Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion–boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.
Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion–boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.
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
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 propose theoretically a scheme for implementing a spin quantum bit in a quantum dot circuit with ferromagnetic leads. This setup does not rely on any specific band structure and can therefore be realized with many different types of nanoconductors. In this talk, we will discuss its implementation with carbon nanotubes. We can reach the strong coupling limit between the electron spin and a superconducting photon cavity, with experimentally realistic parameters compatible with a slow enough decoherence of the spin quantum state. This allows us to envision the use of circuit cavity quantum electrodynamics methods for single spin manipulation and readout.
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.
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]. The recent generalization of this architecture to more complex open nanocircuits [2,3,4] offers the possibility to go beyond standard cavity quantum electrodynamics experiments usually performed with closed two level systems. A wide variety of experiments can be envisioned, with different types of hybrid nanocircuits combining nanoconductors such as carbon nanotubes or semiconducting nanowires, and metallic electrodes made out from normal metals, superconductors, or ferromagnets. Circuit Quantum Electrodynamics represents a promising method to gain more information on the behavior of electrons in these hybrid nanocircuits. In the first part of this talk, I will discuss the coupling of a Cooper pair splitter to a cavity [5,6]. I will show that a measurement of the cavity dispersive shift provides a rich access to the electronic spectroscopy and dynamics in the Cooper pair splitter [7]. In the second part of this talk, I will discuss the coupling of Majorana quasiparticles (in a semiconducting nanowire) to a cavity [8]. These exotic bound states can cause a significant cavity frequency shift and a strong cavity nonlinearity leading for instance to light squeezing. I will show that the dependence of these effects on the nanowire gate voltages should give direct signatures of the unique properties of Majorana fermions, such as their self-adjoint character and their exponential confinement. References [1] A., Wallraff et al., Nature 431, 162 (2004). [2] M.R. Delbecq et al., Phys. Rev. Lett. 107, 256804 (2011). [3] T. Frey et al., Phys. Rev. Lett. 108, 046807 (2012). [4] K.D. Petersson et al., Nature 490, 380 (2012). [5] A. Cottet, T. Kontos, A. Levy Yeyati, Phys. Rev. Lett. 108, 166803 (2012). [6] A. Cottet, Phys. Rev. B 86, 075107 (2012). [7] A. Cottet et al., in preparation. [8] A. Cottet, T. Kontos, and B. Douçot, arXiv:1307.4185 (2013).