Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots

Abstract

The central-spin problem is a widely studied model of quantum decoherence. Dynamic nuclear polarization occurs in central-spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in quantum information processing for coherent spin manipulation. However, the mechanisms limiting this process remain only partially understood. Here we show that spin-orbit coupling can quench dynamic nuclear polarization in a GaAs quantum dot, because spin conservation is violated in the electron-nuclear system, despite weak spin-orbit coupling in GaAs. Using Landau-Zener sweeps to measure static and dynamic properties of the electron spin-flip probability, we observe that the size of the spin-orbit and hyperfine interactions depends on the magnitude and direction of applied magnetic field. We find that dynamic nuclear polarization is quenched when the spin-orbit contribution exceeds the hyperfine, in agreement with a theoretical model. Our results shed light on the surprisingly strong effect of spin-orbit coupling in central-spin systems.

Figure 1. Experimental set-up.

(a) Scanning electron micrograph of the double quantum dot. A voltage difference between the gates adjusts the detuning ɛ between the potential wells, and a nearby quantum dot on the left senses the charge state of the double dot. The gate on the right couples the double dot to an adjacent double dot, which is unused in this work. The angle between B and the z axis is ϕ. (b) Energy level diagram showing the two-electron spin states and zoom-in of the S−T₊ avoided crossing. (c) The hyperfine interaction couples |(1,1)S〉 and |(1,1)T₊〉 when the two dots are symmetric, regardless of the orientation of B, and the spin–orbit interaction couples |(0,2)S〉 and |(1,1)T₊〉 when B has a component perpendicular to , the effective spin–orbit field experienced by the electrons during tunnelling.

Figure 2. Measurements of σ_ST.

(a) Data for a series of LZ sweeps with varying rates, showing reduction in maximum probability due to charge noise. The horizontal axis is proportional to the sweep time. Upper inset: data and linear fit for fast sweeps such that 0<〈P_LZ〉<0.1. Lower inset: in a LZ sweep, a |(0,2)S〉 state is prepared, and ɛ is swept through ɛ_ST (dashed line) with varying rates. Here h=2πħ is Planck's constant. (b) σ_ST versus ϕ (dots) and simulation (solid line). (c) σ_ST versus B for ϕ=0° and ϕ=90° (dots) and fits to equation (3) (solid lines). When ϕ=0°, Δ_SO is fixed at zero, and the only fit parameter is σ_HF. When ϕ=90°, σ_HF is fixed at the fitted value, and Δ_SO is the only fit parameter (see Methods section). Error bars are fit errors.

Figure 3. Correlations and power spectrum of P_LZ(t).

(a) Pulse sequence to measure R_PP(τ) using two LZ sweeps. (b) R_PP(τ) for ϕ=0° and B=0.1 T. The data extend to τ=200 μs, but for clarity are only shown to 75 μs here. (c) S_P(ω) versus ϕ obtained by Fourier-transforming R_PP(τ). At ϕ=0°, the differences between the nuclear Larmor frequencies are evident, but for |ϕ|>0°, the absolute Larmor frequencies appear, consistent with a spin–orbit contribution to σ_ST. The reduction in frequency with ϕ is likely due to the placement of the device slightly off-centre in our magnet, and the reduction in amplitude of the difference frequencies occurs because the sweep rate β was increased with ϕ to maintain constant 〈P_LZ〉 (see Methods section). (d) Line cuts of S_P(ω) at ϕ=0°, 25° and 80°.

Figure 4. DNP quenching by spin–orbit coupling.

(a) Protocol to measure DNP. δB_z is measured before and after 100 LZ sweeps by evolving the electrons around δB_z. (b) dDNP versus ϕ at fixed 〈P_LZ〉=0.4 for B=0.8 and 0.2 T, and theoretical curves (solid lines). dDNP is suppressed for |ϕ|>0 because of spin–orbit coupling. (c) Data and theoretical curves for fixed 〈P_LZ〉 collapse when normalized and plotted versus σ_HF/σ_ST. Vertical error bars are statistical uncertainties and horizontal error bars are fit errors.