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arXiv:2302.10744

An on-demand source of non-local energy-entangled quantum states using Levitons

Bruno Bertin-Johannet, Laurent Raymond, Flavio Ronetti, Jérôme Rech, Thibaut Jonckheere, Benoît Grémaud, Thierry Martin

Published Feb 21, 2023• 0 citations
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Abstract

We propose a device where Electronic Quantum Optics (EQO) is combined with a BCS superconductor -- a reservoir of Cooper pairs. With spin polarized wave guides, this version of the Cooper pair beam splitter is driven by an AC drive, and observables such as period-averaged noise are computed using a Keldysh-Nambu-Floquet formalism. When the (low frequency) voltage applied to the superconductor consists of a train of periodic Lorentzian pulses and the Andreev regime is specified (large gap limit), this allows to propose an on-demand source of non-local energy-entangled states (which we characterise with perturbation theory) operating in the AC regime. We study realistic experimental parameters for our device in order to examine its feasibility.

DOI
10.48550/arxiv.2302.10744

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We propose a device where Electronic Quantum Optics (EQO) is combined with a BCS superconductor -- a reservoir of Cooper pairs. With spin polarized wave guides, this version of the Cooper pair beam splitter is driven by an AC drive, and observables such as period-averaged noise are computed using a Keldysh-Nambu-Floquet formalism. When the (low frequency) voltage applied to the superconductor consists of a train of periodic Lorentzian pulses and the Andreev regime is specified (large gap limit), this allows to propose an on-demand source of non-local energy-entangled states (which we characterise with perturbation theory) operating in the AC regime. We study realistic experimental parameters for our device in order to examine its feasibility.
We propose a device where Electronic Quantum Optics (EQO) is combined with a BCS superconductor -- a reservoir of Cooper pairs. With spin polarized wave guides, this version of the Cooper pair beam splitter is driven by an AC drive, and observables such as period-averaged noise are computed using a Keldysh-Nambu-Floquet formalism. When the (low frequency) voltage applied to the superconductor consists of a train of periodic Lorentzian pulses and the Andreev regime is specified (large gap limit), this allows to propose an on-demand source of non-local energy-entangled states (which we characterise with perturbation theory) operating in the AC regime. We study realistic experimental parameters for our device in order to examine its feasibility.
We propose a source of purely electronic energy-entangled states implemented in a solid-state system with potential applications in quantum information protocols based on electrons. The proposed device relies on the standard tools of electron quantum optics and exploits entanglement of the Cooper pairs of a BCS superconductor. The latter is coupled via an adjustable quantum point contact to two opposite spin-polarized electron wave-guides, which are driven by trains of Lorentzian pulses. This specific choice for the drive is crucial to inject purely electronic entangled states devoid of spurious electron–hole pairs. In the Andreev regime, a perturbative calculation in the tunnel coupling confirms that entangled electrons states are generated at the output of the normal side. For arbitrary tunnel coupling and for a periodic drive, direct current and noise (auto and cross correlations) are computed numerically using a Keldysh–Nambu–Floquet formalism. Importantly, for a periodic drive, the production of these states can be controlled in time, thus implementing an on-demand source of entangled states. We exploit realistic experimental parameters for our device to identify its optimal functioning point.
We propose a source of purely electronic energy-entangled states implemented in a solid-state system with potential applications in quantum information protocols based on electron flying qubits. The proposed device relies on the standard tools of electron quantum optics and exploits entanglement of the Cooper pairs of a BCS superconductor. The latter is coupled via an adjustable quantum point contact to two opposite spin-polarized electron waveguides, which are driven by trains of Lorentzian pulses. This specific choice for the drive is crucial to inject purely electronic entangled states devoid of spurious electron-hole pairs. In the Andreev regime, a perturbative calculation in the tunnel coupling confirms that entangled electron states are generated at the output of the normal side. We introduce a quantity related to charge current cross correlations which allows one to experimentally verify the entangled nature of the emitted state.
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 quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.
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 interdot tunneling term with a spin symmetry determined by the Zeeman field. Together with electrostatically tunable quantum dots, we show that this makes it possible to engineer a spin triplet state shared between the quantum dots. Compared to previous works, we thus extend the capabilities of the Cooper pair splitter to create entangled nonlocal electron pairs.
New strategies to generate and to detect spin-entangled pairs of electrons in mesoscopic solid-state heterostructures are proposed. A bilayer-graphene device is designed in which Cooper pairs from an s-wave superconductor are injected into an electrostatically-defined topological channel. Due to a particular band structure, two electrons of a Cooper pair propagate in opposite directions and are hence spatially separated if atomic-scale defects are sparse. Neither energy filtering nor Coulomb repulsion are required. The device can be interpreted as a normal/superconducting/normal junction, in which emission of nonlocal singlets is equivalent to local Andreev reflection, in contrast to the widespread identification of Cooper pair splitting with crossed Andreev reflection. To detect entanglement, the Josephson current through two parallel single-level quantum dots is investigated at all occupations. Combining exact diagonalization and perturbation theory, signatures of nonlocal Cooper pair transport are identified in the critical current, a macroscopic quantity. The model reproduces recent experimental observations and predicts a nonlocal triplet ground state on the quantum dots due to a tunable superconductor-mediated exchange coupling, which, too, is visible in the critical current exactly if nonlocal Cooper pairs are transported. Entanglement detection is pursued, too, by converting spin-entangled Cooper pairs into polarization-entangled photons, which are subsequently probed by a Bell-type measurement. A closed emission cycle is constructed, such that no correlations between the photons and the electrons remain, which are detrimental for entanglement transfer. Inevitable side channels and imperfections are identified and accounted for by a particular measurement protocol. Furthermore, it is discussed how spin-charge separation can be used to extract signatures of nonlocal spin singlets from the average current through an electronic beam splitter. This complements a known mechanism based on exchange statistics by which only the more difficult-to-access noise is sensitive for entanglement. The device can be realized by two crossed nanowires or by quantum-Hall edge states in Corbino geometry. The thesis also contains a review on entanglement and on recent theoretical and experimental progress in solid-state systems towards entanglement detection and generation, focusing on Cooper pair splitting.