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.
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.
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
This thesis investigates experimentally the coupling mechanism of the charge and spin degrees of freedom in double quantum dots to high finesse superconducting microwave cavities. We use carbon nanotubes as a coherent conductor to host our quantum dots.We conceived an experimental setup and developed new fabrication methods in order to achieve control over these devices. With these methods, we scrutinize the resonant coupling of the dot's charge electronic transitions to a microwave cavity. We drive the system out of equilibrium to characterise its dynamics and extract its relevant intrinsic parameters. We examine a possible coupling of single photons to a single electron spin, using non-collinear exchange fields induced from ferromagnetic interfaces as a key ingredient to engineer this coupling. The preliminary results in this circuit architecture are promising for future spin-based QED experiments with single spins.
Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
Coupling on-chip microwave cavities to superconducting microcircuits has provided a new platform to study the light/matter interaction at the most elementary level. Generalizing such a coupling 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 aspects of the effect of a double quantum dot on cavity photons. I will discuss the case of normal, ferromagnetic and superconducting reservoirs. In particular, the coupling of a Cooper pair splitter with cavity photons will be discussed
We present our recent experiments where we demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic ¯eld. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube dot using a dispersive readout in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits. We extend our architecture to two quantum dot circuits in a microwave cavity. These circuits are separated by 200 times their own size, but share the same anti-node of the cavity ¯eld. We demonstrate their interaction mediated by the cavity photons.
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.