We use a quantum path-integral approach to describe the behavior of a microwave cavity coupled to a dissipative mesoscopic circuit. We integrate out the mesoscopic electronic degrees of freedom to obtain a cavity effective action at fourth order in the light/matter coupling. By studying the structure of this action, we establish sufficient conditions in which the cavity dynamics can be described with a Lindblad equation. This equation depends on effective parameters set by electronic correlation functions. It reveals that the mesoscopic circuit induces an effective Kerr interaction and two-photon dissipative processes. We use our method to study the effective dynamics of a cavity coupled to a double quantum dot with normal metal reservoirs. If the cavity is driven at twice its frequency, the double-dot circuit generates photonic squeezing and nonclassicalities visible in the cavity Wigner function. In particular, we find a counterintuitive situation where mesoscopic dissipation enables the production of photonic Schr\"odinger cats. These effects can occur for realistic circuit parameters. Our method can be generalized straightforwardly to more complex circuit geometries with, for instance, multiple quantum dots and other types of fermionic reservoirs such as superconductors and ferromagnets.
We use a quantum path-integral approach to describe the behavior of a microwave cavity coupled to a dissipative mesoscopic circuit. We integrate out the mesoscopic electronic degrees of freedom to obtain a cavity effective action at fourth order in the light/matter coupling. By studying the structure of this action, we establish sufficient conditions in which the cavity dynamics can be described with a Lindblad equation. This equation depends on effective parameters set by electronic correlation functions. It reveals that the mesoscopic circuit induces an effective Kerr interaction and two-photon dissipative processes. We use our method to study the effective dynamics of a cavity coupled to a double quantum dot with normal metal reservoirs. If the cavity is driven at twice its frequency, the double-dot circuit generates photonic squeezing and nonclassicalities visible in the cavity Wigner function. In particular, we find a counterintuitive situation where mesoscopic dissipation enables the production of photonic Schr"odinger cats. These effects can occur for realistic circuit parameters. Our method can be generalized straightforwardly to more complex circuit geometries with, for instance, multiple quantum dots and other types of fermionic reservoirs such as superconductors and ferromagnets.
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
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.
Superconducting circuits provide an architecture upon which cavity quantum electrodynamics (QED) can be implemented at microwave frequencies in a highly tunable environment. Known as circuit QED, these systems can achieve larger nonlinearities, stronger coupling and greater controllability than can be achieved in cavity QED, all in a customisable, solid state device, making this technology an exciting test bed for both quantum optics and quantum information processing. These new parameter regimes open up new avenues for quantum technology, while also allowing older quantum optics results to finally be tested. In particular is is now possible to experimentally produce nonclassical states, such as squeezed and Schr\\"odinger cat states, relatively simply in these devices. Using open quantum systems methods, in this thesis we investigate four problems which involve the use of nonclassical states in circuit QED. First we investigate the effects of a Kerr nonlinearity on the ability to preserve transported squeezed states in a superconducting cavity, and whether this setup permits us to generate, and perform tomography, of a highly squeezed field using a qubit, with possible applications in the characterisation of sources of squeezed microwaves. Second, we present a novel scheme for the amplification of cat states using a coupled qubit and external microwave drives, inspired by the stimulated Raman adiabatic passage. This scheme differs from similar techniques in circuit QED in that it is deterministic and therefore compatible with a protocol for stabilising cat states without the need for complex dissipation engineering. Next we use solutions of Fokker-Planck equations to study the exact steady-state response of two nonlinear systems: a transmon qubit coupled to a readout resonator, where we find good agreement with experiments and see simultaneous bistability of the cavity and transmon; and a parametrically driven nonlinear resonator, where we compare the classical and quantum phases of the system and discuss applications in the generation of squeezed states and stabilisation of cat states. Finally, we investigate the use of two different types of superconducting qubits in a single experiment, seeing that this enables engineering of the self- and cross-Kerr effects in a line of cavities. This could provide a valuable means of entangling cavity states, in addition to a resource for quantum simulation.
This manuscript summarizes my research activities devoted to the study of nonequilibrium phenomena in mesoscopic superconducting and semiconducting circuits. The work develops along two directions: the dynamics of metallic Josephson junctions driven out of equilibrium and the interaction between electrons and microwave photons in mesoscopic quantum circuits.The first part investigates diffusive superconductor–normal metal–superconductor Josephson junctions subjected to strong perturbations such as microwave irradiation or stochastic injection of high-energy quasiparticles. These experiments reveal how nonequilibrium excitations modify the Andreev spectrum and the phase dynamics of the junction. The second part addresses electron–photon coupling in mesoscopic circuits across different interaction regimes. Early work focused on semiconductor double quantum dots coupled to low-impedance microwave cavities in the weak coupling regime. Later work involved the fabrication and characterization of high-kineticinductance superconducting materials, allowing the realization of high-impedance resonators and stronger light-matter coupling. Finally, a superconducting tunnel junction coupled to a high-impedance granular aluminum cavity allowed bath engineering based on photo-assisted quasiparticle tunneling, efficient photon-toelectron conversion, and continuous single microwave photon detection.
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
The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.