Spectrum of the Nuclear Environment for GaAs Spin Qubits

Abstract

Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as 1/f 2 for frequency f 1 Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electronmediated spin diffusion, which decreases spectral content in the 1/f 2 region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime ( 16 π-pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime ( 32 π-pulses), where longitudinal Overhauser fluctuations with a 1/f spectrum dominate.

Coherence of a Driven Electron Spin Qubit Actively Decoupled from Quasistatic Noise

“…The power spectral density of δf in Ramsey measurements is calculated by the fast Fourier transform of δf (t). The spectral density taken with small SEC and feedback off (blue) shows the f −1.7 dependence (black dashed line) similar to those observed for nuclear spin diffusion noise [15,16]. The spectral density is significantly suppressed with feedback on (orange) down to a level determined by the precision of the feedback control.…”

“…Approximating S(f ) = A 2 /f , however, we find A ∼ 0.6 MHz being two orders of magnitude larger than A ∼ 1.6 kHz found in the 28 Si device. It is also an order of magnitude larger than A ∼ 0.1 MHz observed in a GaAs device without micromagnet [16]. The difference can be partly attributed to large SEC in the present device, as S(f ) is reduced by two orders of magnitude by decreasing SEC (see Fig.…”

“…It suggests that the f −1 noise background in the range of tens of MHz is the dominant limiting factor of the qubit control fidelity. The f −β dependence with β = 1 differs from β ∼ 1.7 for the nuclear spin diffusion noise [15,16] at low frequencies (see Fig. 5b) extracted from the data in Figs.…”

Discrete time crystal in the gradient-field Heisenberg model

“…2. Here we have treated the disorder as quasistatic, but in a QD system it is mostly due to the fluctuations of the nuclear spins, and so it varies slowly over timescales longer than a few microseconds [30,43]. Thus, the true limits on the spin preservation time are likely shorter than the ones obtained within the present model.…”

The dynamical-decoupling-based spatiotemporal noise spectroscopy

“…The application of such a sequence leads then to dynamical decoupling [5,[14][15][16][17]] that on one hand extends qubits's coherence time by suppressing the influence of most of environmental fluctuations, and on the other makes the qubit sensitive to noise frequencies determined by the inverse of applied sequence period [5][6][7][8][9]. This method has been successfully implemented with many kinds of qubits: superconducting circuits [7], trapped ions [9], ultracold atoms [18], semiconductor-based quantum dots [19][20][21], donors in silicon [22], and nitrogen-vacancy centers in diamond [23,24]. The information obtained in this way led to multiple new insights into the dynamics of environments affecting various kind of qubits.…”