Gate-controlled unitary operation on flying spin qubits in quantum Hall edge states

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Gate-controlled unitary operation on flying spin qubits in quantum Hall edge states

Takase Shimizu, Taketomo Nakamura, Yoshiaki Hashimoto, Akira Endo, and Shingo Katsumoto

Phys. Rev. B 102, 235302 – Published 16 December 2020

Abstract

The spin and orbital freedoms of electrons traveling on spin-resolved quantum Hall edge states (quantum Hall ferromagnets) are maximally entangled. The unitary operations on these two freedoms are hence equivalent, which means that one can manipulate the spins with nonmagnetic methods through the orbitals. Taking the quantization axis of the spins along the magnetization axis, the zenith angle is determined by the partition rate of spin-separated edges, while the azimuth angle is defined as the phase difference between the edges. Utilizing these properties, we have realized an electrically controlled unitary operation on the electron spins on quantum Hall ferromagnets. The zenith angle of the spin was controlled through the radius of gyration at a corner by applying voltage to a thin gate placed at one edge. The subsequent rotation in the azimuth angle was controlled via the distance between the edge channels also by a gate voltage. The combination of the two operations constitutes a systematic electric operation on spins in quantum Hall edge channels.

Received 7 October 2020
Revised 30 November 2020
Accepted 1 December 2020

DOI:https://doi.org/10.1103/PhysRevB.102.235302

Physics Subject Headings (PhySH)

Integer quantum Hall effect Quantum information with solid state qubits Spin-orbit coupling Spintronics

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Takase Shimizu ^*, Taketomo Nakamura , Yoshiaki Hashimoto, Akira Endo , and Shingo Katsumoto

Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan

^*takase@issp.u-tokyo.ac.jp

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Issue

Vol. 102, Iss. 23 — 15 December 2020

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Images

Figure 1
(a) Schematic diagram of the “quantum circuit” for electron wave packets (red and blue circles with arrows indicating spin), with an illustration of the Bloch sphere description of an FSQ. (b) Optical micrograph of the sample with an external circuit illustration. The orange regions are metallic gates, three of which are annotated. The 2DES substrate is trimmed at the white dashed lines. (c) illustrates the hybridization of (a) and (b) around the lower ends of the gate SL, C, and SR.
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Figure 2
(a) $V_{C}$ dependence of the current distribution ratio $D$ at $B = 4.84 T$ . Side gate voltages were set to $V_{SR} = V_{SL} = - 0.6 V$ , where the 2DES under the gates was completely depleted. (b) Calculation example of $D$ as a function of $V_{C}$ based on the model of Eq. (7). $d = 66$ nm from the one-dimensional Poisson-Schrödinger calculation on the layered structure of the sample (see the Supplemental Material [33]). Other parameters are as follows: $g = - 0.6$ [19]; $ε = 12.35$ [34]; $C_{1} sin (θ) = 0.05$ , $C_{0} = 0.53$ , $Δ ϕ = 0$ , $L_{C} = 7.5 μ m$ ; $L_{SL} = L_{SR} = 1.25 μ m$ ; the offset in the gate voltage $V_{C}$ , $V_{SL}$ , and $V_{SR}$ resulting from the contact built-in potential is $V_{offset} = - 0.05 V$ . See the text for $n (y)$ .
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Figure 3
(a) Current partition rate $D$ as a function of $B$ within the plateau regime encompassing the filling factor $ν = 4$ for several values of gate C voltage $V_{C}$ (traces are offset for clarity). $V_{ac} = 32.8 {μ V}_{rms}$ . (b) $Δ y$ calculated from the equation $Δ y = (2 / 3) (h / e) / L Δ B$ for $V_{C} = - 0.86 V$ . $Δ B$ is given by twice the distance between the adjacent oscillation peak and dip. The blue line indicates $Δ y_{average} = [Δ y (V_{SL}) L_{SL} + Δ y (V_{C}) L_{C} + Δ y (V_{SR}) L_{SR}] / (L_{SL} + L_{C} + L_{SR})$ from Eq. (7) with the parameters used in Fig. 2.
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Figure 4
(a) Color plot of the measured $D$ as a function of $B$ and $V_{C}$ . $V_{SR} = V_{SL} = - 0.6 V$ . (b) Color plot of the theoretically given $D$ as a function of $B$ and $V_{C}$ . $C_{0} = 0.42 B - 1.45$ and $C_{1} sin (θ) = 0.1$ are used. The other parameters are the same as those in Fig. 2.
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Figure 5
Three oscillation patterns corresponding to three different values of $V_{SR}$ . $B = 4.5 T$ and $V_{SL} = - 0.605 V$ . $V_{ac} = 23.8 μ V_{rms}$ . The line for $D = 0.57$ is indicated by dashed lines to show that there is almost no movement in the oscillation baseline.
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Figure 6
(a) Schematic time evolution of quasieigenenergies $E_{↑} = 〈 ↑ | 〈 1 | H_{loc} (t) | 1 〉 | ↑ 〉$ and $E_{↓} = 〈 ↓ | 〈 2 | H_{loc} (t) | 2 〉 | ↓ 〉$ . (b) Illustration of spin-polarized edge states for a straight edge (solid and dashed lines) and a corner (dotted lines). $ξ$ represents the distance from an edge of infinite potential $[V (0) = \infty]$ . For simplicity, the Landau levels are drawn in the single-electron picture.
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