Nuclear spin dynamics and Zeno effect in quantum dots and defect centers

Abstract

We analyze nuclear spin dynamics in quantum dots and defect centers with a bound electron under electron-mediated coupling between nuclear spins due to the hyperfine interaction ("J-coupling" in NMR). Our analysis shows that the Overhauser field generated by the nuclei at the position of the electron has short-time dynamics quadratic in time for an initial nuclear spin state without transverse coherence. The quadratic short-time behavior allows for an extension of the Overhauser field lifetime through a sequence of projective measurements (quantum Zeno effect). We analyze the requirements on the repetition rate of measurements and the measurement accuracy to achieve such an effect. Further, we calculate the long-time behavior of the Overhauser field for effective electron Zeeman splittings larger than the hyperfine coupling strength and find, both in a Dyson series expansion and a generalized master equation approach, that for a nuclear spin system with a sufficiently smooth polarization the electron-mediated interaction alone leads only to a partial decay of the Overhauser field by an amount on the order of the inverse number of nuclear spins interacting with the electron.Comment: 11 pages, 3 figure

Hyperfine induced electron spin and entanglement dynamics in double quantum dots: The case of separate baths

“…This is exactly the part of the Hamiltonian that is eliminated in most of the approaches by applying a strong magnetic field to the central spin system (see Refs. [31][32][33][34][35][36]. In Refs.…”

“…29 Following the idea to take advantage of the hyperfine interaction, in a recent paper 30 we investigated a system of two exchange-coupled electron spins, each of which is interacting with an individual bath of nuclear spins via the hyperfine interaction. In contrast to most of the approaches considered in the context of hyperfine interaction, [31][32][33][34][35][36] no magnetic field, enabling for a perturbative treatment of the problem, was applied to the electron spins. Using exact diagonalization studies, we demonstrated that the nuclear baths can be swapped and fully entangled, provided they are large enough.…”

Self-quenching of nuclear spin dynamics in the central spin problem

“…However, a controllable nuclear spin polarization, acting as an effective magnetic field, can also become a resource for manipulating electron spins [21,22]. In particular, the difference (gradient) in the nuclear polarization of the left and right dots can be used for σ x rotations of a S-T 0 singlet-triplet qubit on the Bloch sphere [8].…”

Quantum-Dot Spin Qubit and Hyperfine Interaction

“…For the case of a static exchange interaction J(t) = J 0 , the decay of the two-electron spin states in the S z = 0 subspace due to the Gaussian distribution of nuclear spin states may be calculated in several interesting limits [24,35]. Assuming the initial state of the two-electron system is ρ e (0) = |+ +|, the probability P + to measure the |+ state as a function of time is given by…”

“…Under these conditions the relevant spin Hamiltonian becomes block diagonal with blocks labeled by the total electron spin projection along the magnetic field S z . In the subspace of S z = 0 the Hamiltonian can be written as (h = 1) [24,35] …”