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Nonlocal Two Particle Interferometry & Entanglement Generation from Majorana Bound States

Sougato Bose, Pasquale Sodano

Published Oct 4, 2010• 0 citations
OpenAlex

Abstract

We show that a one dimensional device supporting a pair of Majorana bound states at its ends can produce remarkable Hanbury-Brown Twiss like interference effects between well separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the Majorana bound states leads exclusively to an electron-hole final state. This anti-bunching in electron-hole internal pseudospin space can be detected through current-current correlations. Further, we show that, by scattering appropriate spin polarized electrons from the Majorana bound states, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling to detect the presence of low energy Majorana modes.

Related papers

Nonlocal Handbury-Brown Twiss Interferometry & Entanglement Generation from Majorana Bound States

Sougato Bose, Pasquale Sodano

We show that a one dimensional device supporting a pair of Majorana bound states at its ends can produce remarkable Hanbury-Brown Twiss like interference effects between well separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the Majorana bound states leads exclusively to an electron-hole final state. This "anti-bunching" in electron-hole internal pseudospin space can be detected through current-current correlations. Further, we show that, by scattering appropriate spin polarized electrons from the Majorana bound states, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling to detect the presence of low energy Majorana modes.

arXiv:1010.0709•Oct 4, 2010•0 citations

Nonlocal Hanbury–Brown–Twiss interferometry and entanglement generation from Majorana bound states

Sougato Bose, Pasquale Sodano

We show that a one-dimensional device supporting a pair of Majorana bound states (MBS) at its ends can produce remarkable Hanbury–Brown–Twiss-like interference effects between well-separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the MBS leads exclusively to an electron–hole final state. This 'anti-bunching' in electron–hole internal pseudospin space can be detected through current–current correlations. Further, we show that, by scattering appropriate spin-polarized electrons from the MBS, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling us to detect the presence of low-energy Majorana modes.

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Majorana fermions (MFs) are exotic particles that are their own anti-particles. Recently, the search for the MFs occurring as quasi-particle excitations in solid-state systems has attracted widespread interest, because of their fundamental importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Here we study the quantum correlations between two spatially separate quantum dots induced by a pair of MFs emerging at the two ends of a semiconductor nanowire, in order to develop a new method for probing the MFs. We find that without the tunnel coupling between these paired MFs, quantum entanglement cannot be induced from an unentangled (i.e., product) state, but quantum discord is observed due to the intrinsic nonlocal correlations of the paired MFs. This finding reveals that quantum discord can indeed demonstrate the intrinsic non-locality of the MFs formed in the nanowire. Also, quantum discord can be employed to discriminate the MFs from the regular fermions. Furthermore, we propose an experimental setup to measure the onset of quantum discord due to the nonlocal correlations. Our approach provides a new, and experimentally accessible, method to study the Majorana bound states by probing their intrinsic non-locality signature.

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Detecting Majorana fermions by nonlocal entanglement between quantum dots

Zhi Wang, Xueyuan Hu, Qifeng Liang +1 more

Nonlocal entanglement between two quantum dots (QDs) can be generated through Majorana fermions. The two Majorana fermions at the ends of a one-dimensional topological superconductor form a nonlocal electronic level, which couples the occupation states of the two QDs located close to the two ends and brings the whole system into an entangled state, even at low temperatures and zero bias voltage. Upon introducing a charging energy by a capacitor, entanglement of the whole system can manifest itself through the nonlocal entanglement between the two QDs. Explicitly, the conditional probabilities of electron occupation on one QD with and without electron occupation on the other QD deviate from each other, with the difference proportional to the concurrence of quantum entanglement between the two QDs. Therefore detecting the difference in conditional probabilities, which is achievable experimentally by established techniques, provides evidence of the nonlocal nature of the fermion level constructed by the two end Majorana fermions.

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Coupling Single Electrons to Single Photons and Probing their Entanglement

Jan-Wilke Henke, Hao Jeng, Claus Ropers

Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R⁠, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H⁠, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (⁠λ/2⁠), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).

Microscopy and Microanalysis•Jul 1, 2025•0 citations
We show that a one dimensional device supporting a pair of Majorana bound states at its ends can produce remarkable Hanbury-Brown Twiss like interference effects between well separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the Majorana bound states leads exclusively to an electron-hole final state. This anti-bunching in electron-hole internal pseudospin space can be detected through current-current correlations. Further, we show that, by scattering appropriate spin polarized electrons from the Majorana bound states, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling to detect the presence of low energy Majorana modes.
We show that a one dimensional device supporting a pair of Majorana bound states at its ends can produce remarkable Hanbury-Brown Twiss like interference effects between well separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the Majorana bound states leads exclusively to an electron-hole final state. This "anti-bunching" in electron-hole internal pseudospin space can be detected through current-current correlations. Further, we show that, by scattering appropriate spin polarized electrons from the Majorana bound states, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling to detect the presence of low energy Majorana modes.
We show that a one-dimensional device supporting a pair of Majorana bound states (MBS) at its ends can produce remarkable Hanbury–Brown–Twiss-like interference effects between well-separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the MBS leads exclusively to an electron–hole final state. This 'anti-bunching' in electron–hole internal pseudospin space can be detected through current–current correlations. Further, we show that, by scattering appropriate spin-polarized electrons from the MBS, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling us to detect the presence of low-energy Majorana modes.
Two-particle Hanbury Brown--Twiss interferometry with chiral Majorana modes produces maximally entangled electron-hole pairs. We promote the electron-hole quantum number to an interferometric degree of freedom and complete the set of linear tools for single- and two-particle interferometry by introducing a key phase gate that, combined with a Mach-Zehnder, allows full electron-hole rotations. By considering entanglement witnesses built on current cross-correlation measurements, we find that the possibility of independent local-channel rotations in the electron-hole subspace leads to a significant boost of the entanglement detection power.
Majorana fermions (MFs) are exotic particles that are their own anti-particles. Recently, the search for the MFs occurring as quasi-particle excitations in solid-state systems has attracted widespread interest, because of their fundamental importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Here we study the quantum correlations between two spatially separate quantum dots induced by a pair of MFs emerging at the two ends of a semiconductor nanowire, in order to develop a new method for probing the MFs. We find that without the tunnel coupling between these paired MFs, quantum entanglement cannot be induced from an unentangled (i.e., product) state, but quantum discord is observed due to the intrinsic nonlocal correlations of the paired MFs. This finding reveals that quantum discord can indeed demonstrate the intrinsic non-locality of the MFs formed in the nanowire. Also, quantum discord can be employed to discriminate the MFs from the regular fermions. Furthermore, we propose an experimental setup to measure the onset of quantum discord due to the nonlocal correlations. Our approach provides a new, and experimentally accessible, method to study the Majorana bound states by probing their intrinsic non-locality signature.
Nonlocal entanglement between two quantum dots (QDs) can be generated through Majorana fermions. The two Majorana fermions at the ends of a one-dimensional topological superconductor form a nonlocal electronic level, which couples the occupation states of the two QDs located close to the two ends and brings the whole system into an entangled state, even at low temperatures and zero bias voltage. Upon introducing a charging energy by a capacitor, entanglement of the whole system can manifest itself through the nonlocal entanglement between the two QDs. Explicitly, the conditional probabilities of electron occupation on one QD with and without electron occupation on the other QD deviate from each other, with the difference proportional to the concurrence of quantum entanglement between the two QDs. Therefore detecting the difference in conditional probabilities, which is achievable experimentally by established techniques, provides evidence of the nonlocal nature of the fermion level constructed by the two end Majorana fermions.
Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R⁠, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H⁠, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (⁠λ/2⁠), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).