Effective boson-spin model for nuclei-ensemble-based universal quantum memory

We study the collective excitation of a macroscopic ensemble of polarized nuclei fixed in a quantum dot. Under the approximately homogeneous condition that we explicitly present in this paper, this many-particle system behaves as a single-mode boson interacting with the spin of a single conduction-band electron confined in this quantum dot. Within this effective spin-boson system, the quantum information carried by the electronic spin can be coherently transferred into the collective bosonic mode of excitation in the ensemble of nuclei. In this sense, the collective bosonic excitation can serve as a stable quantum memory to store the quantum spin information of the electron.

Figure 1

Polarized nuclei interacting with an electron in a quantum dot. Because of the overlap between the electronic wave function and the nuclear wave functions, an effective spin-spin coupling between the electron and the nuclei is induced.

Figure 2

Spectrums of $H_s$ (a) and $H_c-{\omega }_z$ (b) for $N=80$ and $I_0=1∕2$ system in the subspace $J_z=-N∕2+1$. The slight deviation between the two spectrums is because of the hardcore effect of two bosons and should vanish in macroscopic limit.

Figure 3

The decoherence factor $D(T,t)$ for a small-size system as the function of time and temperature.