Spin Digitizer for High-Fidelity Readout of a Cavity-Coupled Silicon Triple Quantum Dot

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Spin Digitizer for High-Fidelity Readout of a Cavity-Coupled Silicon Triple Quantum Dot

F. Borjans, X. Mi, and J.R. Petta

Phys. Rev. Applied 15, 044052 – Published 30 April 2021

Abstract

An important requirement for spin-based quantum information processing is reliable and fast readout of electron spin states, allowing for feedback and error correction. However, common readout techniques often require additional gate structures, hindering device scaling, or impose stringent constraints on the tuning configuration of the sensed quantum dots. Here, we operate an in-line charge sensor within a triple quantum dot, where one of the dots is coupled to a microwave cavity and used to readout the charge states of the other two dots. Owing to the proximity of the charge sensor, we observe a near-digital sensor response with a power signal-to-noise ratio greater than $450$ at an integration time of $t_{int} = 1 μ s$ . Despite small singlet-triplet splittings of approximately 40 $μ eV$ , we further utilize the sensor to measure the spin relaxation time of a singlet-triplet qubit, achieving an average single-shot spin readout fidelity greater than 99%. Our approach enables high-fidelity spin readout, combining minimal device overhead with flexible qubit operation in semiconductor quantum devices.

Received 15 February 2021
Revised 29 March 2021
Accepted 1 April 2021

DOI:https://doi.org/10.1103/PhysRevApplied.15.044052

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Charge Quantum information with solid state qubits Quantum measurements Radio frequency techniques Semiconductor quantum optics

Double quantum dots Semiconductor compounds

Quantum Information, Science & Technology

Authors & Affiliations

F. Borjans , X. Mi^†, and J.R. Petta ^*

Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

^*petta@princeton.edu
^†Present address: Google Inc., Santa Barbara, California 93117, USA.

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Vol. 15, Iss. 4 — April 2021

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Figure 1
Nearly digital charge detection. (a) False-colored scanning electron micrograph of the TQD device. The electric field of the cavity schematically illustrated at the top couples to the device through the CP gate. Three $Al$ gate layers define the TQD confinement potential shown in the bottom cross section through the active area of the device (white dashed line). (b) The cavity transmission amplitude $A / A_{0}$ is gated by the charge dynamics between dot 3 and the drain, $D$ . In Coulomb blockade, the cavity and sensor dot are decoupled leading to a large cavity transmission $A / A_{0}$ (“bright” state). When tunneling between dot 3 and $D$ is permitted ( $μ_{3} = μ_{D}$ ), the charge dynamics lead to dissipation and reduce the cavity transmission $A / A_{0}$ (“dark” state). (c) The amplitude $A / A_{0}$ as a function of $V_{P 2}$ and $V_{P 3}$ , while dot 1 is empty. The uncoupled dot-lead transition for dot 2 is indicated by a dashed line. (d) The amplitude $A / A_{0}$ as a function of $V_{P 3}$ , at $V_{P 2}$ indicated by colored circles in (c). Loading an electron on dot 2 causes a capacitive shift of $μ_{3}$ , resulting in a large voltage shift $Δ V = 2.1 mV$ that can digitally gate the cavity transmission.
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Figure 2
Adaptive sensing of a DQD. (a) Dispersive phase response $Δ ϕ$ as a function of $V_{P 1}$ and $V_{P 2}$ . Interdot transitions between dots 1 and 2 are visible in only a portion of the plot. (b) Charge sensing using dot 3 as a charge sensor and mapping out $Δ V$ over the same range of $V_{P 1}$ and $V_{P 2}$ as in (a). Changes in $N_{1}$ and $N_{2}$ shift $μ_{3}$ due to mutual capacitance, requiring a compensation $α Δ V$ with energy lever arm $α$ to maintain the “dark” state. We refer to this mode of operation as “adaptive sensing.” The blue and green dashed lines indicate qualitative $μ_{3}$ shifts corresponding to the addition of an electron to dot 1 or 2. (c) The cavity transmission amplitude $A / A_{0}$ measured as a function of $V_{P 1}$ and $V_{P 2}$ in the single electron regime without dynamic tracking. (d) Histograms of $A / A_{0}$ acquired at $1 MS/s$ for one second on the $(0, 0, d) - (1, 0, d)$ and $(0, 0, d) - (0, 1, 0)$ transitions. We extract a power SNR = 128 for dot 1 and 471 for dot 2. (e) Time traces of corresponding electron hopping events of less than $10 μ s$ duration.
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Figure 3
Pauli spin blockade in a singlet-triplet qubit. (a) Singlet-triplet energy level diagram near the $(2, 0, d) - (1, 1, 0)$ interdot charge transition with $B$ = 0. For $- Δ_{PSB} < ϵ < 0$ , only singlets access the $(2, 0, d)$ charge ground state. (b) Averaged signal when a continuous rectangular pulse described in (c) is applied across the interdot detuning axis. The brown region near the $(1, 1, 0)$ charge state is due to PSB. A linecut through the data along $ϵ$ (inset) shows the PSB signal as an additional step indicated by the arrows. (c) A continuous train of square pulses is applied to $ϵ$ , inducing charge transitions dependent on the starting position in gate voltage space. Data are signal averages over multiple complete cycles (shaded light red). Four different zones of charge dynamics are observed. Deep in $(2, 0, d)$ and $(1, 1, 0)$ the charge state and corresponding signal is static “dark” (“bright”). For $ϵ < - Δ_{PSB}$ (cross), both spin states can access the $(2, 0, d)$ charge state and charge hops are always observed when pulsing, while for $- Δ_{PSB} < ϵ < 0$ (circle), the charge dynamics are spin dependent, causing a shift in the time-averaged signal.
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Figure 4
Single shot readout using Pauli spin blockade. (a) Pulse sequences used to characterize PSB and extract the spin lifetime $T_{1}$ . Measurements are performed during the shaded intervals of the pulse sequence. (b) Single shot analysis of the PSB region. Averaged $A / A_{0}$ are histogrammed as a function of $V_{P 1}$ , showing charge transitions corresponding to $S (1, 1, 0)$ - $S (2, 0, d)$ and $T (1, 1, 0)$ - $T^{*} (2, 0, d)$ . (c) Normalized triplet probability $P / P_{0}$ as a function of $τ$ . Triplet relaxation is measured at the readout point indicated by the triangle in (b). The time spent at point B is increased and data are acquired as a function of delay time $τ$ , ensemble averaging over $10 000$ shots. (d) Readout fidelity analysis performed using a histogram of $A / A_{0}$ taken from (b) at the white dashed line. The SNR obtained from the histogram combined with $T_{1}$ from (c) yields $F_{avg} = 99.2 %$ , modeled by the black dashed line.
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Figure 5
Optimizing the cavity readout signal. The cavity signal $A / A_{0}$ is shown as a function of gate voltages $V_{P 3}$ and $V_{B 4}$ . The visible reduction in microwave transmission corresponds to the condition $μ_{3} = μ_{D}$ , where the first electron can both be loaded and unloaded from dot 3 via the drain reservoir. We observe a clear minimum of $A / A_{0}$ around $V_{B 4} \approx 265 mV$ , away from which the signal strength decreases monotonically in both directions.
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