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arXiv:cond-mat/0604634 · Physical Review Letters

Restoring Coherence Lost to a Slow Interacting Mesoscopic Spin Bath

Wang Yao, Ren‐Bao Liu, Lu Jeu Sham

Published Feb 12, 2007• 163 citations
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Abstract

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.

DOI
10.1103/physrevlett.98.077602

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Publisher’s Note: Restoring Coherence Lost to a Slow Interacting Mesoscopic Spin Bath [Phys. Rev. Lett. 98, 077602 (2007)]

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Received 16 February 2007DOI:https://doi.org/10.1103/PhysRevLett.98.099901©2007 American Physical Society

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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.
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.
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.
We present a unified description of cooling and manipulation of a mesoscopic bath of nuclear spins via coupling to a single quantum system of electronic spin (quantum bit). We show that a bath cooled by the quantum bit rapidly saturates. Although the resulting saturated states of the spin bath ("dark states") generally have low degrees of polarization and purity, their symmetry properties make them a valuable resource for the coherent manipulation of quantum bits. Specifically, we demonstrate that the dark states of nuclear ensembles can be used to coherently control the system-bath interaction and to provide a robust, long-lived quantum memory for qubit states.
Decoherence of a quantum system arising from its interaction with an environment is a key concept for understanding the transition between the quantum and classical world as well as performance limitations in quantum technology applications. The effects of large, weakly coupled environments are often described as a classical, fluctuating field whose dynamics is unaffected by the qubit, whereas a fully quantum description still implies some backaction from the qubit on the environment. Here we show direct experimental evidence for such a backaction for an electron-spin qubit in a GaAs quantum dot coupled to a mesoscopic environment of order 10^{6} nuclear spins. By means of a correlation measurement technique, we detect the backaction of a single qubit-environment interaction whose duration is comparable to the qubit's coherence time, even in such a large system. We repeatedly let the qubit interact with the spin bath and measure its state. Between such cycles, the qubit is reinitialized to different states. The correlations of the measurement outcomes are strongly affected by the intermediate qubit state, which reveals the action of a single electron spin on the nuclear spins.