Narrowing of the Overhauser field distribution by feedback-enhanced dynamic nuclear polarization

Abstract

In many electron spin qubit systems coherent control is impaired by the fluctuating nuclear spin bath of the host material. Previous experiments have shown dynamic nuclear polarization with feedback to significantly prolong the inhomogeneous dephasing time T * 2 by narrowing the distribution of nuclear Overhauser field fluctuations. We present a model relating the achievable narrowing of the Overhauser field to both the pump rate and the noise magnitude and find reasonable agreement with experimental data. It shows that former experiments on gated GaAs quantum dots were limited by the pump rate of the pumping mechanism used. Here we propose an alternative feedback scheme using electron dipole spin resonance. Sequentially applying two ac electric fields with frequencies slightly detuned from the desired Larmor frequency results in a pump curve with a stable fixed point. Our model predicts that T * 2 values on the order of microseconds can be achieved.One limiting factor of spin qubits based on semiconductor quantum dots is the fluctuation of the effective magnetic field arising from nuclear spins. The interaction of these nuclear spins in the host material with the electron spin in the quantum dot induces decoherence. Several techniques have been developed to reduce decoherence.1-8 Narrowing the distribution of the nuclear fluctuations was shown to prolong the inhomogeneously broadened dephasing time for gate defined GaAs quantum dots 5 and for self-assembled InAs quantum dots. 3,7To reduce fluctuations the nuclear field is regulated by dynamic nuclear polarization (DNP). DNP controls the Overhauser field by transferring the electron spin angular momentum to the nuclear spins via the hyperfine interaction. If the effectiveness of the polarization step depends on the current state of the nuclear spin bath, the qubit can be used as a closed feedback loop. In gate defined GaAs double quantum dots, a roughly tenfold enhancement of T * 2 has been achieved by LandauZener-sweep driven electron-nuclear spin flip-flops that were preceded by a free evolution of the qubit to create a feedback effect.5 In self-assembled InAs quantum dots a DNP feedback effect was also observed as the quantum dot resonance exhibited locking to frequency 3,7,9 or repetition rate 10 of the incident laser. Driving GaAs gate defined quantum dots with electron dipole spin resonance (EDSR) showed locking to the spin-resonance condition as well. 11The narrowing effect has been examined theoretically in various studies but these were focussed on microscopic models and optical manipulation.12-15 A phenomenological rate-equation model to describe the effectiveness of DNP in reducing the Overhauser field variance was derived by Vink et al.11 and by Latta et al. 9 The model relates the maximum nuclear field achievable by polarization to the nuclear field variance by treating the polarization as a random variable influenced by DNP and relaxation proportional to the current value. This model was further refined by Yang et al. 16 However, the dominant relax...

Feedback-tuned noise-resilient gates for encoded spin qubits

“…23 that a substantial improvement is possible with previously measured lower charge noise levels. Enhanced suppression of hyperfine fluctuations 30 would enable further improvement. Reducing one noise source, either charge or hyperfine noise, generally also allows making gates less sensitive to the other noise source since optimal gates will exploit tradeoffs between the sensitivity to different types of decohering noise.…”

Spatial noise correlations beyond nearest-neighbor in ${}^{28}$Si/SiGe spin qubits

“…The dynamics of the nuclei with their magnetic dipole-dipole interaction show a diffusion-like behavior in the absence of nuclear spin relaxation [33][34][35]70]. Thus, we write the evolution of the nuclear polarization as:…”

“…In spin qubits defined by trapping of individual electrons in semiconductor quantum dots (QDs) [31,32], the coherence time is limited by magnetic and/or electric noise sources. The most relevant magnetic source is the ensemble of nuclei with a finite spin in the host material, that couples to the qubit via hyperfine interaction creating a fluctuating Overhauser field [33][34][35][36]. The shift to materials with a low concentration of isotopes with finite nuclear spin like Si has led to a significant improvement on coherence times [37][38][39].…”

Dynamic Nuclear Spin Polarization Induced by the Edelstein Effect at Bi(111) Surfaces

“…The steady increase towards saturation of B OH vs t p and the saturation after tens of min are both consistent with expectations for DNP in Bi. The maximal B OH obtainable, assuming full NP and full wavefunction overlap, can be estimated as B OH,max = AI/(g * µ B ) [47]. Using values of A = 6.1 µeV to 27 µeV [17,20,22,23] we find B OH,max ≈ 14.5 mT to 64 mT.…”