Optical Pumping of Quantum-Dot Nuclear Spins

Hyperfine interactions with randomly oriented nuclear spins present a fundamental decoherence mechanism for electron spin in a quantum dot, that can be suppressed by polarizing the nuclear spins. Here, we analyze an all-optical scheme that uses hyperfine interactions to implement laser cooling of quantum-dot nuclear spins. The limitation imposed on spin cooling by the dark states for collective spin relaxation can be overcome by modulating the electron wave function.

Figure 1

All-optical manipulation of electron-nuclear spin-flip in a single quantum dot. (a) In the presence of a large Zeeman splitting, electron-nuclear spin-flip events are energetically forbidden. (b) Introduction of a red-detuned laser field can effectively cancel the Zeeman splitting and allow for resonant spin-flip processes due to hyperfine interaction. (c) The spin-flipped electron is repumped into the initial state by a combination of a $\pi$ pulse, followed by spontaneous emission.

Figure 2

Optical pumping of a quantum dot with 10 nuclear spins. We assume a Gaussian wave function for the electron and choose its center such that pairs of nuclear spins have identical $\alpha$. Starting from a completely unpolarized nuclear state with density matrix ${\rho }_i=1/2^N$, we find that the nuclear polarization saturates at 0.75 (solid line). This saturation is a clear indication of the influence of dark states. We then shift the electron wave function (after 5000 pulse sequences) in a way to ensure that $\alpha$’s are identical for different sets of nuclei: Since the new coupling distribution has a different set of dark states, the polarization increases abruptly and then saturates at a higher level. Further shifts after 15 000 and 20 000 pulse sequences result in 95% polarization of the nuclear spins (solid line). The dashed line shows $⟨{\widehat{I}}_z⟩$ when the electron wave function is shifted by the same small amounts, but now after every 50 cooling pulse sequences. The dotted line shows the simulation result for a single Gaussian wave function that ensures ${\alpha }_i\ne {\alpha }_j,\forall i\ne j$: In this case there are no dark states and the final nuclear spin polarization $\ge 99\%$ is achieved after only 2000 pulses (inset).