Spin manipulation and spin-lattice interaction in magnetic colloidal quantum dots

We report on the spin-lattice interaction and coherent manipulation of electron spins in Mn-doped colloidal PbS quantum dots (QDs) by electron spin resonance. We show that the phase memory time,$T_M$, is limited by Mn–Mn dipolar interactions, hyperfine interactions of the protons (${}^1\mathrm{H}$) on the QD capping ligands with Mn ions in their proximity (<1 nm), and surface phonons originating from thermal fluctuations of the capping ligands. In the low Mn concentration limit and at low temperature, we achieve a long phase memory time constant $T_M\sim 0.9\mu \mathrm{s}$, thus enabling the observation of Rabi oscillations. Our findings suggest routes to the rational design of magnetic colloidal QDs with phase memory times exceeding the current limits of relevance for the implementation of QDs as qubits in quantum information processing.

Figure 1

Continuous-wave ESR spectra of PbS:Mn QDs at different Mn concentrations, $x$. Inset: sketch of the PbS:Mn crystal lattice with substitutional $\mathrm{M}{\mathrm{n}}_{\mathrm{Pb}}$.

Figure 2

Spin echo (a) and inversion recovery (b) measurements at different $x$ at 5 K. The cyan curve in (a) is the simulation to Eq. (4), as discussed in the text. Inset in (a) shows the ESEEM spectrum and cartoon of the PbS:Mn QDs. Pulse sequence schemes are also shown in (a) and (b).

Figure 3

Dependence of $1/T_1$ (circles) and $1/T_M$ (stars) on the (a) Mn content and (b) temperature for $x=0.05\%$. Experimental errors are within the size of the symbols. The line in (a) is the calculated dipolar limit, $1/T_{\mathrm{dip}}$. The line in (b) is a fit to $1/T_1=A_{1}T$ with $A_1=\left(6.44\pm 0.05\right)\times {10}^{-3}\mu {\mathrm{s}}^{-1}{\mathrm{K}}^{-1}$.

Figure 4

(a) Rabi oscillations and (b) fast Fourier transform for PbS:Mn QDs with $x=0.05\%$ at various values of $B_1=0.2-1.6\mathrm{mT}$ at $T=5\mathrm{K}$ and $B_0=345\mathrm{mT}$. The nutation pulse scheme, the electron-${}^1\mathrm{H}$ nutation frequency (red dashed line) and the Rabi frequencies (arrows) are shown.