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International Journal of Modern Physics B

CONTROL OF ELECTRON SPIN DECOHERENCE IN MESOSCOPIC NUCLEAR SPIN BATHS

Ren‐Bao Liu, Wang Yao, Lu Jeu Sham

Published Jan 20, 2008• 1 citation
Publisher

Abstract

The electron spin decoherence by nuclear spins in semiconductor quantum dots is caused by quantum entanglement between the electron and the nuclei. The many-body dynamics problem of the interacting nuclear spins can be solved with the pair-correlation approximation which treats the nuclear spin flip-flops as mutually independent. The nuclear spin dynamics can be controlled by simply flipping the electron spin so that the electron is disentangled from the nuclei and hence its lost coherence is restored.

DOI
10.1142/s0217979208046013

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The electron spin decoherence by nuclear spins in semiconductor quantum dots is caused by quantum entanglement between the electron and the nuclei. The many-body dynamics problem of the interacting nuclear spins can be solved with the pair-correlation approximation which treats the nuclear spin flip-flops as mutually independent. The nuclear spin dynamics can be controlled by simply flipping the electron spin so that the electron is disentangled from the nuclei and hence its lost coherence is restored.
Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of the nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip–flops, as elementary excitations in the mesoscopic bath, can be mapped into the precession of non-interacting pseudo-spins. Such mapping provides a geometrical picture for understanding the decoherence and for devising control schemes. A close examination of nuclear bath dynamics reveals a wealth of phenomena and new possibilities of controlling the electron spin decoherence. For example, when the electron spin is flipped by a π-pulse at τ, its coherence will partially recover at as a consequence of quantum disentanglement from the mesoscopic bath. In contrast to the re-focusing of inhomogeneously broadened phases by conventional spin-echoes, the disentanglement is realized through shepherding quantum evolution of the bath state via control of the quantum object. A concatenated construction of pulse sequences can eliminate the decoherence with arbitrary accuracy, with the nuclear–nuclear spin interaction strength acting as the controlling small parameter.
For a two-state quantum object interacting with a slow mesoscopic interacting spin bath, we show that a many-body solution of the bath dynamics conditioned on the quantum-object state leads to an efficient control scheme to recover the lost quantum-object coherence through disentanglement. We demonstrate the theory with the realistic problem of one electron spin in a bath of many interacting nuclear spins in a semiconductor quantum dot. The spin language can be easily generalized to a quantum object in contact with a bath of interacting multilevel quantum units with the caveat that the bath is mesoscopic and its dynamics is slow compared with the quantum object.
Single electron spin in a semiconductor quantum dot (QD) and single photon wavepacket propagating in an optical waveguide are investigated as carriers of quantum bit (qubit) for information processing. Cavity quantum electrodynamics of the coupled system composed of charged QD, microcavity and waveguide provides a quantum interface for the interplay of stationary spin qubits and flying photon qubits via cavity assisted optical control. This interface forms the basis for a wide range of essential functions of a quantum network, including transferring, swapping, and entangling qubits at distributed quantum nodes as well as a deterministic source and an efficient detector of a single photon wavepacket with arbitrarily specified shape. The cavity assisted optical process also made possible ultrafast initialization and QND readout of the spin qubit in QD. In addition, the strong optical nonlinearity of dot-cavity-waveguide coupled system enables phase gate and entanglement operation for flying single photon qubits in waveguides. The coherence of the electron spin is the wellspring of these quantum applications being investigated. At low temperature and strong magnetic field, the dominant cause of electron spin decoherence is the coupling with the interacting lattice nuclear spins. We present a quantum solution to the coupled dynamics of the electron with the nuclear spin bath. The decoherence is treated in terms of quantum entanglement of the electron with the nuclear pair-flip excitations driven by the various nuclear interactions. A novel nuclear interaction, mediated by virtue spin-flips of the single electron, plays an important role in single spin free-induction decay (FID). The spin echo not only refocuses the dephasing by inhomogeneous broadening in ensemble dynamics but also eliminates the decoherence by electron-mediated nuclear interaction. Thus, the decoherence times for single spin FID and ensemble spin echo are significantly different. The quantum theory of decoherence also leads to a method of coherence recovery of the electron by disentanglement, realized through maneuvering the nuclear bath evolution by control of the electron spin-flip. The studies form the basis to outline the construction of a solid-state quantum network for scalable and distributed processing of quantum information
In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the static Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from superexponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.
We theoretically study the decoherence and the dynamical decoupling control of nitrogen vacancy center electron spins in high-purity diamond, where the hyperfine interaction with 13{}^{13}13C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flip flops. The importance of different elementary processes in the decoherence depends on the strength of the external magnetic field.
The hyperfine coupling of the electronic spins in quantum dots to nuclear spins in the semiconductor host material poses a major challenge, as it can lead to decoherence of the electron spins. In this work, the authors revert the typical approach in which the nuclear spins are considered as an environment for the electronic spin, but rather rather view the nuclear spins as the quantum system coupled to an electronic environment with an exceptional degree of tunability. They show that nuclear spin bath could be turned from the dominant source of decoherence into a useful resource for manipulating an electron spin qubit.