Entangled Electron Pairs Research Articles

The Second Quantum Revolution: Development of Subatomic Quantum Nanotechnologies of Intelligent Materials

The article analyzes the future development of quantum nanotechnology based on attosecond physics of the subatomic level of the condensed state. The ways of realizing the main achievements of the second quantum revolution in subatomic nanotechnologies of materials, namely quantum entanglement, quantum contextuality and quantum dissipativity are considered. The theoretical analysis of the prospects for this direction in the development of quantum subatomic nanotechnologies has been carried out within the framework of the well-known theory of thermal field dynamics of the condensed state. The analysis shows that subatomic entanglement of electron pairs is realized by attosecond single-cycle photons. The entangled electron pairs form the interfaces of supra-atomic capsules — quantum nanoelectromechanical systems (NEMS) of the condensed state of the material. The Coulomb blockade of quantum NEMS interfaces is complemented by the fact that they are controlled by the infrastructure of subatomic two-electron sensors and actuators located at the interface boundaries. When the primary subatomic interfaces of NEMS function, secondary supra-atomic scale entangled pairs of electrons are generated, which dissipate the NEMS energy and form a dissipative multilevel hierarchy of condensed state interfaces at higher spatio-temporal scales of intelligent materials

From Cooper pair splitting to nonlocal spectroscopy of a Shiba state

Cooper pair splitting (CPS) is a way to create spatially separated, entangled electron pairs. To this day, CPS is often identified in experiments as a spatial current correlation. However, such correlations can arise even in the absence of CPS, when a quantum dot is strongly coupled to the superconductor, and a subgap Shiba state is formed. Here, we present a detailed experimental characterization of those spatial current correlations, as the tunnel barrier strength between the quantum dot and the neighboring normal electrode is tuned. The correlation of the non-local signal and the barrier strength reveals a competition between CPS and the non-local probing of the Shiba state. We describe our experiment with a simple transport model, and obtain the tunnel couplings of our device by fitting the model's prediction to the measured conductance correlation curve. Furthermore, we use our theory to extract the contribution of CPS to the non-local signal.

Crossed Andreev reflection in FSF Weyl semimetal junctions

We have investigated crossed Andreev reflection in a ferromagnet-superconductor-ferromagnet junction based on the time-reversal invariant Weyl semimetals. We demonstrate that this junction can provide a suitable platform for generating pure crossed Andreev reflection signals. For bipolar junction, n-doped left ferromagnet and p-doped right ferromagnet, pure co-tunneling can happen in the antiparallel configuration of the magnetizations of ferromagnets, while a pure crossed Andreev reflection is possible only in the parallel configuration. However, when both of the ferromagnetic leads have the same polarity, n-doped or p-doped, the situation is reversed. Furthermore, we find that we can tune the chemical potentials and magnetizations of the ferromagnets separately to on or off co-tunneling and crossed Andreev reflection signals. Moreover, we show that the pure crossed Andreev reflection signal can be enhanced by tuning the chemical potentials of two ferromagnetic leads. Our findings may be employed for generating entangled electron pairs in the condensed matter systems.

Dominant nonlocal superconducting proximity effect due to electron-electron interaction in a ballistic double nanowire.

Cooper pair splitting (CPS) can induce nonlocal correlation between two normal conductors that are coupled to a superconductor. CPS in a double one-dimensional electron gas is an appropriate platform for extracting a large number of entangled electron pairs and is one of the key ingredients for engineering Majorana fermions with no magnetic field. In this study, we investigated CPS by using a Josephson junction of a gate-tunable ballistic InAs double nanowire. The measured switching current into the two nanowires is significantly larger than the sum of the switching current into the respective nanowires, indicating that interwire superconductivity is dominant compared with intrawire superconductivity. From its dependence on the number of propagating channels in the nanowires, the observed CPS is assigned to one-dimensional electron-electron interaction. Our results will pave the way for the utilization of one-dimensional electron-electron interaction to reveal the physics of high-efficiency CPS and to engineer Majorana fermions in double nanowire systems via CPS.

Entanglement balance of quantum (e,2e) scattering processes

The theory of quantum information constitutes the functional value of the quantum entanglement, i.e., quantum entanglement is essential for high fidelity of quantum protocols, while fundamental physical processes behind the formation of quantum entanglement are less relevant for practical purposes. In the present work, we explore physical mechanisms leading to the emergence of quantum entanglement in the initially disentangled system. In particular, we analyze spin entanglement of outgoing electrons in a nonrelativistic quantum $(e,2e)$ collision on a target with one active electron. Our description exploits the time-dependent scattering formalism for typical conditions of scattering experiments, and contrary to the customary stationary formalism operates with realistic scattering states. We quantify the spin entanglement in the final scattering channel through the pair concurrence and express it in terms of the experimentally measurable spin-resolved $(e,2e)$ triple differential cross sections. Besides, we consider Bell's inequality and inspect the regimes of its violation in the final channel. We address both the pure and the mixed initial spin state cases and uncover kinematical conditions of the maximal entanglement of the outgoing electron pair. The numerical results for the pair concurrence, entanglement of formation, and violation of Bell's inequality obtained for the $(e,2e)$ ionization process of atomic hydrogen show that the entangled electron pairs indeed can be formed in the $(e,2e)$ collisions even with spin-unpolarized projectile and target electrons in the initial channel. The positive entanglement balance---the difference between entanglements of the initial and final electron pairs---can be measured in the experiment.

Cooling by Cooper pair splitting

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 close to the thermodynamic bounds. As such, our work introduces an experimentally accessible heat engine and a refrigerator driven by entangled electron pairs in which the role of quantum correlations can be tested.

Entanglement‐symmetry control in a quantum‐dot Cooper‐pair splitter

AbstractThe 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 realized in a semiconducting nanowire. In the presence of interdot tunneling 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 the spin‐orbit coupling does not impact over the entanglement purity of the nonlocal state generated in the double quantum dot system.Cooper‐pair splitter realized in a nanowire acting as double quantum dot which is coupled to one superconductor (S) and two normal leads (N). Electron singlets in the superconductor are split nonlocally into the different dots as schematically shown in the figure. The entangled electrons in the two quantum dots are then transferred by tunneling, with rate , to the normal leads.

A project to measure quantum spin correlations of relativistic electron pairs in Møller scattering

A project to measure quantum spin correlations for relativistic particles with mass is presented. It aims at testing spin observables in relativistic quantum mechanics. The measurement will be performed for pairs of entangled electrons originating from Moller scattering. A double Mott polarimeter, allowing for simultaneous measurement of the spin projections of both electrons, was designed for this purpose.

Coexistence of perfect spin filtering for entangled electron pairs and high magnetic storage efficiency in one setup.

For Entangled electron pairs superconducting spintronics, there exist two drawbacks in existing proposals of generating entangled electron pairs. One is that the two kinds of different spin entangled electron pairs mix with each other. And the other is a low efficiency of entanglement production. Herein, we report the spin entanglement state of the ferromagnetic insulator (FI)/s-wave superconductor/FI structure on a narrow quantum spin Hall insulator strip. It is shown that not only the high production of entangled electron pairs in wider energy range, but also the perfect spin filtering of entangled electron pairs in the context of no highly spin-polarized electrons, can be obtained. Moreover, the currents for the left and right leads in the antiferromagnetic alignment both can be zero, indicating 100% tunnelling magnetoresistance with highly magnetic storage efficiency. Therefore, the spin filtering for entangled electron pairs and magnetic storage with high efficiencies coexist in one setup. The results may be experimentally demonstrated by measuring the tunnelling conductance and the noise power.

Cooper pair splitting in parallel quantum dot Josephson junctions.

Devices to generate on-demand non-local spin entangled electron pairs have potential application as solid-state analogues of the entangled photon sources used in quantum optics. Recently, Andreev entanglers that use two quantum dots as filters to adiabatically split and separate the quasi-particles of Cooper pairs have shown efficient splitting through measurements of the transport charge but the spin entanglement has not been directly confirmed. Here we report measurements on parallel quantum dot Josephson junction devices allowing a Josephson current to flow due to the adiabatic splitting and recombination of the Cooper pair between the dots. The evidence for this non-local transport is confirmed through study of the non-dissipative supercurrent while tuning independently the dots with local electrical gates. As the Josephson current arises only from processes that maintain the coherence, we can confirm that a current flows from the spatially separated entangled pair.

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

Superconducting Light-Emitting Diodes

Cooper pairs form spin singlet states and are regarded as entangled electron pairs. Extracting entangled electrons has been actively studied by the use of superconductor-normal metal junctions. We have proposed to convert Cooper pairs to entangled photon pairs via interband radiative recombination of Cooper pairs penetrated into a semiconductor by the proximity effect. We fabricated a superconducting (SC) light emitting diode, where a superconductor is used for the n-type electrode. We observed light output enhancement and recombination lifetime shortening below the SC critical temperature. Our observations were very well explained with an analysis based on a time-dependent perturbation theory of the radiative recombination. Superconductivity was included via the Bogoliubov transformation. We present our measurements on the Cooper-pair-enhanced luminescence from InAs quantum dots. We demonstrate the observation of sharp edge in the luminescence spectra that reflects the SC density of states.

Probing spin entanglement by gate-voltage-controlled interference of current correlation in quantum spin Hall insulators

We propose an entanglement detector composed of two quantum spin Hall insulators and a side gate deposited on one of the edge channels. For an ac gate voltage, the differential noise contributed from the entangled electron pairs exhibits the nontrivial step structures, from which the spin entanglement concurrence can be easily obtained. The possible spin dephasing effects in the quantum spin Hall insulators are also included.

Spin filtering and entanglement detection due to spin-orbit interaction in carbon nanotube cross-junctions

We demonstrate that due to their spin-orbit interaction carbon nanotube cross-junctions have attractive spin projective properties for transport. First, we show that the junction can be used as a versatile spin filter as a function of a backgate and a static external magnetic field. Switching between opposite spin filter directions can be achieved by small changes of the backgate potential, and a full polarization is generically obtained in an energy range close to the Dirac points. Second, we discuss how the spin filtering properties affect the noise correlators of entangled electron pairs, which allows us to obtain signatures of the type of entanglement that are different from the signatures in conventional semiconductor cross-junctions.

Selective focusing of electrons and holes in a graphene-based superconducting lens

We show that a graphene pnp junction with a central superconducting electrode acts as a Veselago lens for incoming electrons by focusing them and their phase-conjugated counterpart (holes) into different points of the optical axis. This selective focusing suggested by a simple trajectory analysis is confirmed by fully microscopic calculations. Although the focusing pattern is degraded by deviations from the ideal conditions, we show that it remains visible for a wide range of parameters. We discuss how this property can be useful for the detection of entangled electron pairs.

Josephson and Andreev transport through quantum dots

In this article we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single level Anderson type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of \pi-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states which characterized the spectral properties of most of these systems. We give technical details on the several different analytical and numerical methods which have been developed for describing these properties. We further discuss the recent theoretical efforts devoted to extend this analysis to more complex situations like multidot, multilevel or multiterminal configurations in which novel phenomena is expected to emerge. These include control of the localized spin states by a Josephson current and also the possibility of creating entangled electron pairs by means of non-local Andreev processes.

Andreev bound states in supercurrent-carrying carbon nanotubes revealed

Carbon nanotubes (CNTs) are not intrinsically superconducting but they can carry a supercurrent when connected to superconducting electrodes. This supercurrent is mainly transmitted by discrete entangled electron-hole states confined to the nanotube, called Andreev Bound States (ABS). These states are a key concept in mesoscopic superconductivity as they provide a universal description of Josephson-like effects in quantum-coherent nanostructures (e.g. molecules, nanowires, magnetic or normal metallic layers) connected to superconducting leads. We report here the first tunneling spectroscopy of individually resolved ABS, in a nanotube-superconductor device. Analyzing the evolution of the ABS spectrum with a gate voltage, we show that the ABS arise from the discrete electronic levels of the molecule and that they reveal detailed information about the energies of these levels, their relative spin orientation and the coupling to the leads. Such measurements hence constitute a powerful new spectroscopic technique capable of elucidating the electronic structure of CNT-based devices, including those with well-coupled leads. This is relevant for conventional applications (e.g. superconducting or normal transistors, SQUIDs) and quantum information processing (e.g. entangled electron pairs generation, ABS-based qubits). Finally, our device is a new type of dc-measurable SQUID.

A sparse framework for the derivation and implementation of fermion algebra

Algorithms useful in the construction of electron correlation models are collected alongside new developments for cases of high rank and sparsity. In the first part of this paper a Brandow diagram manipulation program is presented. The complementary second section describes a general-rank sparse contraction algorithm which exploits the permutational symmetries of many-fermion quantities. Several recently published local correlation models (perfect quadruples and perfect hextuples) were built using these codes. This paper should facilitate reproduction and extension of high-rank electron correlation models that combine truncation by level of substitution with truncation by locality, such as the number of entangled electron pairs.

Carbon nanotubes help pairs survive a breakup

A new experiment shows that entangled electron pairs can be spatially split into different arms of a carbon nanotube. Is a nanotube quantum teleporter on the horizon?

Efficient polarization entanglement concentration for electrons with charge detection

We present an entanglement concentration protocol for electrons based on their spins and their charges. The combination of an electronic polarizing beam splitter and a charge detector functions as a parity check device for two electrons, with which the parties can reconstruct maximally entangled electron pairs from those in a less-entanglement state nonlocally. This protocol has a higher efficiency than those based on linear optics and it does not require the parties to know accurately the information about the less-entanglement state, which makes it more convenient in a practical application of solid quantum computation and communication.