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Physical Review A

Enhanced nonlinear optics in coupled optical microcavities with an unbroken and broken parity-time symmetry

Jiahua Li, Xiaogui Zhan, Chunling Ding, Duo Zhang, Ying Wu

Published Oct 21, 2015• 39 citations
Publisher

Abstract

We present a perturbation technique to study the linear and nonlinear output characteristics of coherent photon transport in a parity-time ($\mathcal{PT}$)-symmetric double-microcavity system where one passive cavity contains a single quantum emitter. It is found that (i) for the linear transmission of a low-power input probe field, the output spectra of the proposed $\mathcal{PT}$-symmetric system exhibit a single transparent resonance dip and two symmetric, strongly amplifying sidebands, i.e., an inverted dipole-induced transparency; and (ii) for the nonlinear transmission of the input probe field, giant optical third-order nonlinearities with high linear transmission rate and vanishing nonlinear absorption can be achieved efficiently when the system parameters are tuned properly so that a $\mathcal{PT}$-symmetry phase transition occurs. The obtained results can be useful for quantum information processing, quantum nondemolition measurements of photons, and optical signal processing.

DOI
10.1103/physreva.92.043830

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Scientific Reports•Oct 19, 2017•20 citations
We present a perturbation technique to study the linear and nonlinear output characteristics of coherent photon transport in a parity-time (PT\mathcal{PT}PT)-symmetric double-microcavity system where one passive cavity contains a single quantum emitter. It is found that (i) for the linear transmission of a low-power input probe field, the output spectra of the proposed PT\mathcal{PT}PT-symmetric system exhibit a single transparent resonance dip and two symmetric, strongly amplifying sidebands, i.e., an inverted dipole-induced transparency; and (ii) for the nonlinear transmission of the input probe field, giant optical third-order nonlinearities with high linear transmission rate and vanishing nonlinear absorption can be achieved efficiently when the system parameters are tuned properly so that a PT\mathcal{PT}PT-symmetry phase transition occurs. The obtained results can be useful for quantum information processing, quantum nondemolition measurements of photons, and optical signal processing.
Parity-time (PT\mathcal{PT}PT) symmetric systems, which rely on the balanced gain-loss condition and render the Hamiltonian non-Hermitian, have provided a new platform to engineer effective light-matter interactions in recent years. Here we explore the high-order sideband features of the output fields obtained from a PT\mathcal{PT}PT-symmetric optical system consisting of a passive nonlinear cavity coupled to an active linear cavity. By employing a perturbation technique, we derive analytic formulas used to determine the nonlinear transmission coefficient of optical second-order sideband in this structure. Using experimentally achievable parameters, it is clearly shown that the efficiency of the second-order sideband generation can be greatly enhanced in the PT\mathcal{PT}PT-symmetric dimer, extremely in the vicinity of the transition point from unbroken- to broken-PT\mathcal{PT}PT regimes. Moreover, we further analyzed the influences of the system parameters, including the photon-tunneling rate between two cavities, Kerr nonlinearity strength, and optical detuning, on the second-order sideband generation. Subsequently we investigate the higher-order sideband output spectrum by numerical simulations, where the sideband amplitude also is largely enhanced in the PT\mathcal{PT}PT-symmetric arrangement, compared with the passive-passive double-cavity system. Our obtained results provide a new avenue for acquiring optical high-order sidebands and operating light, which may inspire further applications in chip-scale optical communications and optical frequency combs.
Enhanced nonlinear characteristics with the assistance of a PT\mathscr{PT}PT-symmetric trimer system
We study the parity-time (PT) symmetry characteristics and the applications to nonlinear optics in an optical trimer system consisting of two indirectly coupled standing-mode micro-cavities and a two-level quantum emitter (QE) placed at the intersection of two cavities. We find this trimer system can exhibit analogical phenomena as those in typical [Formula: see text]-symmetric dimer systems composed of a passive cavity directly coupled to an active cavity. This system, whose [Formula: see text] symmetry is demonstrated by our analytic results, can be transformed between the [Formula: see text]-symmetric phase and the [Formula: see text]-broken phase by adjusting relevant system parameters. Then, with this system, we observe both the linear and nonlinear parts of the transmission field become remarkably enhanced and can further reach peak values around the [Formula: see text] breaking point. In addition, we show the negative correlation between the gain degree of the linear (nonlinear) transmission part and decay rate of the QE. This trimer proposal is feasible for experiments and may provide a promising platform for [Formula: see text]-symmetric optics of low-light levels. Moreover, novel phenomena arising from the QE-cavity-coupling induced nonlinearity gain could be explored to fabricate photonic devices and controllable nonlinear optical media for quantum information process and communication of photons.
We propose and analyze an effective scheme to enhance the optical higher-order sideband generation in a three-cavity array with local parity-time (PT\mathcal{PT}PT) symmetry. In this three-cavity configuration, a single cavity containing a quantum dot (QD) is coupled to an assisted PT\mathcal{PT}PT-symmetric combination of two cavities. Beyond the weak-excitation approximation, we derive the analytic formulas used to determine the nonlinear coefficient of the optical second-order sideband (OSS) by employing the perturbation technique. Using experimentally achievable parameters, we identify the conditions under which the assisted PT\mathcal{PT}PT-symmetric double-cavity system allows us to modify the transmission of the probe field and improve the efficiency of OSS generation beyond what is achievable in a loss-only QD-cavity system. We examine the influence of the PT\mathcal{PT}PT phase transition from unbroken- to broken-PT\mathcal{PT}PT regimes on the OSS generation. It is found that the efficiency of optical second-order sideband generation can be significantly enhanced when the assisted double-cavity system is in PT\mathcal{PT}PT-symmetric phase, extremely in the vicinity of the transition point. The present results illustrate the potential to utilize PT\mathcal{PT}PT-symmetric physical systems for enhancing optical higher-order sidebands and controlling optical frequency combs, as well as to guide the design of experimental implementation.
Abstract A coupled active–passive double-cavity system with balanced effective gain and loss provides a powerful platform for sideband generation. In different input limits, we explore the gain-saturation nonlinearity of the active cavity with regard to sideband generation. Using a perturbation method, we give an explicit analytical expression for second-order sideband generation (SSG), showing a conversion efficiency of over 80% and pump powers as low as ∼ μ W. A remarkable mode-splitting is also observed during the SSG process in the unbroken parity–time (   ) symmetry phase. With change in the system parameters, our numerical method shows that high-order sideband generation (HSG) in the unbroken   phase is controllable, including increasing its amplitude and changing its order number, especially when switching HSG between perturbative and non-perturbative regimes. In the broken   phase, field localization effect leads to a stronger output spectral intensity than that in the unbroken   phase.
We propose an alternative scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\textrm{PT}) system (i.e., active-passive coupled cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The giant optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.
We propose a scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time ([Formula: see text]) symmetric system (i.e., coupled active-passive cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The increased optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability, and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.