Radio-Frequency Reflectometry in Silicon-Based Quantum Dots
Y. Y. Liu, Stephan G. J. Philips, Lucas Orona, Nodar Samkharadze, Thomas McJunkin, E. R. MacQuarrie, M. A. Eriksson, Lieven M. K. Vandersypen, Amir Yacoby
Radio-frequency (rf) reflectometry offers a fast and sensitive method for charge sensing and spin readout in gated quantum dots. We focus in this work on the implementation of rf readout in accumulation-mode gate-defined quantum dots, where the large parasitic capacitance poses a challenge. We describe and test two methods for mitigating the effect of the parasitic capacitance, one by on-chip modifications and a second by off-chip changes. We demonstrate that on-chip modifications enable high-performance charge readout in $\mathrm{Si}$/${\mathrm{Si}}_{x}$${\mathrm{Ge}}_{1\ensuremath{-}x}$ quantum dots, achieving a fidelity of 99.9% for a measurement time of $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$.
Radio-frequency (rf) reflectometry offers a fast and sensitive method for charge sensing and spin readout in gated quantum dots. We focus in this work on the implementation of rf readout in accumulation-mode gate-defined quantum dots, where the large parasitic capacitance poses a challenge. We describe and test two methods for mitigating the effect of the parasitic capacitance, one by on-chip modifications and a second by off-chip changes. We demonstrate that on-chip modifications enable high-performance charge readout in Si/{\mathrm{Si}}_{x}$${\mathrm{Ge}}_{1\ensuremath{-}x} quantum dots, achieving a fidelity of 99.9% for a measurement time of 1\ensuremathμs.
This thesis focuses on implementing radio frequency (rf) reflectometry techniques for dispersive detection of charge and spin dynamics in nanoscale devices. I have investigated three aspects of rf reflectometry using state-of-the-art silicon (Si) complementary metal-oxide-semiconductor (CMOS) nanowire field effect transistors (NWFETs). First, a high-sensitivity capacitive gate-based charge sensor is developed by optimising the external matching circuit to detect capacitive changes in the high frequency resonator. A new circuit topology is used where superconducting niobium nitride (NbN) inductor is connected in parallel with a single-gate Si NWFET resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, I have achieved a charge sensitivity of 7.7 μe/Hz and, when operating at 616 MHz, I get 1.3 μe/Hz. This gate-based sensor can be used for fast, accurate and scalable techniques for quantum state readout in Si CMOS based quantum computing. Second, this new circuit topology for the resonator is used with a dual-gate Si NWFET. This dual-gate device geometry provides access to a double quantum dot (DQD) system in few electron regime. The spin-state of the two-electron DQD system is detected dispersively using Pauli spin blockade between joint singlet S(2,0) and triplet T−(1,1) states in a finite magnetic field B. The singlet-triplet relaxation time T1 at B=4.5~T is measured to be $\sim$1 ms using standard homodyne detection technique. Third, I expand the range of applications of gate-based sensing to accurate temperature measurements. I have experimentally demonstrated a primary thermometer by embedding a single-gate Si NWFET with the rf capacitive gate-based sensor. The thermometer, termed as gate-based electron thermometer (GET), relies on cyclic electron tunneling between discrete energy levels of a quantum dot and a single electron reservoir in the NWFET. I have found that the full-width-half-maximum (FWHM) of the resonator phase response depends linearly with temperature via well known physical law by using the ratio kB/e between the Boltzmann constant and the electron charge. The GET is also found to be magnetic field independent like other primary thermometers such as Coulomb blockade and shot noise thermometers.
Radio-frequency (RF) reflectometry is widely used for high-bandwidth readout of semiconductor quantum devices at cryogenic temperatures, but its application has mainly been limited to nanoscale structures with relatively small capacitances. Here, we investigate RF readout in a different regime by applying gate-based reflectometry to a large-area silicon carbide transistor with parasitic capacitances orders of magnitude larger than those of typical quantum devices, conditions normally expected to hinder RF readout. We observe a gate-dependent RF response which degrades and eventually vanishes as temperature is lowered, although MOSFET operation in DC transport is maintained down to deep cryogenic temperatures. We attribute this behaviour to impedance changes introduced by carrier freeze-out in the transistor drift region, and propose a modified circuit configuration designed to restore sensitivity under these conditions. These results establish how parasitic pathways and device geometry can limit RF readout, providing insight into the design of scalable cryogenic-CMOS quantum systems.
Sensitive charge detection has enabled qubit readout in solid-state systems. Recently, an alternative to the well-established charge detection via on-chip electrometers has emerged, based on in situ gate detectors and radio-frequency dispersive readout techniques. This approach promises to facilitate scalability by removing the need for additional device components devoted to sensing. Here, we perform gate-based dispersive readout of an accumulation-mode silicon quantum dot. We observe that the response of an accumulation-mode gate detector is significantly affected by its bias voltage, particularly if this exceeds the threshold for electron accumulation. We discuss and explain these results in light of the competing capacitive contributions to the dispersive response.
Sensitive charge detection has enabled qubit readout in solid-state systems. Recently, an alternative to the well-established charge detection via on-chip electrometers has emerged, based on in situ gate detectors and radio-frequency dispersive readout techniques. This approach promises to facilitate scalability by removing the need for additional device components devoted to sensing. Here, we perform gate-based dispersive readout of an accumulation-mode silicon quantum dot. We observe that the response of an accumulation-mode gate detector is significantly affected by its bias voltage, particularly if this exceeds the threshold for electron accumulation. We discuss and explain these results in light of the competing capacitive contributions to the dispersive response.
Frequency-multiplexed radio-frequency (RF) reflectometry is a promising technique for large-scale quantum dot-based qubit systems because it enables simultaneous readout of multiple qubits and helps to reduce the wiring density in peripheral circuits. However, in the conventional L-C-type matching circuits, resonator frequency tunability is limited by poor design flexibility of the shunt capacitance and hence the circuit. Recently, L-L-type matching circuits comprising a series and a shunt inductor have been proposed to address this issue. Here, we report RF reflectometry readout of silicon quantum dot-based charge sensors embedded in L-L-type circuits. We determine the inductance values for target resonance frequencies based on our equivalent circuit model that incorporates the parasitic elements of the inductors and demonstrate resonator frequency tunability of up to 1 GHz with 3-dB resonator bandwidths on the order of MHz. The measured conductance sensitivities, on the order of 10−5(e2/h)/Hz at 4 K, are only moderately dependent on the resonance frequency up to 630 MHz. These results highlight the prospects of L-L-type matching circuits for rapid and multiplex reflectometry readout of semiconductor spin qubits.
This paper reports on the extraction of the equivalent circuit model parameters of a physically defined silicon quantum dot at a cryogenic temperature and design of the impedance matching circuits to improve the performance of a charge sensor for radio-frequency (RF) reflectometry. The I-V characteristics and the S-parameters of the quantum dot device are measured around a Coulomb peak at 4.2 K. The measured results are modeled by an RC parallel circuit, and the model parameters for the quantum dot device were obtained. We consider three impedance matching circuits for RF reflectometry of a quantum dot: shunt capacitor-series inductor type, shunt inductor-series capacitor type, and shunt inductor-series inductor-type. We formulate and compare the sensitivity and bandwidth of RF reflectometry for the three types of circuits. The analysis should be useful for selecting the optimal matching circuit and the circuit parameters for given equivalent circuit parameters and working frequency. This procedure is demonstrated for a quantum dot with the characterized model circuit along with simulated performance. This design technique of matching circuit for RF reflectometry can be applied to any device that can be represented by an RC parallel circuit. These results will facilitate to realize fast semiconductor qubit readout in various quantum dot platforms.