.5\mathrm{T}$ applied magnetic field in the Faraday configuration using $\mathrm{co}\text{−}{\sigma }_{-}$ polarized fields. The experimental configuration requires that the signal is homodyne detected with both fields. Experimental (a)iii degenerate and nondegenerate spectra in (a)i and (a)ii with $E_1$ fixed at ∣10⟩, and at ∣01⟩, respectively. (b)iii Theoretical fit of the two relevant degenerate states. (b)i and (b)ii are calculated responses for (a)i and (a)ii, respectively. The data is well represented by the theory if an interaction energy of $\sim 25\mu \mathrm{eV}$ is included in the calculation.

Figure 4

A comparison of theory and experiment for the cross-circularly polarized data. (a) Cross-circularly polarized spectra taken in a $0.5\mathrm{T}$ applied magnetic field in the Faraday configuration. $E_1$ is fixed at the ∣01⟩ resonance as indicated by an arrow, and $E_2$ scans over the spectrum. When the signal is homodyne detected with $E_2$ (solid circles), an induced absorption dip is seen at ∣10⟩. However, when the signal is homodyne detected with $E_1$ (open circles), the sign is reversed and a peak is seen. (b) A plot of the theoretical spectra expected for each of the cross-polarized experiments. Note that the saturation peak and induced absorption dip features are well represented.

Figure 5

Quantum mechanical pathways leading to a nonlinear signal for (a) the single exciton and (b) the two-exciton states. The dashed (solid) arrows indicate $E_i$ $\left(E_j\right)$ is the resonant field. The nonlinear signal is homodyne detected with $E_j$. The two-exciton and two-photon coherences (TEC and TPC, respectively) require coherent fields and the ability to create a coherence in the system. The stepwise (SW), ground state (GS) depletion and saturation terms are incoherent pathways. The paths shown are for detection along the (a) $\mid 1⟩\to \mid 2⟩$ and (b) $\mid 2⟩\to \mid 4⟩$ transitions, but are analogous for the $\mid 1⟩\to \mid 3⟩$ and $\mid 3⟩\to \mid 4⟩$ transitions.

Figure 6

The zero field PLE spectra of ∣01⟩ (squares) and ∣10⟩ (circles). The two resonances do not share the same PLE states, as would occur if the two resonances were confined to the same dot. For reference, the zero field degenerate nonlinear spectrum is shown as the solid line, with the two states indicated by the dotted vertical lines.