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The entangled photons generation in third order nonlinearity of spontaneous parametric down conversion by whispering gallery mode resonator

Jing-Ming Cao, Jolly Xiaver

Published Oct 25, 2017• 0 citations
Publisher

Abstract

We manipulated the simulation and apparatus to generate the entangled quantum photons by the enhanced higher quality factor in waveguide of whispering gallery mode resonator in silica microsphere. As the several nonlinear optics effects have been validated in micro-disk (lithium niobate materials based), others micro-cavity (microfiber and micro ring on the chip) and second harmonic generation (SHG) on the surface of silica microsphere because of the characterization of enhanced higher quality factor Q and smaller volume mode in these resonator. However until now for the second third nonlinearity of spontaneous parametric down conversion (SPDC), third order nonlinearity of spontaneous parametric down conversion (TOSPDC) and spontaneous four wave mixing (SFWM) in whispering gallery mode (WGM) resonator of silica microsphere rarely have not been fully investigated and verified to generate the triple and pair entangled photons where are widely applied on the applications of biosensor, quantum communications and spectroscopy, respectively. Specially, the features of silica microsphere have attracted many applications due to the simple fabrication, simplified materials melted by silica fiber. The work we demonstrated in this paper based on the breaking of the dispersion rules to make perfect phase matching in normal dispersion in silica microsphere depending on the blue laser spectrum in visible spectrum, then manipulated the modified size of microsphere to detune the pump laser of free spectral range (FSR) and both shift the geometrical dispersion are characterized in the variation of FSR given by (see PDF for equation), where n is refractive index, R is the microspheres radius and m is mode numbers in resonator, to compensate the materials dispersion given by (see PDF for equation), where c is the speed of light and λ is pump laser wavelength to fulfill the perfect phase matching in parametric down conversion regimes and the modeling fabrication coupling results also will be presented.

DOI
10.1117/12.2285365

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We manipulated the simulation and apparatus to generate the entangled quantum photons by the enhanced higher quality factor in waveguide of whispering gallery mode resonator in silica microsphere. As the several nonlinear optics effects have been validated in micro-disk (lithium niobate materials based), others micro-cavity (microfiber and micro ring on the chip) and second harmonic generation (SHG) on the surface of silica microsphere because of the characterization of enhanced higher quality factor Q and smaller volume mode in these resonator. However until now for the second third nonlinearity of spontaneous parametric down conversion (SPDC), third order nonlinearity of spontaneous parametric down conversion (TOSPDC) and spontaneous four wave mixing (SFWM) in whispering gallery mode (WGM) resonator of silica microsphere rarely have not been fully investigated and verified to generate the triple and pair entangled photons where are widely applied on the applications of biosensor, quantum communications and spectroscopy, respectively. Specially, the features of silica microsphere have attracted many applications due to the simple fabrication, simplified materials melted by silica fiber. The work we demonstrated in this paper based on the breaking of the dispersion rules to make perfect phase matching in normal dispersion in silica microsphere depending on the blue laser spectrum in visible spectrum, then manipulated the modified size of microsphere to detune the pump laser of free spectral range (FSR) and both shift the geometrical dispersion are characterized in the variation of FSR given by (see PDF for equation), where n is refractive index, R is the microspheres radius and m is mode numbers in resonator, to compensate the materials dispersion given by (see PDF for equation), where c is the speed of light and λ is pump laser wavelength to fulfill the perfect phase matching in parametric down conversion regimes and the modeling fabrication coupling results also will be presented.
Cavity-assisted spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (SFWM) in nonlinear optical materials are practical and versatile methods to generate narrowband time-energy entangled photon pairs. Time-energy entangled photons with tailored spectro-temporal properties are particularly useful for efficient quantum optical interfaces. In this work we study the generation of photon pairs in cavity-assisted SPDC and SFWM for the general case of off-resonant conversion, namely, when the frequencies of the generated photons do not match the cavity resonances. Such a frequency mismatch in particular depends on temperature and requires an additional control in the experiment. First, we propose a generic model, for description of cavity-assisted SPDC and SFWM. We show that in both processes the mismatch reduces the generation rate of photons, distorts the spectrum and the auto-correlation function of the generated fields, as well as affects the photon generation dynamics. Second, we verify the results experimentally using parametric generation of photon pairs in a nonlinear whispering gallery mode resonator (WGMR) as an experimental platform with controlled frequency mismatch. Our work reveals the role of the frequency mismatch in the photon generation process and shows a way to control it. Obtained results constitute one more step in the direction of full control over the spectro-temporal properties of entangled photon pairs and the heralded generation of single-photon pulses with a tailored temporal mode.
Summary form only given, as follows: The high Q whispering gallery modes of silica microspheres are promising for quantum optics and nonlinear optics experiments involving atoms and photons stored in very small volumes. We have developed the technology of these resonators, learning how to couple light in and out through optical fibers, how to obtain and measure record Q factors, and how to probe, by near-field optical microscopy, the electric field distribution immediately outside the sphere. Whispering gallery mode lasers have also been obtained with microspheres made of silica doped with neodymium ions. We describe these experiments and discuss projects involving the coupling of whispering gallery modes to single atoms or ions to perform cavity QED experiments in the optical domain.
Parametric up- and down-conversion require phase matching between the generating and generated wavelengths, introducing strict requirements on the refractive index dispersion of materials used for this nonlinear processes. Optical microfibers can exploit the different modal overlap with core and cladding materials to phase match different modes at the required wavelengths. Intermodal phase-matching has been successfully exploited in optical microfibres to generate second- and third-harmonics, both in straight waveguides and related resonators. The simultaneous generation of guided higher harmonics also allowed to exploit other nonlinear effects like four wave mixing to generate light at short wavelengths in the UV part of the spectrum. Parametric down-conversion allows to generate entangled photons, but with efficiencies significantly smaller than their up-conversion processes because of their reliance of spontaneous photons generation from vacuum. The use of more complex architectures, based on multiple coupled waveguides, allows to achieve a quasi-phase matching condition, thus a sizeable improvement on the overall conversion efficiency.
The intrinsic third-order nonlinearity in silicon has proven it to be quite useful in the field of quantum optics. Silicon is suitable for producing time-correlated photon pairs that are sources of heralded single-photon states for quantum integrated circuits. A quantum signal source in the form of single photons is an inherent requirement for the principles of quantum key distribution technology for secure communications. Here, we present numerical simulations of a silicon ring with a 6 μ m radius side-coupled with a bus waveguide as the source for the generation of single photons. The photon pairs are generated by exploring the process of degenerate spontaneous four-wave mixing (SFWM). The free spectral range (FSR) of the ring is quite large, simplifying the extraction of the signal/idler pairs. The phase-matching condition is considered by studying relevant parameters like the dispersion and nonlinearity. We optimize the ring for a high quality factor by varying the gap between the bus and the ring waveguide. This is the smallest ring studied for photon pair generation with a quality factor in the order of 10 5 . The width of the waveguides is chosen such that the phase-matching condition is satisfied, allowing for the propagation of fundamental modes only. The bus waveguide is pumped at one of the ring resonances with the minimum dispersion (1543.5 nm in our case) to satisfy the principle of energy conservation. The photon pair generation rate achieved is comparable to the state of the art. The photon pair sources exploiting nonlinear frequency conversion/generation processes is a promising alternative to atom-like single-photon emitters in the field of integrated photonics. Such miniaturized structures will benefit future on-chip architectures where multiple single-photon source devices are required on the same chip.
Nonlinear wavelength conversion is essential for many classical and quantum pho-tonic applications. The underlying second-order nonlinear optical processes, however, generally exhibit limited spectral bandwidths that impact their application potential. Here we use a high-Q X-cut lithium niobate microdisk resonator to demonstrate both second-harmonic generation and spontaneous parametric down-conversion on chip. In particular, our lithium niobate microresonator, with its wide-range cyclic phase matching and rich optical mode structures, is able to achieve ultra-broadband spontaneous parametric down-conversion, with a bandwidth over 400 nm, inferred from recorded spectra of the down-converted photons. The produced biphoton pairs exhibit strong temporal correlation, with a coincidence-to-accidental ratio measured to be 43.1. Our device is promising for integrated quantum photonics where optical frequency could be used as a degree of freedom for signal processing.