Precise measurements of the dipole moment and polarizability of the neutral exciton and positive trion in a single quantum dot

We perform precise measurements of the permanent dipole moment and polarizability of both the neutral exciton ($X^0$) and positive trion ($X^{+}$) in a single InAs/GaAs self-assembled quantum dot (QD). This is achieved through one- and two-color high-resolution photocurrent (PC) spectroscopy of $X^0$ and $X^{+}$, respectively, using ultra-narrow-bandwidth continuous-wave lasers. This technique allows for sub-μeV resolution, which is limited only by the spectral linewidth of the lasers and is more than four orders of magnitude higher than that of previous techniques. We are therefore permitted to obtain precise values for the permanent dipole moment and polarizability of both $X^0$ and $X^{+}$, by fitting an appropriate theoretical model to the measured transition energies as a function of electric field. As a sequence of protocols for the optical initialization, manipulation, and readout of a QD hole spin qubit embedded in a photodiode device relies on the coherent control of both $X^0$ and $X^{+}$ as intermediary states, such precise measurements of their dipole moment and polarizability using high-resolution PC spectroscopy are crucial for implementing these quantum computing protocols with high fidelity.

Figure 1

Single-QD PC spectra of (a) $X^0$ and (b) $X^{+}$ for a series of values of (a) $E_{\mathrm{laser}}^0$ and (b) $E_{\mathrm{laser}}^{+}$ with Lorentzian fit curves (solid lines). For clarity, spectra are shifted vertically with respect to each other.

Figure 2

Plot of the $X^0$ and $X^{+}$ transition energies as a function of $F$ obtained through both PC and μ-PL spectroscopy. Equation (1) is fit to the experimental data (solid lines), yielding precise values for $p$, β, and $E\left(0\right)$, which are given in the table in the inset.