Ground-state resonant two-photon transitions in wurtzite GaN/AlN quantum dots

Two-photon transition rates are investigated in resonance to the ground state in wurtzite GaN/AlN quantum dots. The ground-state transition is two-photon allowed because of the electron-hole separation inherent to polar wurtzite III–nitride heterostructures. We show that this built-in parity-breaking mechanism can allow deterministic triggering of single-photon emission via coherent two-photon excitation. Radiative lifetimes obtained for single-photon relaxation are in good agreement with available time-resolved microphotoluminescence experiments, indicating the reliability of the employed computational framework based on eight-band $\mathit{k}·\mathit{p}$ wave functions. Two-photon singly induced emission is explored in terms of possible cavity and nondegeneracy enhancement of two-photon processes.

Figure 1

Schematic view of the two-photon processes investigated. (a) Two-photon absorption. Two degenerate or nondegenerate input photons of frequency ${\omega }_1$ and ${\omega }_2$, with their combined energy tuned to the ground-state transition energy $E_{gs}$, are absorbed to excite the QD. (b) Two-photon singly induced emission. A below-band-gap photon of frequency ${\omega }_1$ triggers the emission of an identical photon (second photon of frequency ${\omega }_1$) and a photon of the complementary frequency ${\omega }_2$, carrying the energy difference, from the excited QD.

Figure 2

Schematic two-photon transition-matrix element (shown for two-photon absorption). The second-order matrix element in Eq. (2) comprises the sum over all available intermediate states $|m\rangle$ in both VB and CB. Every intermediate state provides a channel $|i\rangle \to |m\rangle \to |f\rangle$, which is summed up to obtain the overall transition rate.

Figure 3

Qualitative sketches of the QD series, the field-induced carrier separation, and the resulting influence on single-photon and two-photon transition rates. (a) Four series of QDs are investigated, where (i) height, (ii) vertical aspect ratio $A{R}_v$, or (iii, iv) base diameter $d_b$ is kept constant. (b) Schematic VB and CB energy structure as a result of polarization charges at the material interfaces. Electron (blue) and hole (red) probability density are vertically shifted along the [0001] direction. (c) Exemplary influence of the carrier separation on both single-photon as well as two-photon transition rates.

Figure 4

Single-photon lifetime in nanoseconds for the QD series i–iv [Fig. 3] as a function of the transition energy $E_{gs}$. A monoexponential decrease in lifetime is observed up to a transition energy of about 4 eV, before converging in the subnanosecond regime. The data show only minor spread between the QD series.

Figure 5

Two-photon absorption rate in gigahertz as a function of the transition energy $E_{gs}$ for the different QD series. Except for the constant height series (i), the series show a saturation (or eventual decrease) towards higher energies, indicating an optimal separation of electron and hole. The single-photon emission rate (inverse lifetime from Fig. 4) is added in grayscale for comparison.

Figure 6

Two-photon singly induced lifetime in microseconds as a function of the transition energy for a pump photon energy of 400 meV. Slight variations between QDs are observed within the series, as a consequence of resonance enhancement if ${\omega }_{mi}\approx {\omega }_1$ for individual QDs.