Edwin E. Hach

Scalable Hong-Ou-Mandel manifolds in quantum-optical ring resonators

Quantum Information Processing, from cryptography to computation, based upon linear quantum optical circuit elements relies heavily on the ability offered by the Hong-Ou-Mandel (HOM) Effect to route photons from separate input modes into one of two common output modes. Specifically, the HOM Effect accomplishes the path entanglement of two photons at a time such that no coincidences are observed in the output modes of a system exhibiting the effect. In this paper, we prove in principle that a significant increase in the robustness of the HOM Effect can be accomplished in a scalable, readily manufactured nanophotonic system comprised of two waveguides coupled, on chip, to a ring resonator. We show that by operating such a device properly, one can conditionally bunch coincident input photons in a way that is far more robust and controllable than possible with an ordinary balanced beam splitter.

Photon-pair generation in a lossy microring resonator. I. Theory

We investigate entangled photon pair generation in a lossy microring resonator using an input-output formalism based on the work of Raymer and McKinstrie (Phys. Rev. A 88, 043819 (2013)) and 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.

Photon-pair generation in a lossy microring resonator. II. Entanglement in the output mixed Gaussian squeezed state

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 loss due to the quantum Langevin noise fields required to preserve unitarity of the composite system,(signal-idler) and environment (noise) structure.

An optical nonlinear sign shift gate using mircoring resonators

In this work we provide a derivation of a nonlinear sign gate (NLSG) configuration using microring resonators (mrr), and an examine of the probability of success as a function of its operational parameters. Such NLSG in a mrr extends the work of Knill-Laflamme-Milburn (KLM) version of an optical CNOT gate for quantum computing from a single point solution for the transmission coefficients using three beam splitters, to a manifold of solutions when the three beam splitters are replaced my three mrrs.

Silicon nanophotonic networks for quantum optical information processing

Silicon nanophotonics show a lot of promise as the basic architecture for quantum information processing devices. This is particularly the case in relation to the scalability of such devices. During this talk I will review our simple theoretical model of a structure that we have identified as a ‘fundamental circuit element’ for linear optical quantum information processing in silicon nanophotonics. In particular, we have shown that, owing to an effect we call Passive Quantum Optical Feedback (PQOF), the topology of this circuit element allows for certain possible operational advantages, in addition to inherent scalability, not expected in bulk linear optics. I will emphasize the extension of our work to larger networks, including the Knill-Laflamme-Milburn (KLM) Controlled-Not (CNOT) gate and its important constituent, the so-called Nonlinear Sign (NS) shifter. Further, I will discuss our ongoing effort to design and optimize scalable networks that seem to have useful applications in quantum metrology and sensing. In developing the discussion, I will examine recent developments related to incorporation of losses and spectral properties in such a way as to generalize our simple, continuous-wave (cw) model of essentially lossless operation. I will also discuss on-chip generation and control of entangled photons within the nanophotonic material itself, especially as related to potentially useful applications in information processing.

Quantum Silicon Photonics: Photon sources and Circuits

We report high performance ring resonator photon sources and the integration of the sources into quantum photonic circuits. We also discuss ring resonators as a building block for compact, reconfigurable, linear quantum optical circuits.

Theoretical analysis of on-chip linear quantum optical information processing networks

We present a quantum optical analysis of waveguides directionally coupled to ring resonators, an architecture realizable using silicon nanophotonics. The innate scalability of the silicon platform allows for the possibility of “on-chip” quantum computation and information processing. In this paper, we briefly review a comprehensive method for analyzing the quantum mechanical output of such a network for an arbitrary input state of the quantized, traveling electromagnetic field in the continuous wave (cw) limit. Specifically, we briefly review a recent theoretical result identifying a particular device topology that yields, via Passive Quantum Optical Feedback (PQOF), dramatic and unexpected enhancements of the Hong-Ou-Mandel Effect, an effect central to the operation of many quantum information processing systems. Next, we extend the analysis to our proposal for a scalable, on-chip realization of the Nonlinear Sign (NS) shifter essential for implementation of the Knill-Laflamme-Milburn (KLM) protocol for Linear Optical Quantum Computing (LOQC). Finally, we discuss generalizations to arbitrary networks of directionally coupled ring resonators along with possible applications is the areas of quantum metrology and sensitive photon detection.

Multi-photon interactions in travelling wave resonators

Here we present a fully quantum mechanical transfer function model for travelling wave whispering gallery mode resonators. Micro-resonators, such as ring and disk resonators, have been key to the development of high performance chip-scale photonic systems due to their compact footprint, sensitivity and low power operation. In this work we present the first understanding of these resonators to any arbitrary multi-photon state. This was achieved by developing a model that utilizes an efficient scheme for determining the quantum electrodynamic transfer functions relating the Bosonic input/output mode operators in the resonator. This approach has been applied to the understanding of both single photon and two-photon states. In this work we will present a key result on a resonant Hong-Ou-Mandel effect that is inherently realized for any resonator-waveguide coupling constants and can operate over a wide range of resonance conditions. Furthermore, the transfer function approach allows for the straightforward understanding of any resonator-waveguide network with arbitrary modes. This will directly enable the application of quantum resonators to the realization of robust, scalable and efficient Linear Optical Quantum Computing (LOQC) gates. Consequently, it is expected that resonators can be used for both Nonlinear Sign Shift and CNOT gates. And these gates can robustly controlled and efficiently tuned using standard electro-optic effects available in a variety of material systems, such as, Silicon.