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arXiv:1804.06921 · Physical Review Letters

All-Optical Control of Linear and Nonlinear Energy Transfer via the Zeno Effect

Xiang Guo, Chang‐Ling Zou, Liang Jiang, Hong X. Tang

Published May 16, 2018• 26 citations
arXivHTMLPDF

Abstract

Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- (χ^{(2)}) or third- (χ^{(3)}) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this paper we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric (χ^{(2)}) coupling to a lossy ancillary mode shortens the lifetime of the target photonic mode and suppresses its density of states, preventing the photon emissions into the target photonic mode via the Zeno effect. Such an effect is then used to control the stimulated four-wave mixing process and realize a suppression ratio of 34.5.

DOI
10.1103/physrevlett.120.203902

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Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- (χ^{(2)}) or third- (χ^{(3)}) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this paper we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric (χ^{(2)}) coupling to a lossy ancillary mode shortens the lifetime of the target photonic mode and suppresses its density of states, preventing the photon emissions into the target photonic mode via the Zeno effect. Such an effect is then used to control the stimulated four-wave mixing process and realize a suppression ratio of 34.5.
Genuine quantum interference between independent nonlinear processes of different order provides a route to coherent control that cannot be reduced to a classical field interference. Here we present an all-optical analogue of coherent carrier injection by exploiting interference between second- and third-order quantum nonlinear processes in an integrated photonic platform. Photon pairs generated via spontaneous parametric down-conversion and spontaneous four-wave mixing coherently contribute to the same final two-photon state, resulting in a phase-dependent modulation of both the generation rate and the spectral structure of the emitted biphoton state. We illustrate the features of such interference and how it can be used to shape biphoton wavefunctions and their quantum correlations. These results identify interference between nonlinear processes of different order as a distinct form of coherent quantum control within quantum nonlinear optics.
Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler are studied. The asymmetric nonlinear optical coupler is composed of a linear waveguide (χ (1)) and a nonlinear waveguide (χ(2)) interacting with each other through the evanescent waves. The nonlinear waveguide has quadratic nonlinearity and it operates under second harmonic generation. A completely quantum mechanical description is used to describe the system. The closed form analytic solutions of Heisenberg's equations of motion for the different field modes are obtained using Sen-Mandal perturbative approach. In the coupler, the linear waveguide acts as a probe on the system (nonlinear waveguide). The effect of the presence of the probe (linear waveguide) on the photon statistics of the second harmonic mode of the system is considered as quantum Zeno and anti-Zeno effects. Further, it is also shown that in the stimulated case, it is easy to switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the asymmetric coupler.
Four Wave Mixing (FWM) is the main nonlinear interaction in integrated silicon devices, which finds diffuse use in all-optical signal processing and wavelength conversion. Despite the numerous works on coupled resonator devices, which showed record conversion efficiencies and broadband operation, the possibility to coherently control the strength of the stimulated FWM interaction on a chip has received very limited attention. Here, we demonstrate both theoretically and experimentally, the manipulation of FWM in a photonic molecule based on two side coupled silicon microring resonators. The active tuning of the inter-resonator phase and of their eigenfrequencies allows setting the molecule in a sub-radiant state, where FWM is enhanced with respect to the isolated resonators. On the other hand, we can reconfigure the state of the photonic molecule to have energy equipartition among the resonators, and suppress FWM by making the two Signal waves to interfere destructively in the side coupled waveguides. This work constitutes an experimental demonstration of the control of a nonlinear parametric interaction via coherent oscillation phenomena in an integrated optical device.
When nonlinear four-wave mixing (FWM) is resonant with a Raman transition, it causes coupling between lightwaves separated by two Raman frequency shifts. This coupling is manifested in effects such as Raman gain suppression, higher-order Stokes generation, and coherent Raman spectroscopies (e.g., CARS). An understanding of these effects, however, has been impeded by a widespread misconception that Raman-resonant FWM does not transfer energy between the lightwaves and the medium. The equations for the photon densities at each light frequency show that, in actuality, two medium excitations are created or destroyed for each photon produced by FWM. This point may be further clarified by consideration of the driving nonlinear polarization and by comparisons with broadband Raman conversion and nonresonant FWM. The Raman gain suppression effect may be understood qualitatively in terms of destructive interference between FWM and the usual stimulated Raman process.
Suppression of noise photons from unwanted nonlinear processes is a major hurdle in generating frequency-degenerate correlated photon pairs for quantum information, e.g. continuous-variable quantum computing [1]. On-chip, telecom-pumped and frequency-degenerate photon pairs have been produced either using second harmonic generation (SHG) followed by spontaneous parametric down conversion (SPDC) in thin film lithium niobate (TFLN) waveguides [2], or by dual-pump spontaneous four-wave mixing (DP-SFWM) in microresonators [3], [4]. However, the former needs careful filtering of the SHG pump, while the latter suffers from single-pump (SP-) SFWM contributions, which decrease the purity of the generated quantum states. SP-SFWM can be suppressed by linearly coupling resonators at the expense of reduced bandwidth [3] or efficiency [4].
Integrated microring resonators have a broad range of applications in diverse fields with the potential to design compact, robust, energy-efficient devices crucial for quantum applications. Degenerate optical parametric oscillations (DOPOs) realized in dual-pumped microring resonator with third-order optical nonlinearity are of special interest. They demonstrate both bistability of the phase of the excited signal mode and generation of nonclassical light, which can be used for coherent photonic computing. Using coupled mode equations, we perform a comprehensive numerical analysis of DOPO conditions with normal group velocity dispersion and with bichromatic pumping. Through analytical and numerical approaches, we identify optimal setup parameter values that minimize the threshold power, highlighting the importance of considering the full spectrum of mode interactions. Additionally, we show that dispersion engineering, achievable in photonic molecules or photonic crystal microresonators, may provide a targeted frequency shift of specific microresonator modes resulting in pump power threshold reduction.