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We demonstrate that an integrated silicon microring resonator is capable of efficiently producing photon pairs that are completely unentangled; such pairs are a key component of heralded single photon sources. A dual-channel interferometric coupling scheme can be used to independently tune the quality factors associated with the pump and signal and idler modes, yielding a biphoton wavefunction with Schmidt number arbitrarily close to unity. This will permit the generation of heralded single photon states with unit purity.

Here we demonstrate quantum interference of photons on a Silicon chip produced from a single ring resonator photon source. The source is seamlessly integrated with a Mach-Zehnder interferometer, which path entangles degenerate bi-photons produced via spontaneous four wave mixing in the Silicon ring resonator. The resulting bi-photon N00N state is controlled by varying the relative phase of the integrated Mach-Zehnder interferometer, resulting in high two-photon interference visibilities of V~96%. Furthermore, we show that the interference can be produced using pump wavelengths tuned to all of the ring resonances accessible with our tunable lasers (C+L band). This work is a key demonstration towards the simplified integration of multiple photon sources and quantum circuits together on a monolithic chip, in turn, enabling quantum information chips with much greater complexity and functionality.

Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of 7.11 ± .04 ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 10 18 -times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

As a tutorial, we examine the absolute brightness and number statistics of photon pairs generated in Spontaneous Parametric Down-Conversion (SPDC) from first principles. In doing so, we demonstrate how the diverse implementations of SPDC can be understood through a single common framework, and use this to derive straightforward formulas for the biphoton generation rate (pairs per second) in a variety of different circumstances. In particular, we consider the common cases of both collimated and focused gaussian pump beams in a bulk nonlinear crystal, as well as in nonlinear waveguides and microring resonators. Furthermore, we examine the number statistics of down-converted light using a non-perturbative approximation (the multi-mode squeezed vacuum), to provide quantitative formulas for the relative likelihood of multi-pair production events, and explore how the quantum state of the pump affects the subsequent statistics of the downconverted light. Following this, we consider the limits of the undepleted pump approximation, and conclude by performing experiments to test the effectiveness of our theoretical predictions for the biphoton generation rate in a variety of different sources.

In this work we examine loss in ring resonator networks from an "operator valued phasor addition" approach (or OVPA approach) which considers the multiple transmission and cross coupling paths of a quantum field traversing a ring resonator coupled to one or two external waveguide buses. We demonstrate the consistency of our approach by the preservation of the operator commutation relation of the out-coupled bus mode. We compare our results to those obtained from the conventional quantum Langevin approach which introduces noise operators in addition to the quantum Heisenberg equations in order to preserve commutation relations in the presence of loss. It is shown that the two expressions agree in the neighborhood of a cavity resonance where the Langevin approach is applicable, whereas the operator valued phasor addition expression we derive is more general, remaining valid far from resonances. In addition, we examine the effects of internal and coupling losses on the Hong-Ou-Mandel manifold first discussed in Hach et al. Phys. Rev.A 89, 043805 (2014) that generalizes the destructive interference of two incident photons interfering on a 50:50 beam splitter (HOM effect) to the case of an add/drop double bus ring resonator.

We propose a scalable version of a KLM CNOT gate based upon integrated waveguide microring resonators (MRR), vs the original KLM-approach using beam splitters (BS). The core element of our CNOT gate is a nonlinear phase-shift gate (NLPSG) using three MRRs, which we examine in detail. We find an expanded parameter space for the NLPSG over that of the conventional version. Whereas in all prior proposals for bulk optical realizations of the NLPSG the optimal operating point is precisely a single zero dimensional manifold within the parameter space of the device, we find conditions for effective transmission amplitudes which define a set of one dimensional manifolds in the parameters spaces of the MRRs. This allows for an unprecedented level flexibility in operation of the NLPSG that and allows for the fabrication of tunable MRR-based devices with high precision and low loss. In 2001, Knill, Laflamme and Milburn (KLM) proposed an efficient scheme for linear optical quantum computing [1]. The KLM proposal is based upon a probabilistic, two-qubit, Controlled NOT (CNOT) gate along with local unitary operations on individual qubits. Some years later, Okamoto, et. al., demonstrated experimentally a realization the KLM CNOT gate in bulk optics [2]. The KLM CNOT gate, shown schematically in Fig. (1), is itself composed of two Non-Linear Phase Shift Gates (NLPSG), the essential two-qubit element of the CNOT gate. Each NLPSG is a probabilistic device involving three optical modes, that, in the bulk optical realization encounter strategically placed and optimally reflective beam splitters that appropriately route the free space evolution of photonic states through the system. The KLM CNOT gate performs a two qubit operation, namely, a flip of the target qubit (t) conditioned on the value of the control qubit (c), as CNOT c t c t i j i i j    .

Silicon ring resonators are used as photon pair sources by taking advantage of silicon's large third order nonlinearity with a process known as spontaneous four wave mixing. These sources are capable of producing pairs of indistinguishable photons but typically suffer from an effective 50% loss. By slightly decoupling the input waveguide from the ring, the drop port coincidence ratio can be significantly increased with the tradeoff being that the pump is less efficiently coupled into the ring. Ring resonators with this design have been demonstrated having coincidence ratios of ∼ 96% but requiring a factor of ∼ 10 increase in the pump power. Through the modification of the coupling design that relies on additional spectral dependence, it is possible to achieve similar coincidence ratios without the increased pumping requirement. This can be achieved by coupling the input waveguide to the ring multiple times, thus creating a Mach-Zehnder interferometer. This coupler design can be used on both sides of the ring resonator so that resonances supported by one of the couplers are suppressed by the other. This is the ideal configuration for a photon-pair source as it can only support the pump photons at the input side while only allowing the generated photons to leave through the output side. Recently, this device has been realized with preliminary results exhibiting the desired spectral dependence and with a coincidence ratio as high as ∼ 97% while allowing the pump to be nearly critically coupled to the ring. The demonstrated near unity coincidence ratio infers a near maximal heralding efficiency from the fabricated device. This device has the potential to greatly improve the scalability and performance of quantum computing and communication systems.