Heralding Two-Photon and Four-Photon Path Entanglement on a Chip

Generating quantum entanglement is not only an important scientific endeavor, but will be essential to realizing quantum-enhanced technologies, in particular, quantum-enhanced measurements with precision beyond classical limits. We investigate the heralded generation of multiphoton entanglement for quantum metrology using a reconfigurable integrated waveguide device in which projective measurement of auxiliary photons heralds the generation of path-entangled states. We use four and six-photon inputs, to analyze the heralding process of two- and four-photon NOON states—a superposition of $N$ photons in two paths, capable of enabling phase supersensitive measurements at the Heisenberg limit. Realistic devices will include imperfections; as part of the heralded state preparation, we demonstrate phase superresolution within our chip with a state that is more robust to photon loss.

Figure 1

Heralding multiphoton path-entangled states in a photonic chip. The waveguide circuit with coupling reflectivities ${\mathrm{DC}}_{1,2}=1/2$, ${\mathrm{DC}}_{3,4}=1/3$.

Figure 2

Heralded $|20⟩+|02⟩$ state. (a) Measurement of photon statistics of the heralded two-photon NOON state. (b) Testing coherence of the heralded two-photon NOON state by measuring the photon statistics after nonclassical interference at ${\mathrm{DC}}_2$ via a fiber Sagnac loop. Both distributions are normalized using single-photon detection rates to account for relative detector scheme, source, and waveguide coupling efficiencies. Error bars are given the standard deviation of detected events, assuming Poissonian statistics.

Figure 3

Superresolution with a heralded four-photon entangled state. (a) Single-photon fringes from inputting light into waveguide $b$ and varying the phase $\varphi$, displaying the expected pattern arising from classical interference pattern with period $2\pi$. Black circles and blue diamonds, respectively, represent the normalized single photons count rate detected at output $j$ and $k$. (b) The increased resolution interference pattern of manipulating $\varphi$ of the state $|3\colon\colon 1{⟩}_{e,f}^{\varphi }$ with period $\pi$. The four data points represent six-photon count rates integrated over four days and normalized using single-photon count rates to account for coupling efficiency over time. Coincidence rates arising from higher-photon number terms or otherwise were not subtracted from the data. Error bars are given the standard deviation of detected events, assuming Poissonian statistics. Blue sinusoidal plot of near unit contrast is plotted as a guide.

Figure 4

Heralded generation of the $|40⟩+|04⟩$ state. The distribution of photon statistics from measuring a heralded four-photon NOON state. The sixfold detection rates are normalized by single-photon detection rates to account for relative source, coupling, and detection scheme efficiencies. Error bars are given the standard deviation of detected events, assuming Poissonian statistics.