Ultrafast Optical Spin Echo for Electron Spins in Semiconductors

Spin-based quantum computing and magnetic resonance techniques rely on the ability to measure the coherence time $T_2$ of a spin system. We report on the experimental implementation of all-optical spin echo to determine the $T_2$ time of a semiconductor electron-spin system. We use three ultrafast optical pulses to rotate spins an arbitrary angle and measure an echo signal as the time between pulses is lengthened. Unlike previous spin-echo techniques using microwaves, ultrafast optical pulses allow clean $T_2$ measurements of systems with dephasing times ($T_2^{*}$) fast in comparison to the time scale for microwave control. This demonstration provides a step toward ultrafast optical dynamic decoupling of spin-based qubits.

Figure 1

(a) Experimental setup to generate optical pulse sequence. (b) The pulse sequence: labels i and ii match those in Fig. 2b. Panels show an inhomogenous spin ensemble (blue dots) on the Bloch sphere at different times during a $\pi /3-\pi /3-\pi /3$ pulse sequence. The green or gray line shows the average spin polarization vector. After the final ultrafast pulse and pumping pulse, the average spin polarization vector shown in panel iid will be proportional to the spin polarization that we observe on the $z$ axis.

Figure 2

(a) Energy level diagram of donor-bound-exciton system in a magnetic field: ground states $|0⟩$ and $|1⟩$ are split by an energy $\hslash {\omega }_L$. They are optically connected to the donor-bound-exciton states, $|e⟩$, via an ultrafast pulse of Rabi frequency $\Omega$ detuned by $\Delta$. (b) Relevant energy levels and applied optical fields: the pumping laser applies electric fields on resonance to pump population to the $|0⟩$ state (orange dashed line, i). The rotation laser performs rotations between the ground states with effective Rabi frequency ${\Omega }_e$ (blue arrows, ii). The pumping laser applies another field on resonance (i) and light is collected from the $|0⟩\leftrightarrow |e⟩$ transition (yellow line, iii).

Figure 3

Results of all-optical spin-echo experiment. (a) Population in $|1⟩$ (green solid line) as a second pulse is scanned in a two pulse experiment with ${\tau }_1=26\mathrm{ns}$. No fringes can be seen, indicating complete dephasing. Population in $|1⟩$ (blue dots) and a fit (red dashed line) to a three pulse experiment with ${\tau }_1=26\mathrm{ns}$. Here, there are clear oscillations. (b) Data and fit to a three pulse experiment with $2{\tau }_1=2\mu \mathrm{s}$. Visibility has decreased compared to (a). (c) Fringe visibility vs pulse separation, $2{\tau }_1$. Error bars are calculated from the standard deviation of several measurements of the fringe visibility at one point. The fit (black line) is a phenomenological decay that includes pulse-induced decoherence and intrinsic $T_2$ decoherence with a decay time of $6.7\pm 2.5\mu \mathrm{s}$. The points shown in (a) and (b) are labeled.