Coherence of a dynamically decoupled quantum-dot hole spin

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Coherence of a dynamically decoupled quantum-dot hole spin

L. Huthmacher, R. Stockill, E. Clarke, M. Hugues, C. Le Gall, and M. Atatüre

Phys. Rev. B 97, 241413(R) – Published 28 June 2018

Abstract

A heavy hole confined to an InGaAs quantum dot promises the union of a stable spin and optical coherence to form a near perfect, high-bandwidth spin-photon interface. Despite theoretical predictions and encouraging preliminary measurements, the dynamic processes determining the coherence of the hole spin are yet to be understood. Here, we establish the regimes that allow for a highly coherent hole spin in these systems, recovering a crossover from hyperfine to electrical-noise dominated decoherence with a few-Tesla external magnetic field. Dynamic decoupling allows us to reach the longest ground-state coherence time, $T_{2}$ , of $4.0 \pm 0.2 μ s$ , observed in this system. The improvement of coherence we measure is quantitatively supported by an independent analysis of the local electrical environment.

Received 24 November 2017
Revised 16 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.241413

Physics Subject Headings (PhySH)

Light-matter interaction Optical transient phenomena Quantum coherence & coherence measures Quantum control Quantum optics Quantum optics with artificial atoms Semiconductor quantum optics

Quantum dots

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

L. Huthmacher¹, R. Stockill¹, E. Clarke², M. Hugues³, C. Le Gall¹, and M. Atatüre^1,*

¹Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
²EPSRC National Centre for III-V Technologies, University of Sheffield, Sheffield S1 3JD, United Kingdom
³Université Côte d'Azur, CNRS, CRHEA, Valbonne, France

^*ma424@cam.ac.uk

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Vol. 97, Iss. 24 — 15 June 2018

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Images

Figure 1
Measurement of magnetic-field-dependent inhomogeneous dephasing time, $T_{2}^{*}$ . (a) Sample geometry featuring the optical axis (orange arrow) and the magnetic field (black arrow). (b) Energy-level diagram of the positively charged QD. (c) Schematic of the Ramsey pulse sequence. (d) Visibility of Ramsey fringes measured at external magnetic fields $B_{x}^{ext}$ of $2 T$ (orange), $4 T$ (purple), and $6.5 T$ (light blue). Error bars represent $\pm 1$ standard deviation. Solid curves are fits to the data to extract $T_{2}^{*}$ . (e) Summary of magnetic-field-dependent measurement of $T_{2}^{*}$ ; data points from panels (d) are presented in the corresponding color and error bars represent $\pm 1$ standard deviation. Gray dotted curve shows decay $\propto 1 / B_{ext}$ for $B_{x}^{ext} > 4 T$ .
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Figure 2
Hahn-echo measurement for different values of $B_{x}^{ext}$ . (a) Visibility of the Hahn-echo signal for $B_{x}^{ext}$ of 1 T (orange), 3 T (purple), 5 T (light blue), and 8 T (green). The data have been normalized to account for pulse imperfections. Error bars represent $\pm 1$ standard deviation. Solid curves are fits to extract $T_{2}^{HE}$ ; for $B_{x}^{ext} = 1 T$ the solid curve only serves as guide to the eye. The inset shows a schematic of the Hahn-echo pulse sequence. (b),(c) Zoom-in for the 1 and 2 T data, revealing a sharp drop and revival of coherence within the first 300 ns. (d) Full behavior of $T_{2}^{HE}$ with respect to $B_{x}^{ext}$ ; values are extracted from the fits for $B_{x}^{ext} \geq 3 T$ and error bars represent $\pm 1$ standard deviation. For $B_{x}^{ext} \leq 2 T$ we show the time where the visibility falls below $1 / e$ for the first time.
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Figure 3
Normalized autocorrelation function of the neutral exciton intensity fluctuations. (a) Extracted autocorrelation function of intensity fluctuations measured on the neutral exciton transition (solid blue circles) at low resonant excitation power (the excited state population was $1 / 20$ ). The orange curve represents a fit to the data containing four exponential functions as well as a $1 / Δ t^{1 - λ}$ component. The gray curve represents only the contribution of the exponential functions. The inset is an illustration of how electrical noise leads to intensity fluctuations, responsible for the bunching of the autocorrelation function. (b) Residuals of the two curves presented in (a), highlighting the strong deviation of the gray curve from the data for $Δ t < 1 ms$ .
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Figure 4
Dynamic decoupling of the hole spin. (a) Visibility for dynamic decoupling at $B_{x}^{ext} = 5 T$ as a function of the number of $π$ pulses, where $N_{π}$ is 1 (orange), 3 (purple), 5 (light blue), and 9 (green). The inset shows a schematic of the employed pulse sequence. Solid curves represent fits to the data to extract the coherence time and error bars are given by $\pm 1$ standard deviation. The data was normalized for the fits to intercept a visibility of 1 at zero delay, factoring out the reduced visibility due to finite pulse fidelity. (b) Scaling of the coherence time with the number of $π$ pulses; data presented in (a) shown in matching color. Gray curve presents a fit of $T_{2}^{HE} {(N_{π})}^{γ}$ to the data, extracted scaling $γ = 0.325 \pm 0.005$ . Error bars represent $\pm 1$ standard deviation.
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