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Applied Physics Letters

Circuit-QED based time-averaged dispersive readout of a semiconductor charge qubit

Ting Chun Lin, Si‐Si Gu, Yong-Qiang Xu, Shun-Li Jiang, Ning Wang, Bao‐Chuan Wang, Hai-Ou Li, Gang Cao, Guo‐Ping Guo

Published Oct 31, 2022• 4 citations
Publisher

Abstract

Maturing hybrid circuit quantum electrodynamics architectures composed of semiconductor quantum dots and on-chip microwave resonators promise an effective approach for quantum nondemolition readouts in semiconductor systems. Here, we study quantum coherence in a semiconductor charge qubit coupled with a high-impedance resonator. The qubit is controlled by a periodic pulse sequence, and a dispersive measurement is performed by measuring the time-averaged resonator response. From the Rabi oscillation and Ramsey fringe measurements, the coherence time of the charge qubit is determined as T2, Rabi ≈2.7 ns and T2, Ramsey ≈3.5 ns. Compared with the time-resolved (pulsed) measurement, this time-averaged dispersive measurement process eliminates the limitation caused by the resonator response time, enabling a high repetition rate of the pulse sequence in the experiments.

DOI
10.1063/5.0108206

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Maturing hybrid circuit quantum electrodynamics architectures composed of semiconductor quantum dots and on-chip microwave resonators promise an effective approach for quantum nondemolition readouts in semiconductor systems. Here, we study quantum coherence in a semiconductor charge qubit coupled with a high-impedance resonator. The qubit is controlled by a periodic pulse sequence, and a dispersive measurement is performed by measuring the time-averaged resonator response. From the Rabi oscillation and Ramsey fringe measurements, the coherence time of the charge qubit is determined as T2, Rabi ≈2.7 ns and T2, Ramsey ≈3.5 ns. Compared with the time-resolved (pulsed) measurement, this time-averaged dispersive measurement process eliminates the limitation caused by the resonator response time, enabling a high repetition rate of the pulse sequence in the experiments.
Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot charge qubit strongly coupled to a frequency-tunable high-impedance resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state-dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation, and Hahn-echo measurements and find significantly reduced decoherence rates down to γ_{2}/2π∼3 MHz corresponding to coherence times of up to T_{2}∼50 ns for charge states in gate-defined quantum dot qubits. We realize Rabi π pulses of width down to σ∼0.25 ns.
Semiconductor quantum dots in silicon demonstrate exceptionally long spin lifetimes as qubits and are therefore promising candidates for quantum information processing. However, control and readout techniques for these devices have thus far employed low frequency electrons, in contrast to high speed temperature readout techniques used in other qubit architectures, and coupling between multiple quantum dot qubits has not been satisfactorily addressed.This dissertation presents the design and characterization of a semiconductor charge qubit based on double quantum dot in silicon with an integrated microwave resonator for control and readout. The 6 GHz resonator is designed to achieve strong coupling with the quantum dot qubit, allowing the use of circuit QED control and readout techniques which have not previously been applicable to semiconductor qubits. To achieve this coupling, this document demonstrates successful operation of a novel silicon double quantum dot design with a single active metallic layer and a coplanar stripline resonator with a bias tee for dc excitation.Experiments presented here demonstrate quantum localization and measurement of both electrons on the quantum dot and photons in the resonator. Further, it is shown that the resonator-qubit coupling in these devices is sufficient to reach the strong coupling regime of circuit QED. The details of a measurement setup capable of performing simultaneous low noise measurements of the resonator and quantum dot structure are also presented here.The ultimate aim of this research is to integrate the long coherence times observed in electron spins in silicon with the sophisticated readout architectures available in circuit QED based quantum information systems. This would allow superconducting qubits to be coupled directly to semiconductor qubits to create hybrid quantum systems with separate quantum memory and processing components.
The need for fast readout to measure the state of a quantum dot device has important applications in the capabilities of using them as a means for quantum information processing. Traditional charge sensors used to readout the charge state of a quantum dot device are very robust and sensitive electrometers that have been in use since the late 1980s. They pose an issue to the future of quantum dots as a viable means of quantum computing, and that is in their slow acquisition times of the charge state of the quantum dot. This rate of measurement means that implementing any quantum error correction scheme becomes very difficult or even unfeasible as the coherence times of these semiconductor systems is short compared to charge sensor’s acquisition times. A possibility to speed up the measurement process of the charge state is possible thanks to the atomic molecular and optical (AMO) physics community.Cavity quantum electrodynamics (CQED) is the study of light-matter interactions when both the light and matter are taken to be quantized. A photon may interact with an atom via a dipole interaction to excite it from its ground state to its excited state, and the reverse can occur where the atom emits a photon and decays from its excited state ii to the ground state. This fundamental interaction which has been extensively studied in the AMO community since the early 1960s had been adopted by the superconducting qubit community to measure the state of their qubits. These superconducting qubits, representing atoms, which are coupled to a resonant structure on chip, which represents the photons that can interact with the artificial atom. Since these systems were not traditional trapped or neutral atoms interacting with a photon via a laser, but instead planar circuit structures, the superconducting qubit community re-coined the term cavity quantum electrodynamics to circuit quantum electrodynamics, which we will refer to as cQED.The quantum dot community adapted these methods of what is known as dispersive readout; a capacitive change of the atomic like system, results in a dispersive shift which then alters the characteristic frequency response of the resonant structure. This has allowed for a new kind of charge sensor by means of measuring the resonators response due to its coupling to a quantum dot system. This can be done with very high frequency microwave circuitry, allowing much faster readout than is capable via traditional charge sensors. Thus, allowing a pathway to implement quantum error correction schemes with reasonable times compared to any dephasing or decoherence times of the semiconductor system. Furthermore, such fast readout allows for feedback protocols to be implemented to the system to correct for certain undesirable effects due to instruments or the system itself. Our work focuses on a limit of this cQED interaction of the quantum dots to a resonant structure allowing us to do fast readout of the quantum dot charge states via a dispersive shift.The work I will demonstrate in this dissertation will be in the efforts of fast readout on the charge occupation of a double quantum dot system which is galvanically coupled to a superconducting microwave resonator. This was done in a Si/SiGe heterostructure system where I designed, simulated, and fabricated the device which was optimized to have a stronger dispersive shift signal due to an enhanced gate lever arm that couples to the resonator. I will discuss our results of attaining a minimum integration time of 34.54 ns for a unity signal to noise ratio. This demonstrates a fast readout system in the community iii which could be extended to allow for even better readout speeds with faster instruments than what were available to me for the experiment. I will further discuss our characterization of the hybrid system and how we extracted a charge noise due to charging events between the two dots in our system up to around 10 kHz. This work demonstrates a robust dispersive readout scheme which helps in the scalability of hybrid superconducting-semiconducting architectures for means of quantum information processing.
Superconducting resonators coupled to semiconductor quantum dots provide a powerful platform to investigate light-matter interaction and decoherence mechanisms in solid-state quantum systems. Here we study a hybrid circuit quantum electrodynamics architecture consisting of a GaAs double-quantum-dot charge qubit capacitively coupled to a high-impedance, frequency-tunable SQUID-array resonator. By tuning the qubit transition frequency over the range ωq/2π∼3ω_\mathrm{q}/2π\sim 3ωq​/2π∼3-666 GHz, we perform frequency-resolved decoherence spectroscopy of the charge qubit across a broad energy window. Time-resolved measurements enable us to disentangle relaxation and pure dephasing processes and to identify distinct decoherence regimes as a function of qubit frequency. We find that at lower frequencies (≤4.5\leq 4.5≤4.5 GHz) dephasing dominates the qubit linewidth, whereas at higher frequencies energy relaxation becomes the leading contribution. The measured frequency dependence of the relaxation rate exhibits a cubic scaling, consistent with charge-qubit decay dominated by coupling to a piezoelectric phonon bath and providing frequency-resolved access to the corresponding phonon-induced spectral density. Our results show that hybrid semiconductor--superconducting circuits can serve as sensitive spectroscopic tools to probe microscopic decoherence mechanisms relevant for a wide range of hybrid quantum devices.
Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). Typically, semiconductor qubit-qubit coupling is short range, effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle (a few hundred nanometers). This is a significant constraint towards scaling of QD-based architectures to realize dense 1D or 2D arrays of QDs. Inspired by techniques originally developed for circuit QED, we recently demonstrated the strong coupling of individual electrons confined in GaAs quantum dots to individual microwave photons, making use of the enhanced electric component of the vacuum fluctuations of a resonator with impedance beyond the typical 50 Ohm of standard coplanar waveguides. In this hybrid technology, we recently realized a proof of concept experiment, where the coupling between a transmon and a double QD (DQD) is mediated by virtual microwave photon excitations in a high impedance SQUID array resonator, which acts as a quantum bus enabling long-range coupling between dissimilar qubits. Similarly, we achieved coherent coupling between two DQD charge qubits separated by approximately 50 um. In the dispersive regime, we spectroscopically observed qubit-qubit coupling as an avoided-crossing in the energy spectrum of the DQD charge qubits. The methods and techniques developed in this work are transferable to QD devices based on other material systems and can be beneficial for spin based hybrid systems.
Coherent and strong coupling between photons and solid-state qubits, in the form of circuit quantum electrodynamics (QED), has been harnessed for two-qubit gates mediated by photons and high-fidelity quantum non-demolition readout, which are the building blocks of large-scale quantum computation. Recently, circuit QED has been extended to gate-defined semiconductor quantum dots. In this thesis, we develop a novel hybrid circuit QED architecture composed of a high-impedance superconducting microwave resonator and spins localized in silicon-MOS quantum dots. To control and measure the spin degrees of freedom, this hybrid system needs to operate at finite magnetic field. Consequently, we develop and characterize microwave resonators based on thin niobium nitride (NbN) films featuring a high kinetic inductance. We demonstrate high-impedance resonators with magnetic field resilience and low photon loss rates. We then co-integrate the NbN resonators on silicon spin qubit chips. With a hole confined in a double quantum dot (DQD), we report the first realization of a strong hole charge-photon interaction bordering the ultra-strong coupling regime. At finite magnetic field, putting the spin transition energy in resonance with the microwave cavity, we observe large vacuum Rabi mode splittings, signature of a strong spin-photon coupling. Our findings are well captured by the modelling of a hole DQD with different anisotropic Zeeman response in each dot and spin-orbit coupling dependent tunnel rates. We also find a sizeable spin-photon coupling when the hole is localized in the single quantum dot, in line with recent theoretical predictions. The different works presented in this manuscript pave the way for circuit QED with hole spins in gate-defined semiconductor quantum dots.