Phase-resolved joint spectra tomography of a ring resonator photon pair source using a silicon photonic chip

Abstract

The exponential growth of photonic quantum technologies is driving the demand of tools for measuring the quality of their information carriers. One of the most prominent is Stimulated Emission Tomography (SET), which uses classical coherent fields to measure the Joint Spectral Amplitude (JSA) of photon pairs with high speed and resolution. While the modulus of the JSA can be directly addressed from a single intensity measurement, the retrieval of the Joint Spectral Phase (JSP) is far more challenging and received minor attentions. However, a wide class of spontaneous sources of technological relevance, as chip integrated micro-resonators, have a JSP with a rich structure, that carries correlations hidden in the intensity domain. Here, using a compact and reconfigurable silicon photonic chip, it is measured for the first time the complex JSA of a micro-ring resonator photon pair source. The photonic circuit coherently excites the ring and a reference waveguide, and the interferogram formed by their stimulated fields is used to map the ring JSP through a novel phase reconstruction technique. This tool complements the traditionally bulky and sophisticated methods implemented so far, simultaneously minimizing the set of required resources.A PREPRINT -JANUARY 10, 2020 the modulus of the JSA, referred as the Joint Spectral Intensity (JSI), since it is directly measurable from the power of the stimulated field. Examples includes silicon nanowires [18], AlGaAs ridge waveguides [19], optical fibers [20,21], All-Pass resonators [22] and coupled rings [23]. A variation of SET, which implements Sum Frequency Generation (SFG), has been used to map the JSA of an array of evanescently coupled Lithium Niobate waveguides [24]. A method for the extraction of the complex JSA in multi-port devices, which implements DFG, has been proposed based on the eigenmode expansion of single channel excitations [25]. SET has been also extended to others degrees of freedom, like space [24] and polarization [26,27]. The Joint Spectral Phase (JSP) is of the same relevance of the JSI, but historically received minor attentions. The JSI itself is, however, an incomplete picture of the quantum state, since it hides the spectral correlations encoded in the phase domain [28]. As an example, only the lower bound of the Schmidt number can be estimated if the JSP is not known [19]. Beside quantum homodyne tomography of two photon states [29,30], which suffers the same time and resolution issues of spectrally resolved coincidence measurements, phase resolved applications of SET have been so far limited to in-line sources as waveguides [28,31] or cold atomic ensembles [32]. In all these works, the Pump, the Seed and the reference beams are all carved from the same laser source to guarantee mutual coherence, and fiber based interferometers are used to extract the JSP.Here, a novel technique which allows to measure the complex JSA of a double bus, integrated silicon ring resonator, is proposed and experimentally validated. The method exploits the on-chip inte...

A silicon source of heralded single photons at 2 μm

“…The unheralded g (2) results to be 1.67(2) at a power of 1.08 W, compatible with the simulated value of 1.66 (dashed line) calculated from the simulated joint spectral intensity (JSI). 31,36 The measured g (2) demonstrates that the source is closer to a thermal emission, justifying the experimental g…”

Beyond photon pairs: Nonlinear quantum photonics in the high-gain regime

“…19, we show the comparison between the joint spectral density measured by SET for a silicon micro ring resonator and the expected theoretical result. Finally, while most of the experiments have been focused on the JSD, there are also cases in which stimulated emission was used to determine the phase of the biphoton wavefunction [134,135].…”

Advances in Silicon Quantum Photonics

“…This was achieved by engineering a coherent phase reference beam with which to interfere the output of the stimulated emission tomorography. Similarly, the JSA of a silicon ring resonator was recently measured using straight waveguide as a nonlinear phase reference [187]. Finally, the spectral overlap of two photon pair source's JSAs corresponds exactly to the contrast of reverse HOM (rHOM) interference [171].…”