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arXiv:1307.2248 · Physical Review B

Cooper-pair-based photon entanglement without isolated emitters

Alex Hayat, Hae‐Young Kee, Kenneth S. Burch, Aephraim M. Steinberg

Published Mar 10, 2014• 44 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.89.094508

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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.
Various applications in the rapidly growing field of quantum information science require reliable and effective quantum light sources. We proposed an efficient approach for generation of entangled photons, based on Cooper-pair luminescence in semiconductors, which does not require isolated emitters. Semiconductor quantum wells, remove the light-heavy-hole degeneracy, allowing efficient photon entanglement generation in simple electrically-driven structures, taking advantage of the superconducting macroscopic coherence [1]. We analyzed a new effect of enhanced light amplification in electrically-driven semiconductor-superconductor structures, including Cooper-pair based two-photon gain [2]. We also proposed a compact and highly-efficient scheme for a complete Bell-state analysis using two-photon absorption in a superconducting proximity region of a semiconductor avalanche photodiode [3]. This Cooper-pair based two-photon absorption results in a strong detection preference of a specified entangled state.
Summary form only given. Various applications in the rapidly growing field of quantum information science require reliable and effective quantum light sources. We observed superconducting proximity in semiconductor light-emitting diodes (Fig. 1). These hybrid structures were proposed by us as an efficient approach for generation of entangled photons, based on Cooper-pair luminescence in semiconductors, which does not require isolated emitters. Semiconductor quantum wells, remove the light-heavy-hole degeneracy, allowing efficient photon entanglement generation in simple electrically-driven structures, taking advantage of the superconducting macroscopic coherence [1]. Based on the developed theory we analyzed a new effect of enhanced light amplification in electrically-driven semiconductor-superconductor structures, including Cooper-pair based two-photon gain [2]. Moreover, we proposed a compact and highly-efficient scheme for a complete Bell-state analysis using two-photon absorption in a superconducting proximity region of a semiconductor avalanche photodiode. This Cooper-pair based two-photon absorption results in a strong detection preference of a specified entangled state.
We theoretically demonstrate that a superconducting circular current induced in a semiconductor results in emission of orbital-angular-momentum (OAM) entangled photon pairs upon carrier recombination. Combining the macroscopic Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, we investigate the emission of a superconducting light-emitting diode (SLED) with a spatially varying phase profile in the superconducting order parameter. We show that in the active region of the SLED with a circular supercurrent, radiative recombination processes inherit the order parameter phase and result in photon pairs emitted into modes of different OAM quantum numbers. We demonstrate that coherent superposition of superconducting qubit eigenstates can also be mapped onto a coherent superposition of emitted photon states. We also show that other recombination processes due to thermally excited quasi particles do not significantly degrade the state purity. Our results introduce an original scheme for generating OAM-entangled photons enabling a new method of transmitting superconducting qubit information to photonic channels thereby bridging the gap between solid-state and photon-based platforms for quantum communications and information processing.
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.
The realization of solid-state photon sources that are capable of on-demand generation of an entangled single-photon pair at a time is highly desired for quantum information processing and communication. A new method of generating an entangled single-photon pair at a time is proposed employing Cooper-pair-related radiative recombination in a quantum dot (QD). Cooper pairs are bosons and the control of their number states is difficult. Pauli's exclusion principle on quasiparticles in a discrete state of a QD regulates the number state of the generated photon pairs in this scheme. The fundamental heterostructures for constructing superconductor-based quantum-dot light-emitting diodes (SQ-LEDs) and the fundamental operation conditions of SQ-LED will be discussed. The experimental studies on Cooper-pair injection into the related semiconductor structures will be also discussed.
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.