We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functions even with moderate electronic relaxation and dephasing in the quantum dots. We provide detailed estimates for the electrical current and output power using realistic parameters. Introduction.-Hybrid quantum systems that couple electronic transport in nano-scale conductors to photons in microwave cavities are currently going through a remarkable and rapid development. Several recent experiments have demonstrated controllable coupling of quantum dots to the fundamental mode of a microwave cavity [1][2][3][4][5][6][7][8][9]. These experimental advances are now paving the way for a broad spectrum of applications, ranging from hybrid quantum information processing [10] and Cooper pair splitters [11] to on-chip micro-masers [12] and quantum dot lasers [13]. The ability to indirectly couple mesoscopic conductors over macroscopic distances via a microwave cavity [6], serving as a robust quantum bus for quantized energy and information flow, opens several intriguing avenues for the use of non-local electronic correlations mediated by cavity photons [14][15][16][17][18][19].

Recent experimental progress in coupling nanoscale conductors to superconducting microwave cavities has opened up for transport investigations of the deep quantum limit of light-matter interactions, with tunneling electrons strongly coupled to individual cavity photons. We have investigated theoretically the most basic cavity-conductor system with strong, single photon induced non-local transport effects; two spatially separated double quantum dots (DQD:s) resonantly coupled to the fundamental cavity mode. The system, described by a generalized Tavis-Cummings model, is investigated within a quantum master equation formalism, allowing us to account for both the electronic transport properties through the DQD:s as well as the coherent, non-equilibrium cavity photon state. We find sizeable non-locally induced current and current cross-correlations mediated by individual photons. From a full statistical description of the electron transport we further reveal a dynamical channel blockade in one DQD lifted by photon emission due to tunneling through the other DQD. Moreover, large entanglement between the orbital states of electrons in the two DQD:s is found for small DQD-lead temperatures.

We investigate theoretically the properties of the photon state and the electronic transport in a system consisting of a metallic quantum dot strongly coupled to a superconducting microwave transmission line cavity. Within the framework of circuit quantum electrodynamics we derive a Hamiltonian for arbitrary strong capacitive coupling between the dot and the cavity. The dynamics of the system is described by a quantum master equation, accounting for the electronic transport as well as the coherent, non-equilibrium properties of the photon state. The photon state is investigated, focusing on, for a single active mode, signatures of microwave polaron formation and the effects of a non-equilibrium photon distribution. For two active photon modes, intra mode conversion and polaron coherences are investigated. For the electronic transport, electrical current and noise through the dot and the influence of the photon state on the transport properties are at the focus. We identify clear transport signatures due to the non-equilibrium photon population, in particular the emergence of superpoissonian shot-noise at ultrastrong dot-cavity couplings.

Abstract. We investigate the second-order von Neumann approach from a diagrammatic point-of-view and demonstrate its equivalence with the resonant tunneling approximation. Investigation of higher-order diagrams shows that the method correctly reproduces the equation of motion for the single-particle reduced density matrix of an arbitrary non-interacting many-body system. This explains why the method reproduces the current exactly for such systems. We go on to show, however, that diagrams not included in the method are needed to calculate exactly higher cumulants of the charge transport. This thorough comparison sheds light on the validity of all these self consistent second-order approaches. We analyze the discrepancy between the noise calculated by our method and the exact Levitov formula for a simple non-interacting quantum dot model. Furthermore we study the noise of the canyon of current suppression in a two-level dot, a phenomenon that requires the inclusion of electron-electron interaction as well as higher-order tunneling processes.

We study the production of spatially separated entangled electrons in ferromagnetic leads from Cooper pairs in a superconducting lead. We give a complete description of the elementary charge transfer processes, i) transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasiparticles among the ferromagnetic leads, in terms of their statistics. The probabilities that entangled electrons flow into spatially separated leads are completely determined by experimentally measurable conductances and polarizations. Finally, we investigate how currents, noise and cross correlations are affected by transport of entangled electrons. [2,3,4,5]. One of the challenges is to prevent processes where pairs of entangled particles reach the same lead, i.e. are not spatially separated. Electrons from Cooper pairs are entangled in spin and energy space, and separation of pairs into different leads using ferromagnets or quantum dots has been suggested [3]. Upon filtering, only the spin or energy part of the two-particle wave function collapses, depending on whether ferromagnets or quantum dots are used. Respectively, energy or spin entanglement remains [4]. Here we consider separation by ferromagnets.Solid state entanglers have been analyzed in Refs. [2,3,4,5] in terms of currents, noise and cross correlations. A more direct approach, describing the elementary charge transfer processes in terms of experimentally controllable parameters is certainly desirable. We demonstrate how this is possible through the full distribution of current fluctuations, the full counting statistics (FCS), of the solid state entangler [6,7,8]. The FCS provides complete information about currents, noise, cross correlations and higher cumulants, and even more importantly, allows direct access to the probability for transfer of charge between different parts of the device.We consider the singlet superconductor-ferromagnet (S-F) device shown in Fig. 1. A normal metal cavity (c) is connected to one superconducting terminal and several ferromagnetic terminals via tunnel junctions. The cavity is under the influence of proximity effect. In this device, charge transport occurs via two processes: i) Transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasi- particles among the ferromagnetic leads. The distribution can occur via Direct Andreev (DA) reflection, where a entangled pair is transferred into lead F n or crossed Andreev reflection (CA), where each particle of the entangled pair is transferred into spatially separated leads F m and F n (n = m). CA produces spatially separated entangled electrons. Since the ferromagnetic terminals are at the same voltage and we consider zero temperature, there is no direct electron transport between the ferromagnetic terminals [9].Our general results for the counting statistics show that the processes i) and ii) are independent and therefore the statistics can be factorized. This novel factorization and the probab...

Recent experiments on nanoscale conductors coupled to microwave cavities put in prospect transport investigations of electron-photon interplay in the deep quantum regime. Here we propose a pump-probe scheme to investigate the transient dynamics of individual electron-photon excitations in a double quantum dot-cavity system. Excitations pumped into the system decay via charge tunneling at the double dot, probed in real time. We investigate theoretically the short-time charge transfer statistics at the dot, for periodic pumping, and show that this gives access to vacuum Rabi oscillations as well as excitation dynamics in the presence of double dot dephasing and relaxation.

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