Collective Quantum Memory Activated by a Driven Central Spin

Emil V. Denning, Dorian A. Gangloff, Mete Atatüre, Jesper Mørk, and Claire Le Gall

Phys. Rev. Lett. 123, 140502 – Published 2 October 2019

Abstract

Coupling a qubit coherently to an ensemble is the basis for collective quantum memories. A single driven electron in a quantum dot can deterministically excite low-energy collective modes of a nuclear spin ensemble in the presence of lattice strain. We propose to gate a quantum state transfer between this central electron and these low-energy excitations—spin waves—in the presence of a strong magnetic field, where the nuclear coherence time is long. We develop a microscopic theory capable of calculating the exact time evolution of the strained electron-nuclear system. With this, we evaluate the operation of quantum state storage and show that fidelities up to 90% can be reached with a modest nuclear polarization of only 50%. These findings demonstrate that strain-enabled nuclear spin waves are a highly suitable candidate for quantum memory.

Received 11 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.140502

Physics Subject Headings (PhySH)

Coherent control Hybrid quantum systems Nuclear & electron resonance Optical quantum information processing Quantum computation Quantum control Quantum information with solid state qubits Quantum memories Quantum optics with artificial atoms Quantum state transfer Semiconductor quantum optics

General PhysicsAtomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Emil V. Denning ^1,2, Dorian A. Gangloff², Mete Atatüre², Jesper Mørk¹, and Claire Le Gall^2,*

¹Department of Photonics Engineering, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
²Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom

^*cl538@cam.ac.uk

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Vol. 123, Iss. 14 — 4 October 2019

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Images

Figure 1
(a) System schematic comprising a pulse-driven electron coupled to a mesoscopic bath of nuclear spins. (b) Structure of the high-spin ( $I > 1 / 2$ ) nuclei, here shown for $I = 3 / 2$ . (c) Spin transitions between states in (b) generated by the noncollinear processes $Φ_{1}^{\pm}$ and $Φ_{2}^{\pm}$ . (d) In the memory write-in process, the stimulated electron–nuclear interaction flips the electron and generates a nuclear spin wave conditionally on the electron spin, thereby transferring the electron state to the nuclear ensemble. Here, the time-evolution operator, $U = e^{- i H_{I} π / (2 g_{ζ})}$ , corresponds to the evolution in Eq. (2) at time $t = π / (2 g_{ζ})$ .
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Figure 2
(a) Collective spin wave excitation starting from a fully polarized state, where all nuclei are in the ground state (gray dots). The black circles emphasize the nuclei that have exchanged energy with the electron. The spin wave contains a single nuclear excitation (blue dots) distributed among all of the nuclei in a superposition. (b) Spin wave excitation from finitely polarized nuclear product state $| M ⟩$ to target state $| {\hat{M}}_{+}^{(1)} ⟩$ , where initially excited nuclei allow leakage transitions, respectively, to orthogonal states $| {\hat{M}}_{-}^{(1)} ⟩$ and $| {\hat{M}}_{+}^{(2)} ⟩$ . (c) Coupling structure in 1D mapping of nuclear state space. The initial state is a superposition of the two green states, and interactions couple these initial states to a 1D structure of states. Double lines signify the fast coupling rate $G_{+}$ , and single lines the slow rate, $G_{-}$ . For a fully polarized ensemble $G_{-} = 0$ and the three upper states remain isolated; at finite polarization, this subspace is coupled to the residual chain of states, $R$ . (d)–(e) Dynamics for initialization in electron states $| ↑ ⟩$ and $| ↓ ⟩$ , respectively. Solid lines signify the fully polarized case, where $G_{-} = 0$ . Lines with decreased opacity signify decreased polarization and thus an increased $G_{-}$ rate, with the maximal value $G_{-} / G_{+} = 0.3$ . Line colors correspond to states in panel (c).
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Figure 3
(a) Leakage factor as ratio of coupling rates, $G_{-} / G_{+}$ as a function of nuclear polarization. Green solid (blue dotted) lines denote $ζ = 2$ ( $ζ = 1$ ). (b) Coupling rate $G_{+}$ for $ζ = 1$ (blue dotted) and $ζ = 2$ (green solid) at $P = 0.5$ for varying nuclear Zeeman splitting. The shaded area corresponds to the range of values from $P = 0$ to $P = 1$ . (c) Transfer fidelity of total write-in and readout cycle as a function of polarization. (d) Transfer fidelity of total write-in and readout cycle at full polarization ( $P = 1$ ) as a function of inhomogeneity in quadrupolar energy shift.
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