Spectroscopy of Few-Electron Collective Excitations in Charge-Tunable Artificial Atoms

We report the investigation of electronic excitations in InGaAs self-assembled quantum dots using resonant inelastic light scattering. The dots can be charged via a gate by $N=1,\dots ,6$ electrons. We observe excitations, which are identified as transitions of electrons, predominantly from the $s$ to the $p$ shell ($s\mathrm{\text{−}}p$ transitions) of the quasiatoms. We find that the $s\mathrm{\text{−}}p$ transition energy decreases and the observed band broadens, when the $p$ shell is filled with $1$ to $4$ electrons. By a theoretical model, which takes into account the full Coulomb interaction in the few-electron artificial atom, we can confirm the experimental results to be an effect of the Coulomb interaction in the quantum dot.

Figure 1

(a) Schematic picture of the band structure of a InGaAs quantum-dot sample. (b) Capacitance measurement of the investigated InGaAs quantum-dot sample.

Figure 2

Polarized ILS spectra for two different gate voltages $V_{\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{e}}$. The right panel sketches the charging state of the dots. Because it is not clear whether a bound d shell exists, the state has been drawn with dashed lines. The black (gray) vertical arrows indicate possible allowed (forbidden) transitions of electrons.

Figure 3

(a) Polarized ILS spectra for gate voltages $V_{\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{e}}=0.2$, 0.25, 0.35, 0.45, $0.55\mathrm{V}$ (from top to bottom). The inset shows the charging states of the dots. (b) Calculated energies of low-energy collective excitations of a two-dimensional parabolic quantum dot for different electron numbers in the dot.

Figure 4

Schematic picture of occupation in the most important Slater determinants, which contribute to the exact many-body wave function of (a) the ground state with $M=1$ and $S=S_z=\frac{1}{2}$, and, (b)–(e) its low-energy excited states [a similar picture with the same eigenenergies can be drawn for $M=-1$, and/or $S_z=-\frac{1}{2}$ for the ground state]. The numbers give the occupation probabilities of the respective determinants. $M$ is the total angular-momentum quantum number, and $m$ is the single-particle angular momentum.