Microwave cavities are widely used to control closed few-level systems in the context of quantum information processing. Now, they also appear as a powerful probe for quantum tunneling in hybrid nanocircuits.
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
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.
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.
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).
Among the most exciting recent advances in the field of superconducting quantum circuits is the ability to coherently couple microwave photons in low-loss cavities to quantum electronic conductors. These hybrid quantum systems hold great promise for quantum information-processing applications; even more strikingly, they enable exploration of new physical regimes. Here we study theoretically the new physics emerging when a quantum electronic conductor is exposed to nonclassical microwaves (for example, squeezed states, Fock states). We study this interplay in the experimentally relevant situation where a superconducting microwave cavity is coupled to a conductor in the tunnelling regime. We find that the conductor acts as a nontrivial probe of the microwave state: the emission and absorption of photons by the conductor is characterized by a nonpositive definite quasi-probability distribution, which is related to the Glauber-Sudarshan P-function of quantum optics. These negative quasi-probabilities have a direct influence on the conductance of the conductor.