Reflectometry of charge transitions in a silicon quadruple dot

Abstract

Gate-controlled silicon quantum devices are currently moving from academic proof-of-principle studies to industrial fabrication, while increasing their complexity from single-or double-dot devices to larger arrays. We perform gate-based high-frequency reflectometry measurements on a 2x2 array of silicon quantum dots fabricated entirely using 300-mm foundry processes. Utilizing the capacitive couplings within the dot array, it is sufficient to connect only one gate electrode to one reflectometry resonator and still establish single-electron occupation in each of the four dots and detect singleelectron movements with high bandwidth. A global top-gate electrode adjusts the overall tunneling times, while linear combinations of side-gate voltages yield detailed charge stability diagrams. We support our findings with k•p modeling and electrostatic simulations based on a constant interaction model, and experimentally demonstrate single-shot detection of interdot charge transitions with unity signal-to-noise ratios at bandwidths exceeding 30 kHz. Our techniques may find use in the scaling of few-dot spin-qubit devices to large-scale quantum processors.

Autonomous estimation of high-dimensional Coulomb diamonds from sparse measurements

“…1b inset and Refs. [10,23] for details). Throughout the manuscript, we refer to dot 4 as the sensor dot and consider the other, singlyoccupied dots as qubit dots.…”

“…This signal is amplified (Stanford Research SR560) such that it can trigger the recording of a time stamp, after which the next ramp is started. Sensitivity of V H to state boundaries (charge rearrangements within the 2×2 array) is achieved by operating the sensor dot at degeneracy with its reservoir (tunneling between dot 4 and the reservoir then results in a maximal value of V H ), and by negatively compensating V 4 such that changes applied to V 1,2,3 do not affect the potential of dot 4 [23]. We indicate the presence of this linear V 4 compensation by a negative superscript for the control voltages, V − 1,2,3 .…”

“…For our choice of reflectometry settings, V H is high whenever dot 4 exchanges electrons with its reservoir, and low whenever dot 4 is in Coulomb blockade. Experi-mentally, this is accomplished by wirebonding the reflectometry tank circuit to gate 4 and by accumulating 8-9 electrons in dot 4 such that an enhanced reflectometry signal arises at the charge degeneracy between dot 4 and its reservoir [10,23]. In gate-voltage space, this degeneracy constitutes a particular charge state boundary, which we refer to as the dot-4 facet.…”

“…To explore their high-dimensional facets, raster scans come up short. While charge stability diagrams of double dots are well established [26] and triple dots have been studied by brute-force raster scans [30], the charge stability diagrams of quadruple dots are largely unexplored [23].…”

“…We start with (2) and show that reflectometry, tuned to be sensitive to charge state boundaries in a binary manner, allows sparse measurements triggered by the device itself, rather than the control software, removing the constraint of raster scans and opening up to new algorithmic acquisition procedures. By monitoring a high-bandwidth sensor dot via high-frequency reflectometry in a 2×2 array of silicon quantum dots [10,23], we map a device property of interest (a particular ground state, for example) onto the sensor signal. Gate voltages are ramped in user-defined directions, however, a data point is only acquired when a charge-state boundary is encountered.…”