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arXiv:cond-mat/0406478 · IEEE Transactions on Nanotechnology

Decoherence of Nuclear Spin Quantum Memory in a Quantum Dot

C. Deng, Xuan Hu

Published Jan 1, 2005• 7 citations
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Abstract

Recently, an ensemble of nuclear spins in a quantum dot have been proposed as a long-lived quantum memory. A quantum state of an electron spin in the dot can be faithfully transfered into nuclear spins through controlled hyperfine coupling. Here we study the decoherence of this memory due to nuclear spin dipolar coupling and inhomogeneous hyperfine interaction during the storage period. We calculated the maximum fidelity of writing, storing, and reading operations. Our results show that nuclear spin dynamics can severely limit the performance of the proposed device for quantum information processing and storage based on nuclear spins.

DOI
10.1109/tnano.2004.840149

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Recently, an ensemble of nuclear spins in a quantum dot have been proposed as a long-lived quantum memory. A quantum state of an electron spin in the dot can be faithfully transfered into nuclear spins through controlled hyperfine coupling. Here we study the decoherence of this memory due to nuclear spin dipolar coupling and inhomogeneous hyperfine interaction during the storage period. We calculated the maximum fidelity of writing, storing, and reading operations. Our results show that nuclear spin dynamics can severely limit the performance of the proposed device for quantum information processing and storage based on nuclear spins.
We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant, it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of nonperfect initial spin polarization and inhomogeneous hyperfine coupling are discussed.
The decoherence and fidelity of spin states in a localized single-electron quantum dot in the presence of a dc magnetic field, arising either from the nuclear hyperfine interaction within the dot or due to its coupling with another localized quantum dot, are examined in detail. A general framework for determining the time evolution of the reduced density matrix. for a single dot is presented, which is exact up to the second order in interaction with any reservoir. In particular, it is applied to the problem of nuclear hyperfine coupling, and approximate estimates of coherence decay time are made when the nuclear spins are either polarized or unpolarized and the internal dynamics of nuclear spins is determined mainly by the nuclear magnetic dipole-dipole interaction. The fidelity of a pure unperturbed electronic one-qubit spin state is obtained as a function of time, which is exact even on a very short timescale of logic gate operations. The time variation of the fidelity of the same one-qubit state on the localized dot as a part of the direct product with another one-qubit state on another localized dot arising because of coupling between these quantum dots is also calculated in this paper. In this case, we include both the single-particle tunnelling between the dots as well as the direct and exchange Coulomb interactions, including on-site Coulomb repulsion. This allows for the double occupation of a single dot. It is found that the loss of fidelity of such two-qubit states due to double occupancy and additional phase errors in the presence of appreciable dot-dot coupling can become a more severe limiting factor than that due to the hyperfine interaction in individual dots.
States with long coherence are a crucial requirement for qubits and quantum memories. Nuclear spins in epitaxial GaAs/AlGaAs quantum dots are a great candidate, offering excellent isolation from external environments and on-demand coupling to optical flying qubits. However, coherence times are limited to ≲ 1 ms by the dipole-dipole interactions between the nuclei and by the nuclear quadrupolar coupling to inhomogeneous crystal strain. Here, we combine strain engineering of the nuclear spin ensemble and tailored dynamical decoupling sequences to achieve nuclear spin coherence times exceeding 100 ms. Recently, a reversible transfer of quantum information into nuclear spin ensembles has been demonstrated in quantum dots: our results provide a path to develop this concept into a functioning solid-state quantum memory suitable for quantum repeaters in optical quantum communication networks.
The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the upper cutoff frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the total width of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling.
Nuclear spins in quantum dots are promising candidates for fast and scalable quantum memory. By utilizing the hyperfine interaction between the central electron and its surrounding nuclei, quantum information can be transferred to the collective state of the nuclei and stored for a long time. However, nuclear spin fluctuations in a partially polarized nuclear bath degrade the quantum memory fidelity. Here, we introduce a noise-resistant protocol to realize fast and high-fidelity quantum memory through Hamiltonian engineering. With analytics and numerics, we show that a high-fidelity quantum state transfer between the electron and the nuclear spins is achievable at relatively low nuclear polarizations, due to the strong suppression of nuclear spin noises. For a realistic quantum dot with 104{10}^{4}104 nuclear spins, a fidelity surpassing 80% is possible at a polarization as low as 30%. Our approach reduces the demand for high nuclear polarization, making experimentally realizing quantum memory in quantum dots more feasible.
We numerically investigate the encoding and retrieval processes for quantum memory realized in a semiconductor quantum dot by focusing on the effect of inhomogeneously polarized nuclear spins whose polarization depends on the local hyperfine coupling strength. We find that the performance of quantum memory is significantly improved by inhomogeneous nuclear polarization, as compared with homogeneous nuclear polarization. Moreover, the narrower the nuclear polarization distribution is, the better is the performance of the quantum memory. We ascribe the improvement in performance to the full harnessing of the highly polarized and strongly coupled nuclear spins by carefully studying the entropy change of individual nuclear spins during the encoding process. Our results shed light on the implementation of quantum memory in a quantum dot.