Theory of electron spin decoherence by interacting nuclear spins in a quantum dot

Abstract

We present a quantum solution to the electron spin decoherence by a nuclear pair-correlation method for the electron-nuclear spin dynamics under a strong magnetic field and a temperature high for the nuclear spins but low for the electron. The theory incorporates the hyperfine interaction, the intrinsic (both direct and indirect) nuclear interactions, and the extrinsic nuclear coupling mediated by the hyperfine interaction with the single electron in question. The last is shown to be important in free-induction decay (FID) of the single electron spin coherence. The spin echo eliminates the hyperfine-mediated decoherence but only reduces the decoherence by the intrinsic nuclear interactions. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The decoherence is explained in terms of quantum entanglement, which involves more than the spectral diffusion.

Electron Spin as a Spectrometer of Nuclear-Spin Noise and Other Fluctuations

“…[31] Yao et al derive a similar quasiparticle picture via direct calculation of the time dependent correlation function for the electron spin. However, the authors did not calculate the quasiparticle relaxation times.…”

“…Recently, it was shown that the electron mediated inter-nuclear coupling [Eq. (70)] may be exploited in order to recover electron spin coherence lost for the nuclear spin bath [42]. We will certainly see many other interesting developments in the near future.…”

“…Recently, Yao et al [31] and Deng et al [28] showed that the electronmediated inter-nuclear coupling may be observed as a magnetic field dependence of the free induction decay time in small quantum dots. There is currently an interesting debate on the correct form of the time dependence for FID decay.…”

“…Eqs. (67), (69) were later derived using an alternative canonical transformation approach [31]. We may expand Eqs.…”

Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization

“…These short operation times together with the demonstrated coherence times of a few microseconds 7 and predicted coherence times of up to 100 microseconds [27][28][29] suggest that the requirements for quantum error correction of two-electron spin qubits are within reach. Furthermore, our ability to record the magnetic field gradient opens the way towards feedback control of the nuclear environment that would prolong T * 2 and thereby reduce the number of error correcting pulses needed.…”