Non-Markovian Dynamics of a Localized Electron Spin Due to the Hyperfine Interaction

We review our theoretical work on the dynamics of a localized electron spin interacting with an environment of nuclear spins. Our perturbative calculation is valid for arbitrary polarization p of the nuclear spin system and arbitrary nuclear spin I in a sufficiently large magnetic field. In general, the electron spin shows rich dynamics, described by a sum of contributions with exponential decay, nonexponential decay, and undamped oscillations. We have found an abrupt crossover in the long-time spin dynamics at a critical shape and dimensionality of the electron envelope wave function. We conclude with a discussion of our proposed scheme to measure the relevant dynamics using a standard spin-echo techniqu

Exponential decay in a spin bath

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.Comment: 4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B

Exchange-controlled single-electron-spin rotations in quantum dots

We show theoretically that arbitrary coherent rotations can be performed quickly (with a gating time ~1 ns) and with high fidelity on the spin of a single confined electron using control of exchange only, without the need for spin-orbit coupling or ac fields. We expect that implementations of this scheme would achieve gate error rates on the order of \eta ~ 10^{-3} in GaAs quantum dots, within reach of several known error-correction protocolsComment: 4+ pages, 3 figures; v2: Streamlined presentation, final version published in PRB (Rapid Comm.

Frequency dependent transport through a spin chain

Motivated by potential applications in spintronics, we study frequency dependent spin transport in nonitinerant one-dimensional spin chains. We propose a system that behaves as a capacitor for the spin degree of freedom. It consists of a spin chain with two impurities a distance $d$ apart. We find that at low energy (frequency) the impurities flow to strong coupling, thereby effectively cutting the chain into three parts, with the middle island containing a discrete number of spin excitations. At finite frequency spin transport through the system increases. We find a strong dependence of the finite frequency characteristics both on the anisotropy of the spin chain and the applied magnetic field. We propose a method to measure the finite-frequency conductance in this system

Free-induction decay and envelope modulations in a narrowed nuclear spin bath

We evaluate free-induction decay for the transverse components of a localized electron spin coupled to a bath of nuclear spins via the Fermi contact hyperfine interaction. Our perturbative treatment is valid for special (narrowed) bath initial conditions and when the Zeeman energy of the electron $b$ exceeds the total hyperfine coupling constant $A$: $b>A$. Using one unified and systematic method, we recover previous results reported at short and long times using different techniques. We find a new and unexpected modulation of the free-induction-decay envelope, which is present even for a purely isotropic hyperfine interaction without spin echoes and for a single nuclear species. We give sub-leading corrections to the decoherence rate, and show that, in general, the decoherence rate has a non-monotonic dependence on electron Zeeman splitting, leading to a pronounced maximum. These results illustrate the limitations of methods that make use of leading-order effective Hamiltonians and re-exponentiation of short-time expansions for a strongly-interacting system with non-Markovian (history-dependent) dynamics.Comment: 13 pages, 9 figure

Nonadiabatic Electron Manipulation in Quantum-Dot Arrays

A novel method of coherent manipulation of the electron tunneling in quantum-dots is proposed, which utilizes the quantum interference in nonadiabatic double-crossing of the discrete energy levels. In this method, we need only a smoothly varying gate voltage to manipulate electrons, without a sudden switching-on and off. A systematic design of a smooth gate-pulse is presented with a simple analytic formula to drive the two-level electronic state to essentially arbitrary target state, and numerical simulations for complete transfer of an electron is shown for a coupled double quantum-dots and an array of quantum-dots. Estimation of the manipulation-time shows that the present method can be employed in realistic quantum-dots

Singlet-triplet decoherence due to nuclear spins in a double quantum dot

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 1/2, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law ($\sim 1/t^{3/2}$) when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\pi/4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence, and find that there is an optimal operating point where orbital dephasing becomes negligible.Comment: 12 pages, 4 figure

Nuclear spin state narrowing via gate--controlled Rabi oscillations in a double quantum dot

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $\ket{\uparrow\downarrow}$--state and the $\ket{\downarrow\uparrow}$--state of the two--electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $\ket{\uparrow\downarrow}$--state and to perform a $\sqrt{\mathrm{SWAP}}$ operation with unit fidelity.Comment: v1:9 pages, 1 figure; v2: 13 pages, 2 figures, added section on measurement, to appear in Phys. Rev.