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arXiv:1807.07980 · Physical review. B./Physical review. B

Anisotropic purity of entangled photons from Cooper pairs in heterostructures

Jacob S. Gordon, Hae‐Young Kee

Published Sep 18, 2018• 1 citation
arXivHTMLPDF

Abstract

It was theoretically proposed that a forward-biased $p\ensuremath{-}n$ junction with a superconducting layer (P-N-S) would produce pure, polarization-entangled photons due to inherent spin-singlet pairing of electrons. However, any heterostructure interface generically induces Rashba spin-orbit coupling, which in turn generates a mixed singlet-triplet superconducting order parameter. Here we study the effect of triplet pairing on the purity of photons produced through Cooper pair recombination. A unique directional dependence of the state purity is found for a triplet superconductor with fixed $\mathbit{d}$: pure, entangled photons are produced when the photon polarization axis is parallel to $\mathbit{d}$. Induced triplet pairing in a singlet superconductor is shown to degrade the state purity, while induced singlet pairing in a triplet superconductor is shown to enhance the production of entangled pairs. These considerations may aid the design of functional devices to produce entangled photons.

DOI
10.1103/physrevb.98.104509

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It was theoretically proposed that a forward-biased p\ensuremath−np\ensuremath{-}np\ensuremath−n junction with a superconducting layer (P-N-S) would produce pure, polarization-entangled photons due to inherent spin-singlet pairing of electrons. However, any heterostructure interface generically induces Rashba spin-orbit coupling, which in turn generates a mixed singlet-triplet superconducting order parameter. Here we study the effect of triplet pairing on the purity of photons produced through Cooper pair recombination. A unique directional dependence of the state purity is found for a triplet superconductor with fixed \mathbitd\mathbit{d}\mathbitd: pure, entangled photons are produced when the photon polarization axis is parallel to \mathbitd\mathbit{d}\mathbitd. Induced triplet pairing in a singlet superconductor is shown to degrade the state purity, while induced singlet pairing in a triplet superconductor is shown to enhance the production of entangled pairs. These considerations may aid the design of functional devices to produce entangled photons.
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.
We show that the recombination of Cooper pairs in semiconductors can be used as a natural source of polarization-entangled photons, making use of the inherent angular momentum entanglement in the superconducting state. Our proposal is not based on opposite spin population of discrete energy levels and thus does not require isolated emitters such as single atoms or quantum dots. We observe that in bulk materials, the photon entanglement would be degraded due to the variety of decay channels available in the presence of light-hole (LH)--heavy-hole (HH) degeneracy. However, we show that the lifting of this degeneracy by use of a semiconductor quantum well should lead to faithful conversion of the Cooper-pair entanglement into photon entanglement. The second-order decay of two-electron states in Cooper-pair luminescence leaves no which-path information, resulting in perfect coherence between two pathways and hence, in principle, perfect entanglement. We calculate the purity of the entangled-photon state and find that it increases for larger LH--HH energy splitting and for lower temperatures. Moreover, the superconducting macroscopic coherence offers an enhancement to the emission rate, making this a promising scheme for efficient generation of entangled photons in simple electrically driven structures.
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Superconductor-semiconductor hybrid devices are an evolving field, combining the technologically mature semiconductors with the unique properties of superconductors, utilized in quantum computing, information and communications. Radiative recombination of Cooper pairs in superconducting light-emitting diodes (SLED) results in superconductor-enhanced light emission. The theory behind this effect is based on a two-photon interaction with Cooper pairs, predicted to enable polarization-entangled photon pairs [1], two-photon amplification in waveguides [2] and Bell-state analyzers [3].
Based on the Bardeen-Cooper-Schrieffer 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 photon pairs produced can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.
We model a superconducting $p\ensuremath{-}n$ junction in which the nnn and the ppp sides are contacted through two optical quantum dots (QDs), each embedded into a photonic nanocavity. Whenever a Cooper pair is transferred from the nnn side to the ppp side, two photons are emitted. When the two electrons of a Cooper pair are transported through different QDs, polarization-entangled photons are created, provided that the Cooper pairs retain their spin singlet character while being spatially separated on the two QDs. We show that a Clauser-Holt-Shimony-Horne (CHSH) Bell-type measurement is able to detect the entanglement of the photons over a broad range of microscopic parameters, even in the presence of parasitic processes and imperfections.