Spontaneous four-wave mixing in lossy microring resonators

Vernon, Z.; Sipe, J. E.

doi:10.1103/physreva.91.053802

Cited by 68 publications

(97 citation statements)

References 27 publications

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“…Spontaneous FWM, which is also sometimes referred to as parametric fluorescence, is a purely quantum phenomenon that results from the coupling between the intracavity pump photons and the vacuum fluctuations of the various sidemodes. The applications of spontaneous FWM belong to the area of quantum optics engineering, where one of the main challenge is the generation of entangled twin-photon pairs with chip-scale RRs [78][79][80][81][82][83][84][85][86][87][88][89][90]. These photon pairs are expected to play a key role in quantum communication protocols.…”

Section: Quantum Applicationsmentioning

confidence: 99%

Kerr optical frequency combs: theory, applications and perspectives

Chembo

2016

Nanophotonics

137

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Abstract:The optical frequency comb technology is one of the most important breakthrough in photonics in recent years. This concept has revolutionized the science of ultra-stable lightwave and microwave signal generation. These combs were originally generated using ultrafast mode-locked lasers, but in the past decade, a simple and elegant alternative was proposed, which consisted in pumping an ultra-high-Q optical resonator with Kerr nonlinearity using a continuous-wave laser. When optimal conditions are met, the intracavity pump photons are redistributed via four-wave mixing to the neighboring cavity modes, thereby creating the so-called Kerr optical frequency comb. Beyond being energy-efficient, conceptually simple, and structurally robust, Kerr comb generators are very compact devices (millimetric down to micrometric size) which can be integrated on a chip. They are, therefore, considered as very promising candidates to replace femtosecond mode-locked lasers for the generation of broadband and coherent optical frequency combs in the spectral domain, or equivalently, narrow optical pulses in the temporal domain. These combs are, moreover, expected to provide breakthroughs in many technological areas, such as integrated photonics, metrology, optical telecommunications, and aerospace engineering. The purpose of this review article is to present a comprehensive survey of the topic of Kerr optical frequency combs. We provide an overview of the main theoretical and experimental results that have been obtained so far. We also highlight the potential of Kerr combs for current or prospective applications, and discuss as well some of the open challenges that are to be met at the fundamental and applied level.

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Section: Quantum Applicationsmentioning

confidence: 99%

Kerr optical frequency combs: theory, applications and perspectives

Chembo

2016

Nanophotonics

137

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“…For the purposes of our discussion the density operator ρ OM is understood to be decomposed only in terms of the vacuum and total one-photon probabilities. We assume the system is pumped by a pulse with bandwidth comparable to that of the resonator modes, almost eliminating the impurity in the heralded OM state that arises from spectral correlations between the OM and HM photons [5,6].…”

Section: Introductionmentioning

confidence: 99%

No free lunch: the trade-off between heralding rate and efficiency in microresonator-based heralded single photon sources

2016

Self Cite

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Generation of heralded single photons has recently been demonstrated using spontaneous four-wave mixing in integrated microresonators. While the results of coincidence measurements on the generated photon pairs from these systems show promise for their utility in heralding applications, such measurements do not reveal all of the effects of photon losses within the resonator. These effects, which include a significant degradation of the heralding efficiency, depend strongly on the relative strengths of the coupling of the ring modes to loss modes and channel modes. We show that the common choice of critical coupling does not optimize the rate of successfully heralded photons, and derive the coupling condition needed to do so, as well as the condition needed to maximize the rate of coincidence counts. Optimizing these rates has a considerable negative effect on the heralding efficiency.Heralded single photons are an important resource both for optical quantum information processing, and for fundamental investigations of nonlinear quantum optics at the single photon level. There is particular interest in developing monolithically integrated sources of heralded single photons, which would enable their use in an onchip optical setting. Several such implementations have recently been demonstrated using spontaneous four-wave mixing (SFWM) in integrated microresonators [1][2][3][4].In typical implementations each photon of a generated pair is emitted into one of two distinct optical modes: a heralding mode (HM) carries a herald photon, the presence of which then indicates the existence of a single photon in an output mode (OM). These modes might correspond to the signal and idler fields generated by SFWM in a microresonator [1,3,5], or to the two outputs of a degenerate photon pair splitter [2]. By discarding experimental runs in which no heralding photon is detected in the HM, the experimenter effectively post-selects on those runs in which a single photon is present in the OM. In an ideal device, detection of an HM photon would guarantee the existence of an OM photon. In practice, even assuming perfect detection efficiency, photon losses within the photon pair source lead to events in which the herald photon is detected but the OM photon is lost. After detecting the herald, the OM mode cannot therefore be represented as the desired pure state ρ OM = |1 1|, but rather ρ OM = P vac |0 0| + P 1 |1 1|, where P vac corresponds to the probability of losing the OM photon given the successful generation of a photon pair and subsequent detection of the HM photon, and P 1 = 1 − P vac . The existence of this vacuum probability degrades the utility of the heralding device: if P vac is significant the very purpose of the herald is compromised. Note that this narrative neglects the effects of spectral correlation between the signal and idler photons, which would lead to the * zachary.vernon@utoronto.ca one-photon state itself being expressed not as |1 1|, but as a mixture of states involving a photon at different frequencie...

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“…where the value of g spdc (ω) and g sf wm (ω) [12,13] depend on the volume V ring of the ring mode, and the nonlinear susceptibilities χ (2) and χ (3) are accessed uniformly in the ring. Heren is the average index of refraction of the ring (assumed constant) and 0 is the permittivity of free space.…”

Section: B Derivation Of Output Operators From Input and Noise Operamentioning

confidence: 99%

“…where we have taken eral [7,13,15,32,34], when the field operators inside the mrr are decomposed in terms of their spatial Fourier components the spatial integral produces a phase matching contribution term,…”

Section: The Output Two-photon Signal-idler Statementioning

confidence: 99%

“…Such high-Q mircoring resonators exhibit nonlinear optical properties allowing for biphoton generation arising from the χ (2) processes of spontaneous parametric down conversion (SPDC), and the χ (3) processes of spontaneous four-wave mixing (SFWM). Much theoretical research has been devoted to study the generation of entangled photon pair within cavities and mrr in the weak pump field driving limit [2,[7][8][9][10][11][12][13][14], and more recently in the strong pump field regime [15] where higher order nonlinear effects such as self-phase and cross-phase modulation become important.…”

Section: Introductionmentioning

confidence: 99%

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

Alsing

Hach

2017

Phys. Rev. A

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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.

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Spontaneous four-wave mixing in lossy microring resonators

Cited by 68 publications

References 27 publications

Kerr optical frequency combs: theory, applications and perspectives

Kerr optical frequency combs: theory, applications and perspectives

No free lunch: the trade-off between heralding rate and efficiency in microresonator-based heralded single photon sources

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

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