Holonomic Quantum Control by Coherent Optical Excitation in Diamond (2024)

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Holonomic Quantum Control by Coherent Optical Excitation in Diamond

Brian B. Zhou, Paul C. Jerger, V. O. Shkolnikov, F. Joseph Heremans, Guido Burkard, and David D. Awschalom
Phys. Rev. Lett. 119, 140503 – Published 2 October 2017
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    Holonomic Quantum Control by Coherent Optical Excitation in Diamond (2)

    Abstract

    Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.

    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (3)
    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (4)
    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (5)
    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (6)
    • Received 1 May 2017

    DOI:https://doi.org/10.1103/PhysRevLett.119.140503

    © 2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas

    Color centersQuantum controlQuantum gatesQuantum information with solid state qubitsSpintronics

    1. Physical Systems

    Nitrogen vacancy centers in diamond

    1. Techniques

    Coherent control

    General PhysicsCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

    Authors & Affiliations

    Brian B. Zhou1, Paul C. Jerger1, V. O. Shkolnikov2, F. Joseph Heremans1,3, Guido Burkard2, and David D. Awschalom1,3,*

    • 1Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
    • 2Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
    • 3Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
    • *awsch@uchicago.edu

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    Vol. 119, Iss. 14 — 6 October 2017

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    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (11)

      Figure 1

      Experimental system and holonomic concept. (a)Optical NV Λ system. The |±1 spin states of the NV triplet ground state (GS) are linked to |A2 within the spin-orbit excited-state (ES) manifold by a two-tone optical field with one-photon detuning Δ and strength Ω(t). (b)Photoluminescence excitation spectrum taken by scanning a single laser frequency across the GS to ES transitions while two microwave tones mix the population among the three GS levels. (c)Geometric interpretation of the holonomic gates. The dark state |d undergoes trivial dynamics, while the bright state |b undergoes precession around a tilted axis with angle α on the |b/|A2 Bloch sphere. After one nonadiabatic cycle, |b acquires a geometric phase γ proportional to the enclosed solid angle.

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    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (12)

      Figure 2

      Phase shift gates Z(γ). (a)Experimental sequence consisting of state preparation, optical excitation with control parameters (θ, ϕ, Δ/Ω), and state tomography. (b)Time-resolved photoluminescence, proportional to the |A2 population, as a function of detuning Δ, showing oscillations between |b=|+1 and |A2 (θ=0). (c)Measured phase shifts γ, averaged over |x and |y input states, as a function of Δ for Z(γ) at two different optical powers. The solid lines delineate the prediction according to Eq.(2). (d)Gate fidelities via process tomography of the same Z(γ) gates. The solid lines are simulated fidelities incorporating an excited-state lifetime T1 and dephasing Tϕ. (e)Dependence of the fidelity of the resonant gate Z(γ=π) on Ω. The purple, orange, and teal lines represent the simulated fidelities by sequentially adding the effects of T1, Tϕ, and the spectral hopping σΔ.

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    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (13)

      Figure 3

      Resonant holonomic gates. (a)Gates with variable θ after initializing |z. The probabilities of the final states to be measured in |z and |z are plotted. (b)Gates with variable ϕ after initializing |x. The Bloch vector projections of the final states along the x and y axes are plotted. For both (a) and (b), solid lines indicate simulated behaviors with T1 and Tϕ decoherence; the dashed lines in (a)indicate decoherence-free behavior. Decoherence is minimized when the initialized state aligns with the gate’s dark state |d. (c)–(e)Process matrices for X, Y, and H at Ω/2π=168MHz. (f)Dependence of X, Y, H process fidelities on Ω. The solid lines are simulated fidelities incorporating all excited-state decoherence effects. X and Y are identical in the simulation.

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    • Holonomic Quantum Control by Coherent Optical Excitation in Diamond (14)

      Figure 4

      Variable rotations around the x and y axes. (a)After initializing |z, a holonomic gate with variable detuning Δ and a fixed rotation axis along |x is applied. The data show Rabi oscillations between |z and |z as Δ is swept across resonance, tuning the rotation angle γ. The solid lines are simulations with T1 and Tϕ decoherence; the dashed lines are decoherence-free behaviors. (b)–(d) Process matrices for the X(π/2) and Y(±π/2) gates at Ω/2π=152MHz and Δ/2π=±88MHz.

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    Holonomic Quantum Control by Coherent Optical Excitation in Diamond (2024)

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