L. G. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, C. Strunk
We report on conductance measurements in carbon nanotube based double quantum dots connected to two normal electrodes and a central superconducting finger. By operating our devices as beam splitters, we provide evidence for Crossed Andreev Reflections \textit{tunable in situ}. This opens an avenue to more sophisticated quantum optics-like experiments with spin entangled electrons.
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Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through the Bell inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and doe…
We analyze microscopically a Cooper pair splitting device in which a central superconducting lead is connected to two weakly coupled normal leads through a carbon nanotube. We determine the splitting efficiency at resonance in terms of geometrical and material parameters, including the effect of spin-orbit scattering. While the efficiency in the linear regime is limited to 50% and decay exponentially as a function of the width of the superconducting region we show that it can rise up to $\sim 100%$ in the non-linear regime for certain regions of the stability diagram.
Electron waiting times are an important concept in the analysis of quantum transport in nano-scale conductors. Here we show that the statistics of electron waiting times can be used to characterize Cooper pair splitters that create spatially separated spin-entangled electrons. A short waiting time between electrons tunneling into different leads is associated with the fast emission of a split Cooper pair, while long waiting times are governed by the slow injection of Cooper pairs from a superconductor. Experimentally, the waiting time distributions can be measured using real-time single-electr…
Quantum transport in Cooper pair splitters using hierarchical equations of motion
研究超越弱耦合和马尔可夫极限的库珀对分裂器电荷输运，采用运动方程分层法，计算不同条件下电流，结果与测量电流定量一致，还能解释热电效应，为描述非平衡量子输运提供有用框架。
Carbon nanotube as quantum point contact valley-filter and valley-splitter
本文通过紧束缚输运计算表明，弹性应变可使扶手椅型单壁碳纳米管成为谷滤波器与谷分束器，并利用量子化电导平台产生极化谷电流、分离两类 K 电子。
A Cooper pair splitter consists of two quantum dots side-coupled to a conventional superconductor. Usually, the quantum dots are assumed to have a large charging energy compared to the superconducting gap, in order to suppress processes other than the coherent splitting of Cooper pairs. In this work, in contrast, we investigate the limit in which the charging energy is smaller than the superconducting gap. This allows us, in particular, to study the effect of a Zeeman field comparable to the charging energy. We find analytically that in this parameter regime the superconductor mediates an inte…
We develop the Bardeen-Cooper-Schrieffer (BCS) formalism for the superconductivity of carbon nanotubes. It is found that the superconducting transition temperature Tc of single-wall carbon nanotubes decreases exponentially with the increase of the tube diameter because the density of states near the Fermi energy is inversely proportional to the tube diameter. For the multi-wall carbon nanotubes, the Cooper paring hopping between layers enhances the superconducting correlation and increases the superconducting transition temperature, which is consistent with the experimental observation.
Motivated by the recent experiments [Scientific reports 6, 23051 (2016), Phys. Rev. Lett. 114, 096602 (2015)], we theoretically investigate Cooper pair splitting current in a graphene based Cooper pair beam splitter geometry. By considering the graphene based superconductor as an entangler device, instead of normal (2D) BCS superconductor, we show that the Cooper pair splitting current mediated by Crossed Andreev process is amplified compared to its normal superconductor counterpart. This amplification is attributed to the strong suppression of local normal Andreev reflection process (arising …
We analyze a model of double quantum dot Cooper pair splitter coupled to two ferromagnetic detectors, and demonstrate the possibility of determination of spin correlation by current measurements. We use perturbation theory taking account of the exchange interaction with the detectors, which leads to complex spin dynamics in the dots. This affects the measured spin and restricts the use of ferromagnetic detectors to the nonlinear current-voltage characteristic regime at current plateau, where the relevant spin projection is conserved, in contrast to the linear current-voltage characteristic reg…
We study adiabatic pumping through a double quantum dot coupled to normal and superconducting leads. For this purpose a perturbation expansion in the tunnel coupling between the dots and the normal leads is performed and processes underlying the pumping current are discussed. Features of crossed Andreev reflection are investigated in the average pumped charge and related to local Andreev reflection in a single quantum dot. In order to distinguish Cooper pair splitting from quasi-particle pumping, we compare the properties of Cooper pair pumping with single-electron pumping in a system with onl…
We investigate the current cross-correlations in a double quantum dot based Cooper pair splitter coupled to one superconducting and two ferromagnetic electrodes. The analysis is performed by assuming a weak coupling between the double dot and ferromagnetic leads, while the coupling to the superconductor is arbitrary. Employing the perturbative real-time diagrammatic technique, we study the Andreev transport properties of the device, focusing on the Andreev current cross-correlations, for various parameters of the model, both in the linear and nonlinear response regimes. Depending on parameters…
Entangled Photon-Pair Emission in Waveguide Circuit QED from a Cooper Pair Splitter
理论上研究了由双量子点构成的Cooper对分离器在波导电路QED架构下的纠缠光子对发射，揭示了其源于Andreev束缚态的频率纠缠机制，并验证了方案在现有技术下的可行性。
Cooper pair splitters are promising candidates for generating spin-entangled electrons. However, the splitting of Cooper pairs is a random and noisy process, which hinders further synchronized operations on the entangled electrons. To circumvent this problem, we here propose and analyze a dynamic Cooper pair splitter that produces a noiseless and regular flow of spin-entangled electrons. The Cooper pair splitter is based on a superconductor coupled to quantum dots, whose energy levels are tuned in and out of resonance to control the splitting process. We identify the optimal operating conditio…
New generation of Cooper pair splitters defined on hybrid nanostructures are devices with high tunable coupling parameters. Transport measurements through these devices revealed clear signatures of interference effects and motivated us to introduce a new model, called the 3-sites model. These devices provide an ideal playground to tune the Cooper pair splitting (CPS) efficency on demand, and displays a rich variety of physical phenomena. In the present work we analyze theoretically the conductance of the 3-sites model in the linear and non-linear regimes and characterize the most representativ…
We consider a double quantum dot coupled to two normal leads and one superconducting lead, modeling the Cooper pair beam splitter studied in two recent experiments. Starting from a microscopic Hamiltonian we derive a general expression for the branching current and the noise crossed correlations in terms of single and two-particle Green's function of the dot electrons. We then study numerically how these quantities depend on the energy configuration of the dots and the presence of direct tunneling between them, isolating the various processes which come into play. In absence of direct tunnelin…
We investigate Andreev transport through a quantum dot attached to two external ferromagnetic leads and one superconducting electrode. The transport properties of the system are studied by means of the real-time diagrammatic technique in the sequential tunneling regime. To distinguish various contributions to Andreev current we calculate the current cross-correlations, i.e. correlations between currents flowing through two junctions with normal leads. We analyze dependence of current cross-correlations on various parameters of the considered model, both in linear and nonlinear transport regime…
Cooper pair splitting (CPS) is a process in which the electrons of naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three - site model, which sho…
We propose an approach allowing the computation of currents and their correlations in interacting multiterminal mesoscopic systems involving quantum dots coupled to normal and/or superconducting leads. The formalism relies on the expression of branching currents and noise crossed correlations in terms of one- and two-particle Green's functions for the dots electrons, which are then evaluated self-consistently within a conserving approximation. We then apply this to the Cooper-pair beam-splitter setup recently proposed [L. Hofstetter et al. Nature (London) 461 960 (2009); Phys. Rev. Lett. 107 1…
We theoretically study the spin-resolved subgap transport properties of a Cooper pair splitter based on a triple quantum dot attached to superconducting and ferromagnetic leads. Using the Keldysh Green's function formalism, we analyze the dependence of the Andreev conductance, Cooper pair splitting efficiency, and tunnel magnetoresistance on the gate and bias voltages applied to the system. We show that the system's transport properties are strongly affected by spin dependence of tunneling processes and quantum interference between different local and nonlocal Andreev reflections. We also stud…
We report an experimental study of Cooper pair splitting in an encapsulated graphene based multiterminal junction in the ballistic transport regime. Our device consists of two transverse junctions, namely the superconductor/graphene/superconductor and the normal metal/graphene/normal metal junctions. In this case, the electronic transport through one junction can be tuned by an applied bias along the other. We observe clear signatures of Cooper pair splitting in the local as well as nonlocal electronic transport measurements. Our experimental data can be very well described by using a modified…
We demonstrate high efficiency Cooper pair splitting in a graphene-based device. We utilize a true Y-shape design effectively placing the splitting channels closer together: graphene is used as the central superconducting electrode as well as QD output channels, unlike previous designs where a conventional superconductor was used with tunnel barriers to the quantum dots (QD) of a different material. Superconductivity in graphene is induced via the proximity effect, thus resulting in both a large measured superconducting gap $Δ=0.5$meV, and a long coherence length $ξ=200$nm. The graphene-graphe…
The quantum entanglement between two qubits is crucial for applications in the quantum communication. After the entanglement of photons was experimentally realized, much effort has been taken to exploit the entangled electrons in solid-state systems. Here, we propose a Cooper-pair splitter, which can generate spatially-separated but entangled electrons, in a quantum anomalous Hall insulator proximity-coupled with a superconductor. After coupling with a superconductor, the chiral edge states of the quantum anomalous Hall insulator can still survive, making the backscattering impossible. Thus, t…
The generation of spin-entangled electrons is an important prerequisite for future solid-state quantum technologies. Cooper pairs in a superconductor can be split into separate electrons in a spin-singlet state, however, detecting their entanglement remains an open experimental challenge. Proposals to detect the entanglement by violating a Bell inequality typically require a large number of current cross-correlation measurements, and not all entangled states can be detected in this way. Here, we instead formulate an entanglement witness that can detect the spin-entanglement using only three cr…
The Andreev transport properties of double quantum dot based Cooper pair splitters with one superconducting and two normal leads are studied theoretically in the Kondo regime. The influence of the superconducting pairing correlations on the local density of states, Andreev transmission coefficient and Cooper pair splitting efficiency is thoroughly analyzed. It is shown that finite superconducting pairing potential quickly suppresses the SU(2) Kondo effect, which can however reemerge for relatively large values of coupling to superconductor. In the SU(4) Kondo regime, a crossover from the SU(4)…
We study the spin-resolved subgap transport in a triple quantum-dot system coupled to one superconducting and two ferromagnetic leads. We examine the Andreev processes in the parallel and antiparallel alignments of ferromagnets magnetic moments in both the linear and nonlinear response regimes. The emphasis is put on the analysis of the current cross-correlations between the currents flowing through the left and right arms of the device and relevant electron waiting time distributions. We show that both quantities can give an important insight into the subgap transport processes and their anal…
Hybrid nanostructures consisting of two parallel InAs nanowires connected by an epitaxially grown superconductor (SC) shell recently became available. Due to the defect-free SC-semiconductor interface and the two quasi-one-dimensional channels being close by, these novel platforms can be utilized to spatially separate entangled pairs of electrons by using quantum dots (QD) in the so-called Cooper pair splitting (CPS) process. The minimized distance between the QDs overcomes the limitations of single-wire-based geometries and can boost the splitting efficiency. Here we investigate CPS in such a…
Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas
本研究首次在半导体二维电子气中实现库珀对分裂，观测到单态与强三重态关联，为片上纠缠和拓扑超导研究提供了可扩展平台。
We simulated the radiative response of the cavity quantum electrodynamics (QED) coupled to the double quantum dot Cooper pair splitter and analyzed its spectral dependence to get insight into dynamics of the Cooper pair transfers. The model is confined to the energy subspace where two entangled electrons are transferred to two normal electrodes through the inter-dot singlet state on two proximitized quantum dots. Our research is focused on the Andreev scatterings in the subgap regime, for which the local charge susceptibility $Π(ω_p)$ is derived, by means of Keldysh Green functions, in a whole…
We measure the tunneling rates and coupling coefficients for local Andreev, non-local Andreev and elastic cotunneling processes. The non-local Andreev process, giving rise to Cooper pair splitting, exhibits the same coupling coefficient as the elastic co-tunneling whereas the local Andreev process is more than two orders of magnitude stronger than the corresponding non-local one. Theory estimates describe the findings and explain the large difference in the non-local and local coupling arising from competition between electron diffusion in the superconductor and tunnel junction transparency.
We investigate theoretically the noise and the full counting statistics of electrons that are emitted from a superconductor into two spatially separated quantum dots by the splitting of Cooper pairs and further on collected in two normal-state electrodes. With negatively-biased drain electrodes and a large superconducting gap, the dynamics of the Cooper pair splitter can be described by a Markovian quantum master equation. Using techniques from full counting statistics, we evaluate the electrical currents, their noise power spectra, and the power-power correlations in the output leads. The cur…
We investigate the nonlocal thermoelectric transport in a Cooper-pair splitter based on a double-quantum-dot-superconductor three-terminal hybrid structure. We find that the nonlocal coupling between the superconductor and the quantum dots gives rise to nonlocal thermoelectric effects which originate from the nonlocal particle-hole breaking of the system. We show that Cooper-pair splitting induces the generation of a thermo-current in the superconducting lead without any transfer of charge between the two normal metal leads. Conversely, we show that a nonlocal heat exchange between the normal …
We propose a device which implements a solid-state nanostructured electron entangler. It consists of a single-walled carbon nanotube connected at both end to normal state electrodes and coupled in its middle part to a superconducting nanowire. Such a device acts as an electronic beam splitter for correlated electrons originating from the superconductor. We first show that it can be used to detect positive (bosonic--like) noise correlations in an fermionic system. Furthermore, it provides a source for entangled electrons in the two arms of the splitter. For generating entangled electron states,…
Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenc…
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 spl…
A Cooper pair splitter consists of a central superconducting contact, S, from which electrons are injected into two parallel, spatially separated quantum dots (QDs). This geometry and electron interactions can lead to correlated electrical currents due to the spatial separation of spin-singlet Cooper pairs from S. We present experiments on such a device with a series of bottom gates, which allows for spatially resolved tuning of the tunnel couplings between the QDs and the electrical contacts and between the QDs. Our main findings are gate-induced transitions between positive conductance corre…
Splitting of Cooper pairs has recently been realized experimentally for s-wave Cooper pairs. A split Cooper pair represents an entangled two-electron pair state which has possible application in on-chip quantum computation. Likewise the spin-activity of interfaces in nanoscale tunnel junctions has been investigated theoretically and experimentally in recent years. However, the possible implications of spin-active interfaces in Cooper pair splitters so far have not been investigated. We analyse the current and the cross correlation of currents in a superconductor ferromagnet beamsplitter includ…
Steady-state dynamics and non-local correlations in thermoelectric Cooper pair splitters
以热电Cooper pair splitter为原型，全面分析其传输信号，通过量子discord识别非局域量子关联工作点，发现能级展宽与杂化导致交叉Andreev过程共振偏移与热电电流宇称反转，为固态量子关联控制提供新途径。
Adiabatic Cooper pair splitter
本文提出一种绝热库珀对分离器，通过周期性门电压沿避让交叉点绝热控制量子点，产生量子化电流并抑制低频噪声，可在千兆赫兹下运行。
Thermoelectric effect generating electricity from thermal gradient and vice versa appears in numerous generic applications. Recently, an original prospect of thermoelectricity arising from the nonlocal Cooper pair splitting (CPS) and the elastic co-tunneling (EC) in hybrid normal metal-superconductor-normal metal (NSN) structures was foreseen. Here we demonstrate experimentally the existence of non-local Seebeck effect in a graphene-based CPS device comprising two quantum dots connected to an aluminum superconductor and theoretically validate the observations. This non-local Seebeck effect off…
The control of nonlocal entanglement in solid state systems is a crucial ingredient of quantum technologies. We investigate a Cooper-pair splitter based on a double quantum dot realised in a semiconducting nanowire. In the presence of interdot tunnelling the system provides a simple mechanism to develop spatial entanglement even in absence of nonlocal coupling with the superconducting lead. We discuss the possibility to control the symmetry (singlet or triplet) of spatially separated, entangled electron pairs taking advantage of the spin-orbit coupling of the nanowire. We also demonstrate that…
We present a proof-of-principle of how electronic transport measurements permits the observation of the Autler-Townes doublet, an optical property of nanodevices. The quantum physical system consists of one optically pumped quantum dot, a second auxiliary quantum dot, and a superconductor lead which provides an effective coupling between the dots via crossed Andreev reflection. Electrodes, working as source and drain, acts as nonequilibrium electronic reservoirs. Our calculations of the photocurrent at both, transient and stationary regimes, obtained using a density matrix formalism for open q…
Electronic transport in bent carbon nanotubes
本文研究均匀弯曲碳纳米管的电子输运，结合紧束缚模型、NEGF和弯曲空间Dirac方程解析求解，发现扶手椅型纳米管在1%弯曲下即可实现谷分离，而锯齿型纳米管几乎不受影响，为谷电子学应用提供新思路。
Exact analytical formulas are derived, by means of Keldysh Green functions, for currents and current correlation functions in a Cooper pair splitter modelled on a double quantum dot system coherently coupled to a superconductor and two normal metallic electrodes. Confining to the subspace with the inter-dot singlet we show perfect entanglement of split electrons in two separated crossed Andreev reflection processes. The studies are focused on the noise power spectrum in a whole bias voltage range. In particular, in the large voltage limit shot noise dominates and its spectrum exhibits two extr…
A Cooper-pair beam splitter as a feasible source of entangled electrons
本文研究由超导体库珀对分束器连接的双量子点系统产生纠缠电子对，通过微扰理论建立有效模型，并用多种纠缠指标及电子检测协方差验证其可行性。
We consider a nanoelectromechanical system composed of a carbon nanotube suspended between two normal leads and coupled to a superconducting scanning tunneling microscope (STM) tip via vacuum tunnel barrier. Treating the nanotube as a single-level quantum dot, it is shown that an applied voltage between the superconducting STM tip and normal leads gives rise to a pumping or a cooling of the mechanical subsystem depending on the direction of the electronic flow. It is also demonstrated that the transition between these two regimes is controlled by the strength of the tunnel coupling between the…
We investigate the Andreev transport through double-quantum-dot Cooper pair splitters with ferromagnetic leads. The analysis is performed with the aid of the real-time diagrammatic technique in the sequential tunneling regime. We study the dependence of the Andreev current, the differential conductance, and the tunnel magnetoresistance on various parameters of the model in both the linear and nonlinear response regimes. In particular, we analyze the spin-resolved transport in the crossed Andreev reflection regime, where a blockade of the current occurs due to enhanced occupation of the triplet…
We consider the sub-gap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunnelling between the dots and finite Coulomb intra- and inter-dot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method which easily yields currents, noise and cross-correlators. In particular, for finite inter- and intra-dot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local an…
Fermionic quantum computation with Cooper pair splitters
本文提出一种基于局域费米子模式而非量子比特的通用量子计算机实现方案，通过量子点与超导岛耦合控制实现通用量子门，并设计了抗电荷噪声的替代方案。
A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based on a pair of helical Luttinger liquids, which arise naturally at the edges of a quantum spin Hall insulator. Equipping each helical liquid with a beam splitter, current-current cross correlations can be used to construct a Bell inequality whose violation would indicate nonlocal orbital entanglement of the injected electrons and/or holes. Due to Luttinger-liqu…
The electrons forming a Cooper pair in a superconductor can be spatially separated preserving their spin entanglement by means of quantum dots coupled to both the superconductor and independent normal leads. We investigate the thermoelectric properties of such a Cooper pair splitter and demonstrate that cooling of a reservoir is an indication of non-local correlations induced by the entangled electron pairs. Moreover, we show that the device can be operated as a non-local thermoelectric heat engine. Both as a refrigerator and as a heat engine, the Cooper pair splitter reaches efficiencies clos…
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.
Controllable Single Cooper Pair Splitting in Hybrid Quantum Dot Systems
本文在隔离于引线库的多量子点器件中实现了单个库珀对的可控分裂与保留，并分别利用GHz色散门传感和双量子点宇称传感器识别分裂电荷跃迁及检测分裂电子。
The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows "holes" (, and not "electrons",) to move inside the tube. This case accounts for a semiconducting behavior with the activation energy of the order of around 3 meV. There is a distribution of the activation energy since the pitch and the circumference can vary. Otherwise nanotubes show metallic behaviors. "Electrons" and "holes" can move in the graphene wall (two dimensions). The conduction in the wall is t…
We investigate the conditions in which superconductivity may develop in ropes of carbon nanotubes. It is shown that the interaction among a large number of metallic nanotubes favors the appearance of a metallic phase in the ropes, intermediate between respective phases with spin-density-wave and superconducting correlations. These arise in samples with about 100 metallic nanotubes or more, where the long-range Coulomb interaction is very effectively reduced and it may be overcome by the attractive interaction from the exchange of optical phonons within each nanotube. We estimate that the proba…
We demonstrate experimentally that non-collinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near four-fold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilita…
We investigate non-linear transport in a double quantum dot connected to two normal electrodes and a central superconducting finger. By this means, we perform a transport spectroscopy of such a system which implements a Cooper pair splitter. The non-linear conductance exhibits strong subgap features which can be associated with the coherence of the injected Cooper pairs. Our findings are well accounted for by the recently developed microscopic theory of Cooper pairs splitters made in SWNTs.
A superconductor is a natural source of spin-entangled spatially separated electron pairs. Although the first Cooper-pair splitter devices have been realized recently, an experimental confirmation of the spin state and the entanglement of the emitted electron pairs is lacking up to now. In this paper a method is proposed to confirm the spin-singlet character of individual split Cooper pairs. Two quantum dots (QDs), each of them holding one spin-prepared electron, serve as the detector of the spin state of a single Cooper pair that is forced to split when it tunnels out from the superconductor …
Hybrid quantum dot-oscillator systems have become attractive platforms to inspect quantum coherence effects at the nanoscale. Here, we investigate a Cooper-pair splitter setup consisting of two quantum dots, each linearly coupled to a local resonator. The latter can be realized either by a microwave cavity or a nanomechanical resonator. Focusing on the subgap regime, we demonstrate that cross-Andreev reflection, through which Cooper pairs are split into both dots, can efficiently cool down simultaneously both resonators into their ground state. Moreover, we show that a nonlocal heat transfer b…
A superconductor connected to normal leads allows to generate Einstein-Podolsky-Rosen pairs by Cooper pair splitting. It has been realized with quantum dots either defined in carbon nanotubes or InAs nanowires. After establishing the presence of Cooper pair splitting in such devices new works have invesigated the effects of a finite potential difference between the quantum dots to improve and characterize the efficiency of Cooper pair splitting. In this paper we present a generic model for Cooper pair splitting and develop two minimal models specifically for the two experimental realisations a…
Entanglement, being at the heart of the Einstein-Podolsky-Rosen (EPR) paradox, is a necessary ingredient in processing quantum information. Cooper pairs in superconductors - being composites of two fully entangled electrons - can be split adiabatically, thus forming entangled electrons. We fabricated such electron splitter by contacting an aluminum superconductor strip at the center of a suspended InAs nanowire; terminated at both ends with two normal metallic drains. Intercepting each half of the nanowire by gate - induced Coulomb blockaded quantum dot strongly impeded the flow of Cooper pair…
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