Ultra-slow orbital and spin dynamics in an electrically tunable quantum dot molecule

Abstract

Tunnel-coupled optically active quantum dot molecules (QDMs), have the potential to operate as spin-photon-interfaces with coupled spins that interact with two different photon frequencies at the same time. A prerequisite is to deterministically prepare two (electron or hole) spins in the QDM and be able to electrically tune the orbital state couplings. Here, we demonstrate the sequential optical charging of a single QDM with two electron spins while simultaneously maintaining the ability to widely tune orbital couplings using static electric fields and optically drive the system for quantum light generation. We optically prepare one- and two-spin states, initialize via optical pumping and explore orbital and spin relaxation dynamics for one and two-spin states as a function of the energy detuning and hybridization of orbital states. For two-spin states, remarkably long S-T relaxation times are observed extending beyond $\sim 100μs$ with strong dependence on the relative energy of ground and excited two-spin states. Qualitative agreement is observed with $\mathbf{k \cdot p}$ calculations of phonon-mediated spin-relaxation. Our results provide new quantitative understanding of the dynamics of one and two-spin states and confirm their suitability of QDMs for creating multidimensional photonic cluster states by exploiting tunable spin-spin exchange couplings at zero magnetic fields combined with optical driving.

Figures (15)

• Figure 1: Voltage-dependent photoluminescence. (a) Voltage-dependent photoluminescence spectrum of a single quantum dot molecule. Different charged excitonic complexes are identified and overlaid with the spectrum in different colors. (b) PL-spectrum of the QDM at $V_G=0.56\,\mathrm{V}$ (marked by the dashed line in (a)). Main transitions are labeled according to the convention explained in the main text.
• Figure 2: Deterministic optical electron charging. (a) Voltage and energy point where 1e and 2e charging is possible. In the PL regime ($V_G > 0$ V) points where luminescence from the lower dot is directly observed, are plotted for the $X^0$ and the $X^-$, along with a few-particle Hamiltonian simulation for these charged complexes. In the regime below 0 V, points where 1e cand 2e charging occurs (experimental data) are also marked. (b) Schematic of the sequential charging experiment. The charging laser pulse (indicated in magenta) is temporally scanned over the different voltage steps by an offset $\Delta t$ that is measured relative to the start of the first charging plateau. The steps of the charging protocol are discussed in the main text. (c) RF signal of $X^0$, $X^-$ and $X^{2-}$ vs. the time offset of the charge laser pulse relative to the first charge voltage plateau.
• Figure 3: Measurements on hybridized two-electron state. (a) Experimental method applied to measure the charge storage time. After the QDM is charged with two electrons, a short readout pulse resonant with the $S_0\leftrightarrow X^{2-}$ transition probes the two-electron state throughout the readout phase IV of the experiment. (b) Intensity of the $X^{2-}$ signal as a function of delay of the readout pulse relative to the charging phase. (c) RF scan over the hybridized two-electron state under application of an external magnetic field of 1 T (Faraday geometry). (d) Level scheme of the two electron states and the doubly charged exciton states used for optical excitation.
• Figure 4: Singlet initialization and probing of singlet-to-triplet transition in an optically controlled QDM. (a) Measurement scheme for demonstrating singlet initialization via charging. Following the preparation of two electrons, a probe pulse (red) resonant with the triplet to trion transition probes the spin population in the triplet state without (top) and with (bottom) a pump pulse (green) resonant with the singlet to trion transition prior to the triplet readout. (b) Level scheme of the two electron state and the respective direct trion used for optical excitation. The ground state is the $(1,1)_S$ state. Optically driving the $(1,1)_S\leftrightarrow X^{2-}$ transition pumps the initial singlet population into the $(1,1)_T$ state. (c) Time-resolved signal of the trion-to-triplet transition. Between 0.5 $\mathrm{\mu s}$ and 0.9 $\mathrm{\mu s}$ a pulse resonantly probing the triplet population is applied. The signal was recorded without (green) and with (orange) a singlet-to-trion pump pulse applied prior to readout. A strong resonant trion-to-triplet signal is only observed when pumping the two-electron population from the singlet to the triplet first, indicating that the bare two-electron state after charging is mostly in the $(1,1)_S$ configuration.
• Figure 5: Orbital pumping and relaxation of one- and two-electron states. (a) Optical driving of the one-electron (1,0) and two-electron (2,0) systems demonstrating Pauli blockade, and optical pumping of (2,0) driven via the direct $X^{2-}$-transition. The insets depict the energy level scheme of the singly and doubly charged QDM subject to resonant optical excitation of the upper dot. (b) Typical results of pump-probe measurements consisting of optical driving of (2,0) via the direct $X^{2-}$-transition to shelve population in (1,1) before a delay without optical driving and a re-pump pulse to test relaxation from (1,1)$\rightarrow$(2,0). (c) Orbital relaxation time measured from cw-pump-probe experiments as a function of the gate voltage. The anticrossing of $(2,0)$ and $(1,1)_{S}$ singlet states is marked by the vertical dashed line and the S-T sweet spot is close to 1.0V. (d) Calculated field dependence of single and triplet states from the 8 band $k \cdot p$ modeling, revealing sweet spot around ${10}$kV/cm. Note the higher energy triplet state shifting below the excited $(1,1)_{T_0}$ triplet at $F\geq18$ kV/cm. (e) Calculated singlet-triplet-relaxation rates as function of the electric field.