Optical Detection of Single-Electron Spin Resonance in a Quantum Dot

We demonstrate optically detected spin resonance of a single electron confined to a self-assembled quantum dot. The dot is rendered dark by resonant optical pumping of the spin with a laser. Contrast is restored by applying a radio frequency (rf) magnetic field at the spin resonance. The scheme is sensitive even to rf fields of just a few $\mu \mathrm{T}$. In one case, the spin resonance behaves as a driven 3-level $\lambda$ system with weak damping; in another one, the dot exhibits remarkably strong (67% signal recovery) and narrow (0.34 MHz) spin resonances with fluctuating resonant positions, evidence of unusual dynamic processes.

Figure 1

(a) Level scheme for optically detected spin resonance. The electron spin states, $|\uparrow ⟩$ and $|\downarrow ⟩$, are split by the electron Zeeman energy $g_e{\mu }_B{B}_{\mathrm{ext}}(g_e<0)$. $|\uparrow \downarrow ,\Uparrow ⟩$ denotes the spin-up exciton state, $X^{1-}$. The ${\sigma }^{+}$-polarized transition $|\uparrow ⟩\leftrightarrow |\uparrow \downarrow ,\Uparrow ⟩$ is driven on resonance with a coherent laser. The spin resonance transition, $|\downarrow ⟩\leftrightarrow |\uparrow ⟩$, is driven with an oscillating magnetic field $B_{\mu \mathrm{W}}$ at right angles to the dc external magnetic field, $B_{\mathrm{ext}}$. Incoherent processes are spontaneous radiative decay, $|\uparrow \downarrow ,\Uparrow ⟩\to |\uparrow ⟩$ (fast), $|\uparrow \downarrow ,\Uparrow ⟩\to |\downarrow ⟩$ (slow); and spin relaxation, $|\downarrow ⟩\leftrightarrow |\uparrow ⟩$ (very slow). (b) Schematic of experimental setup. The laser excitation at wavelengths around 950 nm is focused onto the sample with an objective with numerical aperture 0.5 and gives a spot size of $\sim 1\mu \mathrm{m}$ at the sample. The transmitted light is detected with an in situ photodiode. A dc magnetic field, $B_{\mathrm{ext}}$, is applied perpendicular to the sample. An ac magnetic field, $B_{\mu \mathrm{W}}$, is generated with a closed loop antenna of diameter 2 mm positioned 2 mm along its axis from the quantum dot. The loop is connected to a microwave oscillator via a high frequency cable. The objective, sample, and antenna are all at 4.2 K.

Figure 2

Spin shelving via optical pumping. (a) Differential transmission data on a single quantum dot at 4.2 K as a function of the applied magnetic field, $B_{\mathrm{ext}}$, recorded with a $V_{\mathrm{G}}$ at the center of the charging plateau. The contrast disappears as $B_{\mathrm{ext}}$ increases. (b),(c) Color scale plots of the $V_{\mathrm{G}}$ dependence. (b) At $B_{\mathrm{ext}}=0$, the optical signal is maintained across the plateau; (c) at $B_{\mathrm{ext}}=0.5\mathrm{T}$, the optical signal is suppressed in the plateau center signifying spin shelving, but recovers at the plateau edges signifying rapid spin relaxation via cotunneling. In (c), the two resonances correspond to the two Zeeman-split exciton transitions. The polarization is right-handed circularly polarized with a weak left-handed component.

Figure 3

Optical characterization with 2 coherent lasers. The energy of laser 1 is chosen to come into resonance with the higher energy Zeeman transition, $|\uparrow ⟩\leftrightarrow |\uparrow \downarrow ,\Uparrow ⟩$, at $V_{\mathrm{G}}=-1.01\mathrm{V}$ where the transmission contrast is immeasurably small owing to spin shelving in the $|\downarrow ⟩$ state. The power of laser 1 is 1 nW. The energy of a second laser, $h{\nu }_2$, with power 1 nW is redshifted relative to laser 1, and the differential transmission is recorded as a function of $V_{\mathrm{G}}$. Both lasers are linearly polarized. The process is repeated for different $h{\nu }_2$. (a) The data as a color plot. (b),(c) The transmission spectra for laser 1 alone, for laser 2 alone, and for laser 1 and laser 2 (offset for clarity) for the two double resonances marked in (a). (d),(e) The respective interpretations of the double resonances in terms of the level diagram, Fig. 1. (f) Difference in absorbed photon energy of the two lasers, as in (d), against magnetic field with a linear fit.

Figure 4

Optically detected spin resonance for dot $A$ at $B_{\mathrm{ext}}=0.5\mathrm{T}$. Color scale plot of the optical transmission signal with microwave frequency, $f_{\mu \mathrm{W}}$, along the $x$ axis, and gate voltage (equivalently optical detuning, $\delta$) along the $y$ axis. The Stark shift $d\delta /d{V}_G$ is $0.9\mu \mathrm{eV}/\mathrm{mV}$. For each microwave frequency, the gate voltage is swept from $-1.01$ to $-1.03\mathrm{V}$. The strong signal close to 4.3 GHz is the electron spin resonance (ESR). (c)–(f) Other experimental runs on the same dot under identical conditions; (b) optical transmission versus microwave frequency at zero optical detuning from (c) showing ESR close to 3.98 GHz. (g) Optically detected spin resonance for dot $B$ at 0.5 T and zero optical detuning. The black line corresponds to the experimental data; the red line to the theory.