Microring resonators (MRR) are becoming a standard resource for highly efficient entangled photon pair generation. We examine the nonlinear processes in MRR using an input-output formalism that explicitly accounts for the contribution of the round trip circulation of the fields inside the MRR. This formalism reduces to the standard Langevin operator input-output formalism for cavities in the high cavity Q limit, near cavity resonances. Our approach is more general, applicable for arbitrary internal and bus-ring coupling losses, and away from resonances. We compare/contrast these two formalisms, and apply our approach to the output quantum state resulting from spontaneous parametric down conversion and spontaneous four wave mixing within the MRR. We compare our results to similar calculations employing the standard IO formalism, and note the role of the commutators of the noise operators on the undesired accidental singles rate.
Microring resonators (MRR) are becoming a standard resource for highly efficient entangled photon pair generation. We examine the nonlinear processes in MRR using an input-output formalism that explicitly accounts for the contribution of the round trip circulation of the fields inside the MRR. This formalism reduces to the standard Langevin operator input-output formalism for cavities in the high cavity Q limit, near cavity resonances. Our approach is more general, applicable for arbitrary internal and bus-ring coupling losses, and away from resonances. We compare/contrast these two formalisms, and apply our approach to the output quantum state resulting from spontaneous parametric down conversion and spontaneous four wave mixing within the MRR. We compare our results to similar calculations employing the standard IO formalism, and note the role of the commutators of the noise operators on the undesired accidental singles rate.
We investigate entangled photon-pair generation in a lossy microring resonator using an input-output formalism based on the work of M. G. Raymer and C. J. McKinstrie [Phys. Rev. A 88, 043819 (2013)] and P. M. Alsing et al. [Phys. Rev. A 95, 053828 (2017)] that incorporates circulation factors that account for the multiple round-trips of the fields within the cavity. We consider the nonlinear processes of spontaneous parametric down-conversion and spontaneous four-wave mixing, and we compute the generated biphoton signal-idler state from a single-bus microring resonator, along with the generation, coincidence-to-accidental, and heralding efficiency rates. We compare these generalized results to those obtained by previous works employing the standard Langevin input-output formalism.
We develop a general Hamiltonian treatment of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self- and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function.\n\nIn the limit of a low probability of pair production, photon pair production fficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical “seed” field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless enerated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption\nor free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis.\n\nBiphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This further allows estimation of the suitability of their associated photon pairs for various quantum information processing applications. As an alternative to dispersion engineering a channel waveguide photon pair source, it is calculated that microring resonators can very naturally produce nearly spectrally uncorrelated photon pairs, which behave very much like idealized single-mode photons and are thus useful for applications involving the interference of photons from multiple sources.
In this work we examine the entanglement of the output signal-idler squeezed vacuum state in the Heisenberg picture as a function of the coupling and internal propagation loss parameters of a microring resonator. Using the log negativity as a measure of entanglement for a mixed Gaussian state, we examine the competitive effects of the transfer matrix that encodes the classical phenomenological loss, as well as the matrix that that incorporates the coupling and internal propagation losses due to the quantum Langevin noise fields required to preserve the unitarity of the composite system (signal-idler) and environment (noise) structure.
Integrated photonics is emerging as a key technology for use in quantum information and communication. Driven by classical communication, which already has a swathe of scalable, efficient, and robust components, integrated photonics promises to transfer quantum science from a mere lab curiosity into a commercial reality. Chip-based quantum light sources are increasingly being recognized as a practical and high-performance alternative to bulky and power-hungry, table-top photon-pair sources. In particular, photon-pair sources based on spontaneous four-wave mixing in microring resonators (MRR) have emerged as a viable integrated photonic solution for quantum information and communication. This thesis relies on silicon nitride (Si3N4) MRR to realize narrowband, telecom photonpair sources. High quality factor MRRs are enabled by the low propagation losses in the Si3N4 platform; in this thesis, they are exploited to realize bright photon-pair sources with heralded spectral purity up to 0.98. Low quality factor MRRs are exploited for a proof-of-concept high-rate sequential time-bin entanglement with net visibilities up to 99.96 ± 0.03 %. For the goal of practical, real-world deployment of integrated photon-pair sources, it is not enough to demonstrate the performance of a single source. One also needs to demonstrate their high-performance operation in complex quantum networking protocols, such as entanglement swapping between genuinely independent sources. Here, for the first time, we demonstrate entanglement swapping between two independent, spatially separated, and asynchronously-pumped MRR photon-pair sources. Our sources operate in the continuous-wave regime, and time-resolved detection results in high Hong-Ou-Mandel (93.2 ±1.6 %) and entanglement swapping (91.2 ± 3.4 %) visibilities. Finally, to further improve our rates while maintaining high visibilities in multi-source interference scenarios, the origin of an on-chip-generated noise must be identified and mitigated. Here, we present our first efforts in the quest for tackling this notorious noise problem.
We present two complementary strategies for modeling nonlinear quantum optics in realistic resonant integrated optical devices, where scattering loss is present. In the first strategy, we model scattering loss as an effective absorption; in the second, we employ a Hamiltonian treatment, with the loss modelled as a coupling to a 'phantom' channel. As an example, we use these two approaches to model spontaneous four-wave mixing in (i) a ring-channel system and (ii) an add-drop system. We present the rates of photon pairs, broken pairs, and lost pairs for both systems, as well as the full biphoton wavefunction (BWF) including the effects of scattering. We find that for a high-finesse resonator coupled to an arbitrary number of channels, the full BWF can be extracted from the BWF associated with photon pairs in an experimentally accessible output channel.