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

Alsing, Paul M.; Hach, Edwin E.

doi:10.1103/physreva.96.033847

Cited by 8 publications

(6 citation statements)

References 36 publications

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“…For biphoton generation arising from either the χ (2) process of Spontaneous Parametric Down-Conversion (SPDC), or the χ (3) process of Spontaneous Four-Wave Mixing (SFWM), Alsing and Hach (Alsing and Hach III, 2017a) consider a signal mode â, and an idler mode b circulating within the MRR, and here, we do the same.…”

Section: Biphoton Generation Within the Mrrmentioning

confidence: 99%

“…) (Raymer and McKinstrie 2013, Alsing and Hach 2017a, 2017b, where this time, ĤNL is included in Ĥsys . In the rotating reference frame, the equations for the signal and idler modes are given by: where g¢ k is the internal propagation loss for mode Î { } k a b , , and fk are corresponding Langevin noise operators added to preserve the canonical form of the output commutators.…”

Section: Bs Propagation Loss and Cavitiesmentioning

confidence: 99%

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Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion

Schneeloch

Knarr

Bogorin

et al. 2019

J. Opt.

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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.

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Section: Biphoton Generation Within the Mrrmentioning

confidence: 99%

Section: Bs Propagation Loss and Cavitiesmentioning

confidence: 99%

Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion

Schneeloch

Knarr

Bogorin

et al. 2019

J. Opt.

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“…Our current and future work is focused upon using the theoretical and computational tools we have developed so far in [1,3,12,23] and this current work to inform the design and to optimize the function of devices of high impact for Linear Quantum Optical Information processing, such as the Knill-Laflamme-Milburn (KLM) CNOT gate [24]. Further, we are investigating larger networks of directionally coupled silicon nanophonotonic waveguide/mrr arrays for possible quantum advantages with respect to communications, sensing and metrology [25,26].…”

Section: Summary and Discussionmentioning

confidence: 99%

“…I. Theory," [1] (designated AH-I) we developed the theory for entangled photon pair generation in a microring resonator (mrr) using a recent input-output formalism based on the work of Raymer and McKinstrie [2] and Alsing, et al [3] that incorporates the circulation factors that account for the multiple round trips of the fields within the cavity. In AH-I we considered biphoton pair generation within the mrr via both SPDC and SFWM processes, and computed the generated two-photon signal-idler intra-cavity and output state from a single bus (all-through) mrr.…”

Section: Introductionmentioning

confidence: 99%

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

Alsing

Hach

2017

Phys. Rev. A

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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.

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“…The transmission phases of the MRRs at resonance change abruptly and the group velocities reduce dramatically, providing an efficient way to slow the light wave. Such slow-light phenomenon has been explored to realize many critical optical components/devices, including the high-performance filter such as add-drop filters [64] and wavelength division multiplexers [65], [66], optical delay lines [67], Parity-Time (PT) symmetric devices [68], nonlinear light-wave and materials interaction such as four wave mixing [69], optical parametric generation [70], [86], single-photon/photon-pair source [71], [81], [88], frequency comb generation [92], optical quantum computing [84], as well as high-quality sensors [90], [85], [98], [96]. Depending on its geometry, two typical MRRs are actively studied, i.e., the circular MRRs and the racetrack MRRs.…”

Section: Introductionmentioning

confidence: 99%

High-Q Interstitial Square Coupled Microring Resonators Arrays

Liao

2020

IEEE J. Quantum Electron.

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The properties of the square array of coupled Microring Resonators (MRRs) with interstitial rings are studied. Dispersion behavior of the interstitial square coupled MRRs is obtained through the transfer matrix method with the Floquet-Bloch periodic condition. Analytical formulas of the eigen wave vectors, band gaps and eigen mode vectors are derived for the special cases of the interstitial square coupled MRRs array with identical couplers and the regular square coupled MRRs array without the interstitial rings. Then, the eigen modes' field distribution are calculated for each of the four eigen wave vectors for a given frequency through the secular equation. Finally, numerical simulation is performed for an interstitial square coupled MRRs array with identical couplers and a regular square coupled MRRs array. The simulation result verifies the analytical analysis. Finally, the loaded quality factors of the interstitial 5-ring configuration, the regular 4-ring configuration and the 1-ring configuration are obtained. It is found that the loaded quality factor of the interstitial 5-ring configuration is up to 20 times and 8 times as high as those of the 1-ring configuration and the regular 4-ring configuration respectively, mainly due to the degenerated eigen modes at the resonant frequency. Thus, the interstitial square coupled MRRs array has the great potential to form high-quality integrated photonics components, including filters and resonance based sensing devices like the parity-time symmetric sensors.

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

Cited by 8 publications

References 36 publications

Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion

Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion

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

High-Q Interstitial Square Coupled Microring Resonators Arrays

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