Single-Shot Spin Readout in Graphene Quantum Dots

Electrostatically defined quantum dots in bilayer graphene offer a promising platform for spin qubits with presumably long coherence times due to low spin-orbit coupling and low nuclear spin density. We demonstrate two different experimental approaches to measure the decay times of excited states. The first is based on direct current measurements through the quantum device. Pulse sequences are applied to control the occupation of ground and excited states. We observe a lower bound for the excited state decay on the order of a hundred microseconds. The second approach employs a capacitively coupled charge sensor to study the time dynamics of the excited state using the Elzerman technique. We perform single-shot readout of our two-level system with a signal-to-noise ratio of about 7 and find relaxation times up to 50 ms for the spin-excited state, with a strong magnetic field dependence, promising even higher values for smaller magnetic fields. This is an important step for developing a quantum-information processor in graphene.

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The coherence of a spin qubit depends primarily on the material that houses the charge carriers and with it the spins. In order to obtain information about a spin we use a time-periodic shift of the energy levels in the quantum dot which changes the transport properties depending on the spin state, hence allowing spin-to-charge conversion. With this approach we determine the spin-excited state relaxation time $T_1$ in bilayer graphene which is a measure of the coherence of the spin qubit. We first investigate the relaxation time using pulsed-gate spectroscopy and measure the current flowing through a quantum dot, which allows us to extract a lower bound for the spin decay time only. In order to study the time dynamics of the excited state for time larger than microseconds, we add a charge detector to the device design and perform time-resolved measurements of the tunneling events in the quantum dots. This allows us to perform single-shot readout of the two-level system using the Elzerman technique. We measure spin-relaxation times up to 50 ms at a perpendicular magnetic field of 1.7 T. We find a strong dependence of $T_1$ on the external magnetic field, promising even higher values for smaller spin-splitting. The spin-relaxation time presented in this paper is a few orders of magnitude longer than typical spin-qubit operation times and competes very well with other group IV elements, like silicon. In a next step towards spin qubits the spin dephasing time $T_2$ needs to be determined.

Figure 1

(a) False-color micrograph of the device. The plunger gate (green) is controlled with dc voltage ($V_{\mathrm{PG}}$) and ac pulses ($V_{\mathrm{ac}}$) combined by a bias tee. The black squares with crosses inside symbolize Ohmic contacts. (b) The ac pulse sequence consists of a read phase with pulse level $V_R=-V_A$ and duration $t_R$ and an unload phase with pulse level $V_U=V_A$ and duration $t_U$. (c) Coulomb diamond of the first hole transition taken at $B_{\perp }=1.75\mathrm{T}$. For large source-drain voltage $V_{SD}$ the excited-state resonance can be observed. (d) In-plane magnetic field dependence at fixed plunger gate voltage, corresponding to green horizontal dashed line in (c). The splitting of the GS and the ES at high magnetic field is consistent with a spin $g$ factor of 2. (e) Schematic of transport through ${|\uparrow ⟩}_R$ and ${|\downarrow ⟩}_R$ during read phase and through ${|\uparrow ⟩}_U$ during unload phase. For ease of understanding an electronlike level scheme is used, while hole states are probed in the experiment. (f) Coulomb resonance as a function of pulse amplitude at pulse frequency $f=1.25\mathrm{MHz}$. $V_A=0\mathrm{V}$ corresponds to a line cut along the orange vertical dashed line in (c) at $V_{SD}=40\mu \mathrm{eV}$. For finite pulse amplitudes $V_A$, the transition $|\uparrow ⟩$ splits into two branches, ${|\uparrow ⟩}_R$ and ${|\uparrow ⟩}_U$, due to the two-level pulsing. For pulse amplitudes $e{\alpha }_{\mathrm{att}}{\alpha }_{\mathrm{PG}}{V}_A>E_Z$, see orange arrow, transport through the ES is allowed by the pulse during the read phase and shows up as ${|\downarrow ⟩}_R$ in between the GS peaks.

Figure 2

(a) Four-level pulse scheme for relaxation-time measurements. The hole enters a random state during the load phase. If the hole is loaded into the GS it will stay there and no transport current can flow. If the carrier is loaded into the ES and does not relax during $t_L+t_W$, the charge carrier can tunnel out, resulting in a transport current in the read phase. The QD is then emptied in the unload phase and the cycle is repeated. (b) Current as a function of plunger gate voltage while applying the four-level pulse. We observe various peaks corresponding to GS and ES levels of different pulse phases being aligned with the bias window. This measurement is taken in a second cooldown at a $B_{\perp }=1.9\mathrm{T}$, leading to a slight shift of $V_{\mathrm{PG}}$. (c) Current corresponding to ES transport during the read phase [shaded in green in (b)] as a function of loading and waiting time. We vary the waiting time while the loading time remains constant at $t_L=1\mu \mathrm{s}$. The decay results from a combination of lower cycling rate and ES relaxation time. As described in the main text the decay is dominated by signal decay. (d) Normalized average number of charge carriers per pulse cycle. Dashed color lines represent the decays with the corresponding relaxation time. Our result indicates that relaxation does not play a significant role during the measurement window.

Figure 3

(a) False-color micrograph of a single QD device with a nearby charge detector. The QD is formed beneath the plunger gate (green) in channel 2. TL and TR serve as tunnel barriers (yellow) to the leads. Another QD is formed under one finger gate (purple) in channel 1 and used as a charge detector. The black squares with crosses inside symbolize Ohmic contacts. (b) Three-level pulse scheme applied to the plunger gate. (c) Probability of the QD being occupied as a function of time and plunger gate dc voltage $V_{\mathrm{PG}}$ extracted from 500 single-shot traces. (d) Exemplary traces for different read levels. Top: ideal read-level configuration allowing for single-shot ES-selective readout. Middle: GS level is aligned with $E_F$ corresponding to multiple tunneling events. Bottom: both the ES and GS level are pushed above $E_F$ during the read phase, which results in a single tunneling-out event.

Figure 4

(a) Histogram of maximum detector voltage values during the read phase. The histogram is fitted with two skewed Gaussians with ${\gamma }_{\mathrm{GS}}=-1.7$, ${\mu }_{\mathrm{GS}}=-1.4\mu \mathrm{V}$, ${\sigma }_{\mathrm{GS}}=-0.27\mu \mathrm{V}$ and ${\gamma }_{\mathrm{ES}}=2.76$, ${\mu }_{\mathrm{ES}}=2.3\mu \mathrm{V}$, ${\sigma }_{\mathrm{ES}}=-0.6\mu \mathrm{V}$. (b) Number of blips observed during read phase as a function of loading time. The relaxation time is extracted from the exponential decay. (c) Magnetic field dependence of the relaxation rate $1/T_1$. Data points for one magnetic field correspond to statistically independent measurements.