We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two entities manifests itself via dispersive and dissipative effects observed as frequency shifts and linewidth broadenings of the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation calculation is used to model the combined system response and allows for determining both the coherence properties of the double quantum dot and its interdot tunnel coupling with high accuracy. The value and uncertainty of the tunnel coupling extracted from the microwave read-out technique are compared to a standard quantum point contact charge detection analysis. The two techniques are found to be consistent with a superior precision for the microwave experiment when tunneling rates approach the resonator eigenfrequency. Decoherence properties of the double dot are further investigated as a function of the number of electrons inside the dots. They are found to be similar in the single-electron and many-electron regimes suggesting that the density of the confinement energy spectrum plays a minor role in the decoherence rate of the system under investigation.
We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two entities manifests itself via dispersive and dissipative effects observed as frequency shifts and linewidth broadenings of the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation calculation is used to model the combined system response and allows for determining both the coherence properties of the double quantum dot and its interdot tunnel coupling with high accuracy. The value and uncertainty of the tunnel coupling extracted from the microwave read-out technique are compared to a standard quantum point contact charge detection analysis. The two techniques are found to be consistent with a superior precision for the microwave experiment when tunneling rates approach the resonator eigenfrequency. Decoherence properties of the double dot are further investigated as a function of the number of electrons inside the dots. They are found to be similar in the single-electron and many-electron regimes suggesting that the density of the confinement energy spectrum plays a minor role in the decoherence rate of the system under investigation.
We demonstrate the realization of a hybrid solid-state quantum device, in which a semiconductor double quantum dot is dipole coupled to the microwave field of a superconducting coplanar waveguide resonator. The double dot charge stability diagram extracted from measurements of the amplitude and phase of a microwave tone transmitted through the resonator is in good agreement with that obtained from transport measurements. Both the observed frequency shift and linewidth broadening of the resonator are explained considering the double dot as a charge qubit coupled with a strength of several tens of MHz to the resonator.
As an application in circuit quantum electrodynamics coupled systems, superconducting resonators play an important role in high-sensitivity measurements in a superconducting-semiconductor hybrid architecture. Taking advantage of a high-impedance $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{Ti}\text{\ensuremath{-}}\mathrm{N}$ resonator, we perform excited-state spectroscopy on a GaAs double quantum dot (DQD) by applying voltage pulses to one gate electrode. The pulse train modulates the DQD energy detuning and gives rise to charge state transitions at zero detuning. Benefiting from the outstanding sensitivity of the resonator, we distinguish different spin-state transitions in the energy spectrum according to the Pauli exclusion principle. Furthermore, we experimentally study how the interdot tunneling rate modifies the resonator response. The experimental results are consistent with the simulated spectra based on our model.
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.
We evaluate the charge noise acting on a GaAs/GaAlAs based semiconductor double quantum dot dipole-coupled to the voltage oscillations of a superconducting transmission line resonator. The in-phase (I) and the quadrature (Q) components of the microwave tone transmitted through the resonator are sensitive to charging events in the surrounding environment of the double dot with an optimum sensitivity of 8.5×10−5 e/Hz. A low frequency 1/f type noise spectrum combined with a white noise level of 6.6×10−6 e2/Hz above 1 Hz is extracted, consistent with previous results obtained with quantum point contact charge detectors on similar heterostructures. The slope of the 1/f noise allows to extract a lower bound for the double-dot charge qubit dephasing rate which we compare to the one extracted from a Jaynes-Cummings Hamiltonian approach. The two rates are found to be similar emphasizing that charge noise is the main source of dephasing in our system.
Quantum computing is a powerful way of improving computing efficiency. For some specific problems, quantum processor can exponentially reduce computation time compared to the classical computer. Cavity quantum electrodynamics, which studies the coherent interaction between photons in an optical cavity and atoms or other two-level systems, is of enormous significance to quantum computing and quantum information processing. The strong coupling regime where a cavity photon mode and an atom exchange a single quantum energy coherently has attracted extensive interest in varied experimental platforms and systems such as alkali atoms, Rydberg atoms, large spin ensembles, magnons, etc. The semiconductor gate-defined double quantum dot (DQD) system is one of the most promising platforms that possesses advantages of advanced micro-nano processing technology and outstanding scalability. Introducing the concept of cavity QED into superconducting circuits (circuit QED, cQED), provides an opportunity to study interaction between electrons confined in semiconductor DQD and photons trapped in a superconducting resonator. Reaching strong coupling regime in this hybrid system paves the way to large-scale network of quantum computing. Electrons confined in DQD have large electrical dipoles, thus are able to couple to photons with relatively large coupling rate. Whereas, due to the charge noise and other dissipation channels in the hybrid system, the decoherence rate of the system is larger than the coupling rate, leaving the strong coupling a great challenge. In recent years, different methods have been proposed to access the strong coupling regime. Taking advantage of a high-quality heterojunction structure, an overlapping gate architecture and a low-pass LC filter on the DC bias line, the decoherence of the charge qubit and microwave leakage of the resonator can be effectively suppressed. The coupling strength of the hybrid system can be improved utilizing a high impedance resonator which is comprised of high kinetic inductance materials. Spin, which does not interact directly with the electric field, is insensitive to charge noise and has much longer decoherence time than charge qubit. However, the weak interaction results in a small coupling rate between the spin and the photon. To solve this problem, the method of coherent hybridization between the spin and the charge state is proposed to improve the coupling strength. This hybridization can be achieved by applying a non-uniform magnetic field, utilizing spin-orbit interaction or spin exchange interaction. At present, both charge qubits and spin qubits have achieved strong coupling with the cavity and the coupling distance between long-range qubits is greatly expanded as long as millimeters. This review introduces basic ideas about cQED and fundamental elements in semiconductor cQED systems. Recent progress in strong coupling hybrid system and methods for improving coupling structures are discussed. In future research, more efforts will be devoted into long-range transfer of qubit states and photon-mediated two or multi-qubit gates.
Semiconductor quantum dots in which electrons or holes are isolated via electrostatic potentials generated by surface gates are promising building blocks for semiconductor-based quantum technology.Here, we investigate double-quantum-dot (DQD) charge qubits in GaAs capacitively coupled to highimpedance superconducting quantum interference device array and Josephson-junction array resonators.We tune the strength of the electric-dipole interaction between the qubit and the resonator in situ using surface gates.We characterize the qubit-resonator coupling strength, the qubit decoherence, and the detuning noise affecting the charge qubit for different electrostatic DQD configurations.We find all quantities to be systematically tunable over more than one order of magnitude, resulting in reproducible decoherence rates Γ 2 =2π < 5 MHz in the limit of high interdot capacitance.In the opposite limit, by reducing the interdot capacitance, we increase the DQD electric-dipole strength and, therefore, its coupling to the resonator.Employing a Josephson-junction array resonator with an impedance of approximately 4 kΩ and a resonance frequency of ω r =2π ∼ 5.6 GHz, we observe a coupling strength of g=2π ∼ 630 MHz, demonstrating the possibility to operate electrons hosted in a semiconductor DQD in the ultrastrong-coupling regime (USC).The presented results are essential for further increasing the coherence of quantum-dot-based qubits and investigating USC physics in semiconducting QDs.