Enhanced Spin Coherence of a Self-Assembled Quantum Dot Molecule at the Optimal Electrical Bias

A pair of coupled dots with one electron in each dot can provide improvements in spin coherence, particularly at an electrical bias called the “sweet spot,” but few measurements have been performed on self-assembled dots in this regime. Here, we directly measure the $T_2^{*}$ coherence time of the singlet-triplet states in this system as a function of bias and magnetic field, obtaining a maximum $T_2^{*}$ of 60 ns, more than an order of magnitude higher than an electron spin in a single quantum dot. Our results uncover two main dephasing mechanisms: electrical noise away from the sweet spot, and a magnetic field dependent interaction with nuclear spins due to a difference in $g$ factors.

Figure 1

(a) Detailed energy-level diagram of the two-electron charged QDM in the Faraday external magnetic field with numbering scheme depicting individual transitions. The spin configuration for each state is also indicated. Here, the blue (red) arrow refers to the bottom (top) dot. The single (double) arrow refers to electron (hole). (b) Measured resonance fluorescence spectra as functions of bias. The transitions are identified with numbering and colors that match part (a). The sweet spot is at the center of the optical pumping region (about 0.725 V bias).

Figure 2

(a) Experimental schematic: Intensity modulation of the rotation laser by a microwave source via the electro-optical modulator creates two laser side bands whose energy difference is twice the modulation frequency. The rotation laser is detuned ${\mathrm{\Delta }}_L\approx 250\mathrm{GHz}$ from the excited state, and the side band energy spacing is detuned $\delta$ from the $S\text{−}{T}_0$ resonance. The initialization laser is resonant with the $T_0\leftrightarrow R-$ transition. The $T_0$ state population is then detected via Raman scattering $S\leftrightarrow R-$. (b) Rabi oscillations between the $S$ and $T_0$ spin states at four different Rabi frequencies. (c) The dependence of the Rabi frequency on the peak power of the rotation laser.

Figure 3

(a) Bloch sphere representation of spin control of the $S{T}_0$ subspace. (b) The pulse sequence for Ramsey measurement which consists of a 70 ns initialization pulse, and two $\pi /2$ rotation pulses (2.5 ns duration) with variable separation between them. The sequence is repeated after every 300 ns. (c) Ramsey interference obtained at $B=0.05\mathrm{T}$ and at various biases ${\mathrm{\Delta }}_{\mathrm{bias}}$ relative to the sweet spot. The data are fitted with exponential oscillation decay (black solid lines). (d) $T_2^{*}$ (left vertical axis) and $S\text{−}{T}_0$ energy splitting (right vertical axis) are extracted from the Ramsey interference data and are plotted as functions of the bias offset from the sweet spot. (e) The dephasing rate (${\gamma }_{\mathrm{ph}}$) and magnitude of the derivative of the exchange splitting with respect to bias ($|dJ/dV|$) are plotted against the bias offset from the sweet spot showing a linear correlation between the two quantities.

Figure 4

(a) Ramsey interference data obtained at the sweet spot at various magnetic field strength. (b) Semilog plot of $T_2^{*}$ against the magnetic field. Dotted curve denotes the expected change of $T_2^{*}$ at high field regime.