We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of cavity quantum electrodynamics could be generalized to many other nanoscale circuits.
We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of cavity quantum electrodynamics could be generalized to many other nanoscale circuits.
This article discusses how to demonstrate the entanglement of the split Cooper pairs produced in a double-quantum-dot based Cooper pair beam splitter (CPS), by performing the microwave spectroscopy of the CPS. More precisely, one can study the dc current response of such a CPS to two on-phase microwave gate irradiations applied to the two CPS dots. Some of the current peaks caused by the microwaves show a strongly nonmonotonic variation with the amplitude of the irradiation applied individually to one dot. This effect is directly due to a subradiance property caused by the coherence of the split pairs. Using realistic parameters, one finds that this effect has a measurable amplitude.
This work discusses theoretically the behavior of a microwave cavity and a Cooper pair beam splitter (CPS) coupled nonresonantly. The cavity frequency pull is modified when the CPS is resonant with a microwave excitation. This provides a direct way to probe the coherence of the Cooper pair splitting process. More precisely, the cavity frequency pull displays an anticrossing whose specificities can be attributed unambiguously to coherent Cooper pair injection. This work illustrates that microwave cavities represent a powerful tool to investigate current transport in complex nanocircuits.
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
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 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).