Photon number encoding: superposition, entanglement and Beyond

A two-level system, excited under a pulsed resonant drive of area θ, emits photon-number superposition states composed by vacuum and a single photon in the form cos(θ/2)|├ 0⟩+sin(θ/2)|├ 1⟩. [1,2] It has been observed that such superposition states may affect the performance of heralded quantum gates, and they could be useful in photon-based quantum information protocols. [3] For example, these states have been recently used in a teleportation scheme. [4] In parallel, recent experiments with natural and artificial atoms, using a sequential two-pulse excitation, have demonstrated the generation of time-entangled states of the form 1/√2(|├ 0_e 0_l ⟩+|├ 1_e 1_l ⟩) or 1/√2(|├ 1_e 0_l ⟩+|├ 0_e 1_l ⟩), where the subindex e and l refer to early and late time-bins, respectively. [5,6] The generation of such entanglement is rooted to the atomic spontaneous emission mechanism, and it is easily scalable towards multi-partite entanglement simply by adding more consecutive laser pulses.
In this talk, we will discuss such superposition and entanglement generation schemes and show recent experimental results to generate high-dimensional entanglement (encoded in the photon number basis) from a three-level system (a biexciton-exciton cascade in a semiconductor quantum dot), using again a simple excitation scheme composed by two delayed resonant pulses. These complex states could offer some advantageous solutions in quantum communication protocols. [7]

[1] J. C. Loredo et al., Generation of Non-Classical Light in a Photon-Number Superposition, Nat. Photonics 13, 803 (2019).
[2] Y. Karli et al., Controlling the Photon Number Coherence of Solid-State Quantum Light Sources for Quantum Cryptography, Npj Quantum Inf 10, 1 (2024).
[3] I. M. de B. Wenniger et al., Photonic Quantum Interference in the Presence of Coherence with Vacuum, arXiv:2401.01187.
[4] B. Polacchi, F. Hoch, G. Rodari, S. Savo, G. Carvacho, N. Spagnolo, T. Giordani, and F. Sciarrino, Quantum Teleportation of a Genuine Vacuum-One-Photon Qubit Generated via a Quantum Dot Source, arXiv:2310.20521.
[5] S. C. Wein et al., Photon-Number Entanglement Generated by Sequential Excitation of a Two-Level Atom, Nat. Photon. 16, 5 (2022).
[6] J.-R. Álvarez, M. IJspeert, O. Barter, B. Yuen, T. D. Barrett, D. Stuart, J. Dilley, A. Holleczek, and A. Kuhn, How to Administer an Antidote to Schrödinger’s Cat, J. Phys. B: At. Mol. Opt. Phys. 55, 054001 (2022).
[7] A. C. Santos, C. Schneider, R. Bachelard, A. Predojević, and C. Antón-Solanas, Multipartite Entanglement Encoded in the Photon-Number Basis by Sequential Excitation of a Three-Level System, Opt. Lett. 48, 6332 (2023).