On-chip generation of heralded photon-number states

Abstract

Beyond the use of genuine monolithic integrated optical platforms, we report here a hybrid strategy enabling on-chip generation of configurable heralded two-photon states. More specifically, we combine two different fabrication techniques, i.e., non-linear waveguides on lithium niobate for efficient photon-pair generation and femtosecond-laser-direct-written waveguides on glass for photon manipulation. Through real-time device manipulation capabilities, a variety of path-coded heralded two-photon states can be produced, ranging from product to entangled states. Those states are engineered with high levels of purity, assessed by fidelities of 99.5 ± 8% and 95.0 ± 8%, respectively, obtained via quantum interferometric measurements. Our strategy therefore stands as a milestone for further exploiting entanglement-based protocols, relying on engineered quantum states, and enabled by scalable and compatible photonic circuits.

Figure 1. Integrated tunable N00N state generator.

A ps-laser at 712 nm is coupled to an integrated directional coupler (block I on the left) to simultaneously pump two PPLN/ws (block II in the center). Each produces pairs of photons at 1310/1560 nm by SPDC. Each pair is then coupled to the state-engineering chip (block III on the right) and are deterministically separated by means of integrated WDMs. The two 1310 nm photons herald the complementary 1560 nm photons routed towards a Mach-Zehnder interferometer (MZI), which can be phase-controlled using a thermo-optic, voltage-driven, transducer placed over one of its two arms. Detection scheme: the photons are collected using single mode optical fibers. A filtering stage selects a single temporal mode per pulse. Finally, quantum correlations are measured by recording 4-fold coincidences using two detectors at the two output modes of the MZI, triggered by the detection of two heralding photons in the external modes. Filtering stage: fiber Bragg gratings (FBG) filters, wavelength-division multiplexers (WDM), Detection system: avalanche photodiodes (APD), time-to-digital converter (TDC), DC: 50/50 coupler, V: voltage controller, δt: laser pulse duration, F: laser repetition frequency.

Figure 2. Phase settings dependent coincidence histograms.

The TDC permits the measurement of quantum correlations with a start and a stop given from the heralded detectors, and ΔT is referred to as time interval between associated “start” and “stop” events. (a1) When the two photons enter the MZI simultaneously, they interfere according to Eq. 1. We therefore observe two-photon interference, associated with fringes with a period of π for ΔT = 0. (a2) Single-photon interference can also be observed for events when only one photon-pair has been generated in one of the two PPLN/ws with time interval ΔT = nτ ≠ 0, (n = 0, ±1, ±2…). Since the heralded detectors are only triggered according to the detection scheme described in the main text (see also Fig. 1), we observe single-photon interference patterns with a period of 2π. (b) Coincidence histogram recorded for 3 different phase settings. The coincidence peak at ΔT = 0 comes from simultaneous detection events and is associated with two-photon interference. Note that the coincidence peaks that rise at ΔT = nτ are associated with single photon interference. As can be seen, and as predicted by Eq. 2, no coincidence peak emerges for Δϕ = 3π/2 (coalescence effect) while it rises up for other phase settings.

Figure 3. Experimental results.

Interference patterns recorded at the output of the device as a function of the phase setting in the MZI. Here blue and red data are given for two-photon and single photon interference, respectively. The uncertainty associated with each point has been calculated using standard squared root deviation associated with the Poissonian distribution of the photocounts. The curves are fits of Eqs 5 and 6 to the experimental data where the only free parameters are the visibility and the amplitude.

Figure 4. Calibration of the phase of the MZI as a function of the applied voltage.

The phase control is achieved using an external voltage generation that creates a temperature gradient between the two arms of the MZI. The temperature gradient increases as a function of the applied voltage in a non-linear way due to the thermal diffusion into the chip (The red line is a guide to the eye).