Session U19: Focus Session: Semiconductor Spin Nanostructures for Quantum Computing

Electron spin decoherence by interacting nuclear spins in quantum dot I: Quantum theory

We present a quantum theory to the electron spin decoherence by a nuclear pair-correlation method for the electron-nuclear spin dynamics under a strong magnetic field and low temperature. The theory incorporates the electron nuclear hyperfine interaction, the intrinsic nuclear interactions, and the nuclear coupling mediated by the hyperfine interaction with the electron in question. Results for both single electron spin free-induction decay (FID) and ensemble electron spin echo will be discussed. Single spin FID is affected by both the intrinsic and the hyperfine-mediated nuclear interactions, with the dominance determined by the dot size and external field. The spin echo eliminates the hyperfine-mediated decoherence but only reduces the decoherence by the intrinsic nuclear interactions. Thus, the decoherence times for FID and spin echo are significantly different. Electron spin decoherence is explained in terms of the quantum entanglement with the pair-flip excitations in the nuclear spin environment. This work was supported by NSF DMR- 0403465, NSA/ARO, and DARPA/AFOSR.   

Electron spin decoherence by interacting nuclear spins in quantum dot II: Coherent control

Due to the hyperfine interaction, the nuclear spins in a quantum dot, driven by nuclear spin pair-wise flip-flops, evolve in different pathways in the Hilbert space for different electron spin states, resulting in the electron-nuclei entanglement and hence the electron spin decoherence. When the electron spin is flipped by a pulse, the nuclear spin states for different electron spin states swap their pathways, and could intersect in the Hilbert space, which disentangles the electron and the nuclei and hence restores the electron spin coherence. The coherence restoration by disentanglement and the conventional spin echo in ensemble dynamics are fundamentally different and generally occur at different time. Pulse sequences can be applied to force the disentanglement to coincide with the spin echo, making the coherence recovery observable in ensemble dynamics. This work was supported by NSF DMR-0403465, NSA/ARO, and DARPA/AFOSR.   

Analytical Solution of Electron Spin Decoherence Through Hyperfine Interaction in a Quantum Dot

We analytically solve the {\it Non-Markovian} single electron spin dynamics due to hyperfine interaction with surrounding nuclei in a quantum dot. We use the equation-of-motion method assisted with a large field expansion, and find that virtual nuclear spin flip-flops mediated by the electron contribute significantly to a complete decoherence of transverse electron spin correlation function. Our results show that a 90\% nuclear polarization can enhance the electron spin $T_2$ time by almost two orders of magnitude. In the long time limit, the electron spin correlation function has a non-exponential $1/t^2$ decay in the presence of both polarized and unpolarized nuclei.   

Quantum dot dynamical Quantum dot dynamical nuclear spin polarization in the

Hyperfine interaction in quantum dots (QD) is qualitatively different than in atoms: coupling of a single electron spin to the otherwise well isolated QD nuclear spins plays a key role in spin-based solid-state quantum information processing. Dynamical nuclear spin polarization (DNSP) is observed by resonant optical pumping of single self-assembled QDs in gated structures that allow deterministic charging with a single excess electron or hole. In the absence of external magnetic fields, the optically polarized electron spin induces an effective inhomogeneous magnetic (Knight) field which determines the direction along which the mesoscopic ensemble of nuclear spins could polarize and enables nuclear spin cooling by surpassing depolarization induced by nuclear dipolar interactions. Due to the effective magnetic (Overhauser) field induced by the polarized nuclei, photoluminescence of these charged trion transitions exhibit spin splitting $\approx 15 \mu eV$ which can be determined by high-spectral-resolution ($<1 \mu eV$) spectroscopy based on a scanning Fabry-Perot interferometer. Our experiments constitute a first step towards a quantum measurement of the Overhauser field, which is in turn predicted to suppress electron spin decoherence in QDs.   

Dynamical nuclear spin polarization in a double quantum dot

The hyperfine interaction between an electron spin confined in a semiconductor quantum dot and the nuclear spins in the surrounding lattice has been identified as one of the main sources for decoherence in low temperature GaAs quantum dots. Recent experiments in gated double dot systems [1] have attempted to utilize the degeneracy point between the two-electron singlet and polarized triplet states to polarize the nuclear spins, thereby reducing their decoherence effects on the electron spins. Here we analyze the dynamics of the system of two electrons and a nuclear spin bath subject to the hyperfine interaction. We consider the effective spin Hamiltonian for the two-electron system, and represent the nuclear spins in the basis of their collective states. The nuclear polarization rates are evaluated for various initial conditions of the nuclear spin system, and optimal conditions for efficient polarization are discussed. [1] J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard, Science 309, 2180 (2005).   

Coherent Control of Entangled Spin Pairs in a CdMnTe Quantum Well.

We used ultrafast light pulses to control the spin state of electrons bound to donors in a CdMnTe quantum well. Previously, we reported on the observation of up to three harmonics of the bound electron spin flip transition indicating that at least three bound electron sites were entangled(J.M. Bao, A.V. Bragas, J.K. Furdyna, R. Merlin, Phys. Rev. B 71 045314 (2005)). Using a pulse shaper, we are now able to suppress all coherent oscillations, but the signal of the first spin flip overtone. Therefore, only entangled electron pairs remain oscillating; all non-entangled donor bound electrons have been restored to their ground state. The quantum state of the remaining entangled electron spins is closely related to the Bell state. This technique holds promise for quantum computing applications.   

Electron-spin quantum computation: Three- and four-body interactions and other implementation challenges

Several leading quantum computer proposals are based upon electron spins. While these designs do potentially satisfy the DiVincenzo criteria, subtle implementation challenges have been uncovered that need to be addressed if these designs are to be realized successfully. In this talk, we start by pointing out that, when several spins are engaged mutually in pairwise interactions, a change can arise in those interactions. In the case of three spins, the quantitative strengths of the interactions can change. For four or more spins, qualitatively new terms can arise in the Hamiltonian, including four-body interactions. Other implementation challenges are also considered, including the difficulty of performing strong projective measurements on solid state qubits (weak measurements are generally more natural to implement but their behavior is more subtle). These issues will need to be handled in quantum computer realizations, either as a source of error to be overcome or as new physics to be exploited.   

Transport of Quantum Information Using Spin Wires

One-dimensional antiferromagnetically coupled spin systems have properties that make them useful as conduits for quantum information$_{ }$(PRL \textbf{90}, 047901 (2003)). Here we investigate possible mechanisms for using engineered spin chains as ``spin wires'' that can faithfully transport qubits. An analysis of the spin chains is carried out through numerical diagonalization of the effective spin Hamiltonian. We find that dimerized chains with a defect can support a highly localized qubit. We also demonstrate how it may be possible to propagate these kinks rapidly through a large system, thus providing a mechanism for producing ``flying'' spin qubits in the solid state.   

GHz Optical Spin Transceiver

The ability to measure spin coherence in semiconductor nanostructures is important for determining the feasibility of spin-based quantum computing architectures. Quantum dots are often referred to as 'solid-state atoms' because of their sharp absorption and emission lines that resemble those of single atoms. Electron spins localized on these quantum dots may be useful for storing quantum information, but their small optical cross section makes detection challenging. In order to take advantage of resonant enhancement of spin detection using the magneto-optical Kerr effect, we have developed a GHz Optical Spin Transceiver (GHOST) which uses a cw optical probe to measure Kerr signals in the time domain with 5 GHz bandwidth. Initial results will be presented for a test sample consisting of n-doped GaAs.   

Photocurrent spectroscopy of self--assembled quantum dots.

Quantum dots systems had been envisioned as possible candidates for building the hardware of quantum computers. They provide the necessary localization of electrons on length scales comparable to the electron Fermi wavelength and also exhibit distinct discrete energy spectra due to quantum confinement. Nevertheless, the characterization of optical and coherence properties of single quantum dots, especially at wavelengths larger than 1100 nm, is challenging due to the small SNR in these systems and the lack of high quantum efficiency detectors at these wavelengths. To circumvent these challenges, we use photocurrent measurements as a probe of the absorption spectra of quantum dots systems embedded in Schottky diode structures. The use of spectrally narrow laser sources allows the exciton absorption spectra of single quantum dots to be characterized as a function of temperature and magnetic field.   

Spin dynamics in coupled core/shell quantum dots

Colloidal nanoparticles provide a flexible system for studying individual quantum-confined electrons and holes. By layering different semiconducting materials in a single nanoparticle, we can create a low bandgap (CdSe) core and surrounding shell, separated by a high bandgap (ZnS) barrier. We have studied spin dynamics in such colloidal heterostructures using two-color time-resolved Faraday rotation (TRFR). By tuning the excitation energy, electron spins can be initialized into different states either in the core or the shell of the nanoparticle. The resulting spin dynamics show a g-factor (spin splitting) that depends on the size of the core or the shell. This g-factor dependence, as well as the spectroscopic dependence of the Faraday effect, allow electron spins in the core or the shell to be addressed independently.   

Spin Manipulation in lateral quantum dots under time-dependent confinement.

Single spin manipulations are a critical component to potential realizations of spintronic devices and quantum computers in lateral quantum dots. In this work, we demonstrate a new method for creating spin excitations in lateral quantum dots which uses the interplay between the spin-orbit interaction and a time-dependent lateral confining potential. For an asymmetric dot in the presence of an in-plane magnetic field, the spin quantization axis can be tilted away from the applied magnetic field due to the Rashba spin-orbit coupling, with the degree of tilting depending parametrically upon the confinement potential. By making small modulations to the confinement potential at a frequency given roughly by the Zeeman splitting, efficient spin excitations can be performed. We have performed theoretical and numerical calculations which demonstrate that Rabi frequencies on the order of tens of megahertz can be achieved for experimentally accessible parameters. Extensions to spin excitations in multi-electron quantum dots will also be presented.   

Effect of photon-assisted tunneling through the leads on spin current polarization in ac-driven quantum dot molecules

A new scheme for realizing spin pumping and spin filtering has been recently proposed using an ac-driven double quantum dot in the Coulomb blockade regime. Using a master equation approach for the density matrix, it was shown$^{1}$ that the spin polarization of the current through the system can be controlled by tuning the parameters (amplitude and frequency) of the ac-field. In the present work we extend our previous model to include photon-assisted tunneling through the contact barriers. This introduces new features in the current due to absorption and emission processes affecting the spin polarization of the current. We discuss these new features, their dependence on the ac-field parameters and the effects on the robustness of the proposed device as a spin pump and spin filter. In particular, we find that the spin filtering property depends strongly on the intensity of the applied ac field. The effect of photoassisted cotunneling on the spin current polarization will also be discussed.$^{ 1}$E.Cota, R. Aguado and G. Platero, Phys. Rev. Lett. \textbf{94}, 107202 (2005)