Nuclear Spins as Quantum Memory in Semiconductor Nanostructures

We theoretically consider the possibility of using solid state nuclear spins in a semiconductor nanostructure environment as long-lived quantum memory. In particular, we calculate, in the limit of a strong applied magnetic field, the quantum coherence time for P donor nuclear spins in random bath environments of Si and GaAs, and the lifetime of excited intrinsic spins in polarized Si and GaAs environments. In the former situation, the nuclear spin dephases due to spectral diffusion induced by the dipolar interaction among nuclei in the bath. We calculate this nuclear spin memory time in the context of Hahn and CPMG refocused spin echoes using a formally exact cluster expansion technique which has previously been successful in dealing with electron spin dephasing in a solid state nuclear spin bath. Although limited by the nuclear T2 dephasing time, typically much shorter than its long-lived T1 counterpart, we find that rather long nuclear spin quantum memory times of the order of 100 μs (GaAs:P) and 1-2 ms (natural Si:P) are feasible using composite CPMG pulse sequences with the relative memory loss being less than 10 over these times scales. We also consider the complementary situation of a central flipped intrinsic nuclear spin in a bath of completely polarized nuclear spins where decoherence is caused by the direct flip-flop of the central spin with spins in the bath. Exact numerical calculations that include a sufficiently large neighborhood of surrounding nuclei show lifetimes on the order of 1-5 ms for both GaAs and natural Si. Our calculated nuclear spin coherence times may have significance for solid state quantum computer architectures using localized electron spins in semiconductors where nuclear spins have been proposed for quantum memory storage.