We experimentally and theoretically study a driven hybrid circuit quantum electrodynamics (cQED) system beyond the dispersive coupling regime. Treating the cavity as part of the driven system, we develop a theory applicable to such strongly coupled and to multiqubit systems. The fringes measured for a single driven double quantum dot (DQD)-cavity setting and the enlarged splittings of the hybrid Floquet states in the presence of a second DQD are well reproduced with our model. This opens a path to study Floquet states of multiqubit systems with arbitrarily strong coupling and reveals a new perspective for understanding strongly driven hybrid systems.
We experimentally and theoretically study a driven hybrid circuit quantum electrodynamics (cQED) system beyond the dispersive coupling regime. Treating the cavity as part of the driven system, we develop a theory applicable to such strongly coupled and to multiqubit systems. The fringes measured for a single driven double quantum dot (DQD)-cavity setting and the enlarged splittings of the hybrid Floquet states in the presence of a second DQD are well reproduced with our model. This opens a path to study Floquet states of multiqubit systems with arbitrarily strong coupling and reveals a new perspective for understanding strongly driven hybrid systems.
Coupling on-chip microwave cavities to superconducting microcircuits has provided a new platform to study the light/matter interaction at the most elementary level [1]. Coupling such cavities to more complex quantum circuits, like quantum dot circuits, is of high interest since it would allow the use of different degrees of freedom, like for instance the electronic spin, in a cavity quantum electrodynamics context. In this talk, I will present various theoretical proposals which would exploit this possibility. First, I will present a scheme allowing a strong coupling between cavity photons and a single spin trapped in a double quantum dot with ferromagnetic contacts [2]. Such a scheme would enable a scalable spin quantum bit architecture. Second, I will discuss theoretically the coupling of a double-quantum dot based Cooper pair splitter to a cavity [3]. Such a scheme can be used to test the entanglement of split Cooper pairs, due to a subradiance property of the Cooper pairs singlet state. Third, I will present recent experiments on carbon nanotube based quantum dots coupled to microwave cavities. In particular, I will discuss the observation of a charge coupling between two distant quantum dots mediated by cavity photons. [1] A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.- S. Huang, J. Majer, S. Kumar, S.M. Girvin, and R. J. Schoelkopf, Nature (London) 431, 162 (2004). [2] A. Cottet and T. Kontos, Phys. Rev. Lett. 105, 160502 (2010) [3] A. Cottet, T. Kontos, and A. Levy Yeyati, Phys. Rev. Lett. 108, 166803 (2012). [5] M.R. Delbecq, V. Schmitt, F.D. Parmentier, N. Roch, J.J. Viennot, G. Fève, B. Huard, C. Mora, A. Cottet, and T. Kontos, Phys. Rev. Lett. 107,256804 (2011) [6] M.R. Delbecq et al., unpublished
We experimentally investigate a strongly driven GaAs double quantum dot charge qubit weakly coupled to a superconducting microwave resonator. The Floquet states emerging from strong driving are probed by tracing the qubit-resonator resonance condition. In this way, we probe the resonance of a qubit that is driven in an adiabatic, a nonadiabatic, or an intermediate rate, showing distinct quantum features of multiphoton processes and a fringe pattern similar to Landau-Zener-Stückelberg interference. Our resonant detection scheme enables the investigation of novel features when the drive frequency is comparable to the resonator frequency. Models based on the adiabatic approximation, rotating wave approximation, and Floquet theory explain our experimental observations.
Coupling double-quantum-dot circuits to microwave cavities provides a powerful means to control, couple, and manipulate qubits based on the charge or spin of individual electrons. Here, we revisit this standard configuration by adding superconductivity to the circuit. We combine theory and experiment to study a superconductor--double-quantum-dot circuit coupled to microwave cavity photons. First, we use the cavity as a spectroscopic probe. This allows us to determine the low-energy spectrum of the device and to reveal directly Cooper-pair-assisted tunneling between the two dots. Second, we observe a vacuum Rabi splitting which is a signature of strong charge photon coupling and a premiere with carbon-nanotube-based quantum-dot circuits. We show that our circuit design intrinsically combines a set of key features to achieve the strong coupling regime to the cavity. A low charging energy reduces the device sensitivity to charge noise, while sufficient coupling is provided by the shaping of the spectrum of the double quantum dot by the superconducting reservoir. Our findings could be adapted to many other circuit designs and shed light on the coupling of superconducting nanoscale devices to microwave fields.
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.
The recent development of hybrid circuit quantum electrodynamics allows one to study how cavity photons interact with a system driven out of equilibrium by fermionic reservoirs. We study here one of the simplest combination: a double quantum dot coupled to a single mode of the electromagnetic field. We are able to couple resonantly the charge levels of a carbon-nanotube-based double dot to cavity photons. We perform a microwave readout of the charge states of this system, which allows us to unveil features of the out-of-equilibrium charge dynamics, otherwise invisible in the DC current. We extract the relaxation rate, dephasing rate, and photon number of the hybrid system using a theory based on a master equation technique. These findings open the path for manipulating other degrees of freedom, e.g., the spin and/or the valley in nanotube-based double dots using microwave light.
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.