Entangling Macroscopic Light States by Delocalized Photon Addition

Nicola Biagi, Luca S. Costanzo, Marco Bellini, and Alessandro Zavatta

Phys. Rev. Lett. 124, 033604 – Published 24 January 2020

Abstract

We present a scheme, based on the delocalized heralded addition of a single photon, to entangle two or more distinct field modes, each containing arbitrary light states. A high degree of entanglement can in principle endure light states of macroscopic intensities and is expected to be particularly robust against losses. We experimentally establish and measure significant entanglement between two identical weak laser pulses containing up to 60 photons each.

Received 11 June 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.033604

Physics Subject Headings (PhySH)

Entanglement detection Entanglement production Quantum optics Quantum state engineering Quantum states of light

Homodyne & heterodyne detection

Atomic, Molecular & Optical

Authors & Affiliations

Nicola Biagi , Luca S. Costanzo, Marco Bellini ^*, and Alessandro Zavatta ^†

Istituto Nazionale di Ottica (CNR-INO), L.go E. Fermi 6, 50125 Florence, Italy and LENS and Department of Physics & Astronomy, University of Firenze, 50019 Sesto Fiorentino, Florence, Italy

^*Corresponding author. bellini@ino.it
^†Corresponding author. alessandro.zavatta@ino.it

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Issue

Vol. 124, Iss. 3 — 24 January 2020

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Images

Figure 1
Conceptual experimental scheme to perform a coherent single-photon addition on two different input modes, both containing a coherent state $| α ⟩$ . A click in a single-photon detector $D_{1}$ , placed after a balanced beam splitter BS mixing the herald modes of two photon-addition modules based on parametric down-conversion (PDC) [8, 13], generates entanglement between the two output modes.
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Figure 2
Theoretical entanglement (quantified via the negativity of the partial transpose, NPT) of the odd and even entangled states (yellow and blue solid curves, respectively), according to Eq. (3). Dashed curves present the numerically calculated NPT behavior when both the modes are subjected to 40% of losses.
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Figure 3
Experimental setup for coherent single-photon addition on two different input temporal modes, both containing a coherent state $| α ⟩$ . It is based on a mode-locked laser emitting 1.5-ps pulses at 786 nm with a repetition rate of 81 MHz, providing: the local oscillator (LO) for homodyne detection, the pump for a parametric down-conversion (PDC) process after a frequency-doubling stage (SHG), and the seed coherent states for photon addition in the PDC crystal. PDC photons emitted in the idler channel pass through a set of spectral and spatial filters (F) before entering an unbalanced, fiber-based, Mach-Zehnder interferometer. A detection event by the single-photon detector ( $D_{1}$ ) placed at one of the interferometer outputs heralds the successful implementation of a delocalized single-photon addition, meaning that entanglement has been conditionally generated between the two temporal modes. The state superposition phase $φ$ is remotely controlled by varying the relative phase between the interferometer arms via a fine adjustment of an air-gap length. A feedback loop based on the interference of a counterpropagating pulse train injected in the unused interferometer output port provides phase stabilization.
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Figure 4
Experimental (green dots) and calculated NPT for the odd entangled states (yellow solid curves) as a function of the mean photon number $\bar{n}$ (the calculated NPT curves for even entangled states are also shown in blue for reference). Upper panel: “global-phase-averaged tomography.” The theoretical curves are calculated with a detection efficiency $η = 68 %$ . Bottom panel: Tomography based on correlated quadrature fluctuations shows significant entanglement between modes with up to about 60 photons each. The theoretical curves are calculated by considering a detection efficiency $η = 64 %$ together with a noise of $π / 100$ on both the state phase $φ$ and the LO global phase. In addition, the observed value of entanglement is mainly limited by the state preparation efficiency, degrading with increasing mean photon number due to a nonperfect Mach-Zehnder visibility of 99.6%. Statistical errors are evaluated with a bootstrap method using 100 resampled quadrature data sets. For each data set we reconstructed the density matrix and calculated the NPT. Error bars in the plot are estimated as the standard deviation of these NPT values and are smaller than the corresponding dot symbols.
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