Level Spectrum and Charge Relaxation in a Silicon Double Quantum Dot Probed by Dual-Gate Reflectometry

Abstract

We report on dual-gate reflectometry in a metaloxide-semiconductor double-gate silicon transistor operating at low temperature as a double quantum dot device. The reflectometry setup consists of two radio-frequency resonators respectively connected to the two gate electrodes. By simultaneously measuring their dispersive responses, we obtain the complete charge stability diagram of the device. Electron transitions between the two quantum dots and between each quantum dot and either the source or the drain contact are detected through phase shifts in the reflected radio-frequency signals. At finite bias, reflectometry allows probing charge transitions to excited quantum-dot states, * To whom correspondence should be addressed † Université thereby enabling direct access to the energy level spectra of the quantum dots. Interestingly, we find that in the presence of electron transport across the two dots the reflectometry signatures of interdot transitions display a dip-peak structure containing quantitative information on the charge relaxation rates in the double quantum dot.Keywords: dispersive readout, reflectometry, double quantum dot, charge relaxation, highfrequency resonator, silicon.Integration of charge sensors for the readout of quantum bits (qubits) is one of the necessary ingredients for the realization of scalable semiconductor quantum computers. 1 In most qubits developed so far in silicon, like electron or nuclear spins in quantum dots and single atoms, 2-4 charge 5 or hybrid spin-charge states, 6 qubit readout has been performed with the aid of quantum point contacts (QPCs) or single-electron transistors (SETs). These charge-sensitive devices, however, involve a significant overhead in terms of gates and contact leads, posing an issue for scalability towards many-qubit architectures. Gate-coupled radio-frequency (RF) reflectome-1 arXiv:1610.03657v2 [cond-mat.mes-hall]

Sensitive radiofrequency readout of quantum dots using an ultra-low-noise SQUID amplifier

“…The resulting capacitance difference between the two qubit states can be monitored via a radio-frequency (RF) resonator bonded to one of the quantum dot electrodes. Similar dispersive shifts also occur at charge transitions in the quantum dots, such that the reflected signal assists with tuning to the desired electron occupation [14][15][16]. Dispersive readout has the advantage that it does not require a separate charge sensor, but often the capacitance sensitivity is insufficient for single-shot qubit readout even in systems with a long spin decay time [17][18][19][20][21][22][23].…”

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“…Interdot tunnel coupling results in the formation of molecular bonding (+) and anti-bonding (−) states with energy levels E + and E − , respectively. These states have opposite quantum capacitance since C Q ,± = − α 2 (∂ 2 E ± /∂ ε 2 ) 27 . Here ε is the gate-voltage detuning along a given line crossing the interdot charge transition boundary, and α is a lever-arm parameter relating ε to the energy difference between the electrochemical potentials of the two dots (we estimate α ≃ 0.58 eV V −1 along the detuning line in Fig.…”

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“…The measurement time remains, however, the dominant contribution in the time required to identify transport features. Fast readout techniques such as radiofrequency reflectometry can be used to reduce measurement times [53][54][55][56][57][58] . However, these techniques are better suited to the measurement of small gate voltage windows.…”