Depolarization of Electronic Spin Qubits Confined in Semiconductor Quantum Dots

Quantum dots are arguably the best interface between matter spin qubits and flying photonic qubits. Using quantum dot devices to produce joint spin-photonic states requires the electronic spin qubits to be stored for extended times. Therefore, the study of the coherence of spins of various quantum dot confined charge carriers is important both scientifically and technologically. In this study we report on spin-relaxation measurements performed on five different forms of electronic spin qubits confined in the very same quantum dot. In particular, we use all optical techniques to measure the spin relaxation of the confined heavy hole and that of the dark exciton—a long-lived electron-heavy-hole pair with parallel spins. Our measured results for the spin relaxation of the electron, the heavy hole, the dark exciton, the negative and the positive trions, in the absence of externally applied magnetic field, are in agreement with a central spin theory which attributes the dephasing of the carriers’ spin to their hyperfine interactions with the nuclear spins of the atoms forming the quantum dots. We demonstrate that the heavy hole dephases much slower than the electron. We also show, both experimentally and theoretically, that the dark exciton dephases slower than the heavy hole, due to the electron-hole exchange interaction, which partially protects its spin state from dephasing.

Popular Summary

Electronic spin in a semiconductor is considered to be an excellent quantum bit (qubit) with great potential for future quantum information processors. Communicating with other quantum processors will require interfacing spin qubits with flying qubits realized in photons. This is best done with nanometer-sized semiconductor structures known as quantum dots, which isolates the electronic spin qubits and may store them coherently for extended times. The decoherence of the electronic spins in quantum dots, which is the nemesis of quantum processing, is mainly due to their interactions with the nuclear spins of the atoms that comprise the quantum dot. Here, we experimentally explore ways to protect the electronic spins from this dephasing mechanism.

We measure the spin relaxation times for five different forms of electronic spin qubits, all in the same quantum dot. In particular, we study spin qubits composed of electrons, holes (missing electrons), and dark excitons (electron-hole pairs). We demonstrate that the hole qubit dephases more slowly than the electron qubit. We also show that the dark-exciton qubit dephases more slowly than the hole due to the electron-hole exchange interaction, which partially protects the dark-exciton spin state from dephasing.

Our results are in agreement with the central spin theory, which attributes the dephasing of the carriers’ spin to their hyperfine interactions with the nuclear spins in their vicinity. We believe that by increasing the quantum-dot symmetry and by avoiding alloying, the dark exciton may form an almost nondephasing electronic spin qubit in a semiconductor environment.

Figure 1

(a) Spin wave functions and Bloch-sphere representations of the six matter spin qubits used in this work. The six qubits, represented by their Bloch spheres, are divided into three pairs of ground and excited-level qubits. The spin wave functions of the ground-level (excited-level) qubits are schematically described below (above) the respective Bloch spheres, where $\uparrow$ ($\Downarrow$) represents spin-up electron (down heavy hole), and the blue (red) color represents a carrier in its ground (excited) energy level. Green upward arrows represent laser pulses which convert the ground-level qubit to its respective excited-level qubit. Magenta downward arrows represent single photons emitted from the excited qubits thereby returning to the ground-level qubit. (b) The optical transitions and polarization selection rules for the electron-trion system, which form a ground-level–excited-level qubit pair. Note that in this example (as in all other cases) an optical $\mathrm{\Pi }$ system is described, but the exciting laser pulse is tuned to an excited trion level, in order to facilitate polarization tomography of the emitted photon (magenta downward arrows) by spectrally separating the emission from the exciting laser pulse (green upward arrows). The fast (about 70 ps [29]) phonon-assisted relaxation of the excited trion to the ground trion level is represented by gray curly downward arrows. The right-hand (left-hand) circular polarization of the photons which connect the $1/2$ ($-1/2$) spin state of the ground-level qubit with the $+3/2$ ($-3/2$) spin state of the excited qubit are marked by $R$ ($L$).

Figure 2

Schematic description of the spin dephasing processes of the QD confined electron (a), heavy hole (b), and dark exciton (c). Each process is divided into two temporal stages: During the first stage the initiated central spin precesses around the effective magnetic field which results from the frozen fluctuation of the nuclear spins of about $10^5$ atoms comprising the QD. The electron spin ($\widehat{S}$) interacts with the nuclear spin ($\widehat{I}$) via the isotropic Fermi contact interaction described by ${\gamma }_e$. The heavy-hole spin ($\widehat{J}$) interacts with the nuclear spin via the anisotropic dipole-dipole hyperfine interaction denoted by ${\gamma }_{h_z}$ and ${\gamma }_{h_p}$, where $\widehat{z}$ is the QD growth direction and $p$ denotes direction in a plane perpendicular to $\widehat{z}$. The dark exciton contains an electron and a heavy hole. Both spins interact with the nuclear spin, and in addition, the electron and hole interact with each other mainly via the isotropic exchange interaction denoted by ${\mathrm{\Delta }}_0$ [30]. During the second stage the nuclear spins react to strain-induced electric field gradients (EFG) in the QD [31]. This interaction has a quadrupole nature, and we denote it by ${\gamma }_Q$. The motion of each nuclear spin is described by an effective local magnetic field in a direction marked by $\widehat{n}$ which the nuclear spin slowly precesses around. During the second stage, we use the adiabatic approximation, by which the central spin just follows the slowly varying effective nuclear magnetic field. The various interaction magnitudes are summarized and referenced in Table 1. Inset: schematic description of the InAsP QD (blue) embedded in the InP photonic nanowire (orange). The central spin is represented by the black arrows, the nuclear spin bath are represented by the red arrows, and the EFGs are schematically represented by green arrows in the magnified description of the QD.

Figure 3

Schematic description of the experiments for measuring the spin dynamics of (a) positive and negative trions, (b) single electron and single heavy hole. (c) Dark exciton. The optical transitions in each experiment are described by the energy-level diagram to the right. The carrier’s spins are marked in the figure using the notations of Fig. 1, where blue (red) color represents ground (excited) single carrier states. CW1 and CW2 represent the 20-ns gated CW laser pulses where $P_1$ and $P_2$ represent the 12-ps pulses produced by the synchronously pumped and cavity-dumped dye lasers. $\mathrm{\Delta }t$ is the time delay between the two pulses in each repetition period, controlled by two cavity dumpers and a delay line. $D_1$ and $D_2$ represent the emission and time-resolved detection of the two single photons emitted as a result of the $P_1$ and $P_2$ excitations.

Figure 4

Measured central spin polarization $⟨S_z⟩$ as a function of time after its initialization, for the QD confined electron (blue square symbols), heavy hole (red triangle symbols), dark exciton (black diamond symbols), negative trion (red times symbols), and positive trion (blue times symbols). Error bars represent one standard deviation of the experimental uncertainty. Solid color-matched lines represent the fitted theoretical model (see Appendices), for each case. The spin wave functions are schematically described in the legend, where the notations of Fig. 1 are used.

Figure 5

The calculated normalized Overhauser correlator $f_I(t)$ for the various types of nuclear spins which comprise the QD. $I_{\text{mean}}$ is the mean value of the correlator taking into account the isotopic abundances weighted by their squared magnetic moments.