Weak Nonlinear Interactions Research Articles

Optical to terahertz frequency conversion using near zero-index nonlinear hybrid waveguides

Terahertz communications has emerged as an excellent candidate for the next generation of wireless communication networks. Despite of significant advances, one still looks for a high-efficiency terahertz source using nonlinear optics, such as optical refraction and difference-frequency generation. Concurrently, recent years have witnessed significant progress in metamaterials-assisted nonlinear optical processes. In this study, we propose a theoretical approach using near zero-index nonlinear hybrid waveguides to realize a high generation efficiency of terahertz waves via on-chip difference-frequency generation. Remarkably, thanks to the simultaneous realization of near zero-index both at terahertz and telecom frequencies, such a nonlinear hybrid waveguide can overcome two major bottlenecks in the conversion from optical wave to terahertz waves: phase mismatch and weak nonlinear optical-terahertz waves interactions, resulting in a high conversion as 2.2 × 10−3W−1 just within the propagation length of several terahertz wavelengths. Our results demonstrate the feasibility of an on-chip terahertz source, offering unique properties such as high integration and ultra-low power consumption for terahertz communication systems.

Proposal for Observing XUV-Induced Rabi Oscillation Using Superfluorescent Emission.

Intense x-ray and extreme ultraviolet (XUV) light sources have been available for decades, however, due to weak nonlinear interaction in the XUV photon energy range, observation of Rabi oscillation induced by XUV pulse remains a very challenging experimental task. Here we suggest a scheme where photoionization of a He medium by an intense XUV pump pulse is followed by a strong population inversion and Rabi oscillation at the He^{+}(1s-3p) transition and is accompanied by superfluorescence (SF) of the 7.56eV pulse at the He^{+}(3p-2s) transition. Our numerical simulations show that the Rabi oscillation at the He^{+}(1s-3p) transition induced by an XUV pulse with photon energy 48.36eV results in significant signatures in the SF spectra, allowing us to identify and characterize the XUV induced Rabi-oscillatory regime. The proposed scheme provides a sensitive tool to monitor and control ultrafast nonlinear dynamics in atoms and molecules triggered by intense XUV.

Generation of magnonic frequency combs via a two-tone microwave drive

Magnonic frequency combs, a direct analog of optical frequency combs in the field of spin waves, have recently received considerable attentions due to their potential applications in high-precision magnonic frequency metrology. However, due to the weak nonlinear interaction of magnons, it is difficult to generate a wide-bandwidth magnonic frequency comb under a low power drive. Here, we present an efficient mechanism for the generation of a wide-bandwidth magnonic frequency comb via a two-tone microwave driving in a magnomechanical system. Numerical simulations show that the magnetostrictive effect can be greatly enhanced by the beat frequency signal from the two-tone microwave driving field, and a robust magnonic frequency comb can be observed at low power. Furthermore, abundant nonperturbative features appear in the magnonic spectrum, implying that the magnons as bosons may also be similar to photons in atom-molecular systems. Our scheme thus provides a pathway for the generation of a flat magnonic frequency comb under a low-power driving condition that may be beneficial for precision metrology based on magnonic platforms as well as the understanding of nonlinear magnomechanic dynamics.

Spanning the full range of neutron star properties within a microscopic description

The high-density behavior of nuclear matter is analyzed within a relativistic mean-field description with non-linear meson interactions. To assess the model parameters and their output, a Bayesian inference technique is used. The Bayesian setup is limited only by a few nuclear saturation properties, the neutron star maximum mass larger than 2 M$_\odot$, and the low-density pure neutron matter equation of state (EOS) produced by an accurate N$^3$LO calculation in chiral effective field theory. Depending on the strength of the non-linear scalar vector field contribution, we have found three distinct classes of EOSs, each one correlated to different star properties distributions. If the non-linear vector field contribution is absent, the gravitational maximum mass and the sound velocity at high densities are the greatest. However, it also gives the smallest speed of sound at densities below three times saturation density. On the other hand, models with the strongest non-linear vector field contribution predict the largest radii and tidal deformabilities for 1.4 M$_\odot$ stars, together with the smallest mass for the onset of the nucleonic direct Urca processes and the smallest central baryonic densities for the maximum mass configuration. These models have the largest speed of sound below three times saturation density, but the smallest at high densities, in particular, above four times saturation density the speed of sound decreases approaching approximately $\sqrt{0.4}c$ at the center of the maximum mass star. On the contrary, a weak non-linear vector contribution gives a monotonically increasing speed of sound. A 2.75 M$_\odot$ NS maximum mass was obtained in the tail of the posterior with a weak non-linear vector field interaction. We found that pQCD favors models with a large non-linear vector field contribution or hyperons.

Adaptive Neural Network Command Filtered Backstepping Control for the Underactuated TORA System

An adaptive neural network command-filtered backstepping design algorithm is proposed for the underactuated translational oscillator with a rotating actuator (TORA). The system dynamics are transformed into a nonlinear cascade system through a global change of coordinates. Considering the weak sinusoid-type nonlinear interaction and affine-free appearance in the cascade model, the TORA is looked at as a pure feedback system. Two neural networks are used to approximate the unknown functions and a command filter is used to produce the virtual control and its first and second-order derivatives to overcome the explosion of complexity problems in backstepping. A filter error compensation dynamic system is designed to overcome the error influence on control performance. Taking full account of the cascade model structure of the underactuated TORA, each backstepping step is designed for a second-order subsystem to reduce the design steps and simplify the design process. The system stability is proved through the Lyapunov stability theorem and verified by numerical simulations.

The cradle of nonlinear asteroseismology: observations of oscillation mode variability in compact pulsating stars

We briefly review progress in developing a pathway to nonlinear astereoseismology, both from theoretical and observational aspects. As predicted by the theory of weak nonlinear interactions between resonant modes, their amplitude and frequency can be modulated according to various kinds of patterns. However, those subtle modulations could hardly be well characterized from ground-based photometric monitoring. The Kepler spacecraft offered a new window to find clear-cut evidence of well-determined amplitude and frequency modulations, leading to the first discoveries of such variations in pulsating white dwarf and hot B subdwarf stars. Fol-lowing that direction, a systematic survey of oscillation mode properties in compact pulsators monitored by Kepler suggests that mode variability is likely a common phenomenon, which remain unaccounted for by standard linear non-radial pulsation theory. To reach this conclusion firmly, the survey has now been extended to a larger context including compact stars observed by K2 and TESS. We expect that this extended survey will help to constrain key parameters governing weak nonlinear effects in stellar oscillations.

All-optical modulation based on MoS2-Plasmonic nanoslit hybrid structures

Abstract Two-dimensional (2D) materials with excellent optical properties and complementary metal-oxide-semiconductor (CMOS) compatibility have promising application prospects for developing highly efficient, small-scale all-optical modulators. However, due to the weak nonlinear light-material interaction, high power density and large contact area are usually required, resulting in low light modulation efficiency. In addition, the use of such large-band-gap materials limits the modulation wavelength. In this study, we propose an all-optical modulator integrated Si waveguide and single-layer MoS2 with a plasmonic nanoslit, wherein modulation and signal light beams are converted into plasmon through nanoslit confinement and together are strongly coupled to 2D MoS2. This enables MoS2 to absorb signal light with photon energies less than the bandgap, thereby achieving high-efficiency amplitude modulation at 1550 nm. As a result, the modulation efficiency of the device is up to 0.41 dB μm−1, and the effective size is only 9.7 µm. Compared with other 2D material-based all-optical modulators, this fabricated device exhibits excellent light modulation efficiency with a micron-level size, which is potential in small-scale optical modulators and chip-integration applications. Moreover, the MoS2-plasmonic nanoslit modulator also provides an opportunity for TMDs in the application of infrared optoelectronics.

Dissipative dynamics of a particle coupled to a field via internal degrees of freedom

We study the non-equilibrium dissipative dynamics of the center of mass of a particle coupled to a field via its internal degrees of freedom. We model the internal and external degrees of freedom of the particle as quantum harmonic oscillators in 1+1 D, with the internal oscillator coupled to a scalar quantum field at the center of mass position. Such a coupling results in a nonlinear interaction between the three pertinent degrees of freedom -- the center of mass, internal degree of freedom, and the field. It is typically assumed that the internal dynamics is decoupled from that of the center of mass owing to their disparate characteristic time scales. Here we use an influence functional approach that allows one to account for the self-consistent backaction of the different degrees of freedom on each other, including the coupled non-equilibrium dynamics of the internal degree of freedom and the field, and their influence on the dissipation and noise of the center of mass. Considering a weak nonlinear interaction term, we employ a perturbative generating functional approach to derive a second order effective action and a corresponding quantum Langevin equation describing the non-equilibrium dynamics of the center of mass. We analyze the resulting dissipation and noise arising from the field and the internal degree of freedom as a composite environment. Furthermore, we establish a generalized fluctuation-dissipation relation for the late-time dissipation and noise kernels. Our results are pertinent to open quantum systems that possess intermediary degrees of freedom between system and environment, such as in the case of optomechanical interactions.

Wave-Turbulence Origin of the Instability of Anderson Localization against Many-Body Interactions.

Whether Anderson localization is robust against many-body interactions and, closely related, whether a disordered many-body system can be thermalized are long outstanding issues. In this Letter, we address these issues with the wave-turbulence theory. We show that, in general, the thermalization time in one-dimensional disordered lattice systems is inversely proportional to the squared interaction strength in the thermodynamic limit. It leads to the conclusion that such systems can always be thermalized by arbitrarily weak many-body interactions and thus the localized states are unstable.

Asymptotic models for free boundary flow in porous media

We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to be very small. The models we derive capture the nonlinear interaction of the original free boundary Darcy and Forchheimer problem up to quadratic terms. Furthermore, we provide models that consider both the two-dimensional and three-dimensional cases, with and without bottom topography.

Quantum Parametric Oscillator with Trapped Ions.

A strong nonlinear coupling between harmonic oscillators is highly desirable for quantum information processing and quantum simulation, but is difficult to achieve in many physical systems. Here, we exploit the Coulomb interaction between two trapped ions to achieve strong nonlinear coupling between normal modes of motion at the single-phonon level. We experimentally demonstrate phonon up- and down-conversion and apply this coupling to directly measure the parity and Wigner functions of the ions' motional states. Our results represent the fully quantum operation of a degenerate parametric oscillator and hold promise for quantum computation schemes that involve continuous variables.

Directed momentum current of Bose–Einstein condensate in the presence of spatially modulated nonlinear interaction

We investigate the quantum transport dynamics of periodically delta-kicked Bose–Einstein condensate under the effect of spatially modulated nonlinear interactions. The spatial modulation frequency can dramatically affect the transport behaviors of the ultra-cold atoms. For odd frequency, the linear growth of the directed current is close to that of the noninteracting case for not very strong nonlinear interaction. Both the acceleration and the quantum state evolution gradually approach that of the noninteracting case with increasing frequency. For other values of frequency, a very weak nonlinear interaction can dramatically reduce the linear growth of the directed current. The quantum state evolution differs rapidly from that of the noninteracting case. The underlying dynamic mechanism is uncovered and some important implications are addressed.

Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem.

We present a scheme for encoding single logical qubit information, which is immune to collective decoherence acting on Hilbert space spanned by the corresponding states. The scheme needs a spatial entanglement gate and a polarization entanglement gate, which are realized with the assistance of weak cross-Kerr nonlinear interaction between photons and coherent states via Kerr media. Under the condition of sufficient large phase shifts, single logical qubit information can be encoded into this minimal optical decoherence-free subsystem with near-unity fidelity. Together with the mature techniques of measurement and classical feed forward, simple linear optical elements are applied to complete the encoding task, which offers the feasibility of this scheme for protecting quantum information against decoherence.

Spin-orbit coupled Bose-Einstein condensates in a double well

We study the quantum dynamics of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) in a double-well potential inspired by the experimental protocol recently developed by NIST group. We focus on the regime where the number of atoms is very large and perform a two-mode approximation. An analytical solution of the two-site Bose-Hubbard-like Hamiltonian is found for several limiting cases, which range from a strong Raman coupling to a strong Josephson coupling, ending with the complete model in the presence of weak nonlinear interactions. Depending on the particular limit, different approaches are chosen: a mapping onto an SU(2) spin problem together with a Holstein-Primakoff transformation in the first two cases and a rotating wave approximation (RWA) when dealing with the complete model. The quantum evolution of the number difference of bosons with equal or different spin between the two wells is investigated in a wide range of parameters; finally the corresponding total atomic current and the spin current are computed. We show a spin Josephson effect which could be detected in experiments and employed to build up realistic devices.

Wave kinetics of random fibre lasers.

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

A GENERATION SCHEME OF THE DISTRIBUTED FOUR-PHOTON CLUSTER-TYPE POLARIZATION-ENTANGLED STATES EXPLOITING THE INTEGRATION OF ENTANGLEMENT GATES AND THE CONTROLLED PHASE GATE

We propose a scheme for preparing the distributed four-photon cluster-type polarization-entangled states associated with the integration of the controlled phase gate and two kinds of entanglement gates. Employing weak cross-Kerr nonlinear interactions and Homodyne measurement, two individual photons entangle together based on the bus function of coherent states. Assisted by optical elements mainly including polarization beam splitters, the entanglement of the signal photons is converted from the spatial mode to the polarization mode. The application of classical feed forward provides the high-efficiency to the preparation of Einstein–Podolsky–Rosen (EPR) states, Greenberger–Horne–Zeilinger (GHZ) states, and four-photon cluster-type polarization-entangled states. With regard to the four-photon cluster-type state, it can be generated in two distributed nodes with less experimental requirements, integrating the features of three logical gates.

Nonlinear Interaction Effects in a Strongly Driven Optomechanical Cavity

We consider how nonlinear interaction effects can manifest themselves and even be enhanced in a strongly driven optomechanical system. Using a Keldysh Green's function approach, we calculate modifications to the cavity density of states due to both linear and nonlinear optomechanical interactions, showing that strong modifications can arise even for a weak nonlinear interaction. We show how this quantity can be directly probed in an optomechanically induced transparency-type experiment. We also show how the enhanced interaction can lead to nonclassical behavior, as evidenced by the behavior of g(2) correlation functions.

Submicron bidirectional all-optical plasmonic switches

Ultra-small all-optical switches are of importance in highly integrated optical communication and computing networks. However, the weak nonlinear light-matter interactions in natural materials present an enormous challenge to realize efficiently switching for the ultra-short interaction lengths. Here, we experimentally demonstrate a submicron bidirectional all-optical plasmonic switch with an asymmetric T-shape single slit. Sharp asymmetric spectra as well as significant field enhancements (about 18 times that in the conventional slit case) occur in the symmetry-breaking structure. Consequently, both of the surface plasmon polaritons propagating in the opposite directions on the metal surface are all-optically controlled inversely at the same time with the on/off switching ratios of >6 dB for the device lateral dimension of <1 μm. Moreover, in such a submicron structure, the coupling of free-space light and the on-chip bidirectional switching are integrated together. This submicron bidirectional all-optical switch may find important applications in the highly integrated plasmonic circuits.

Spin Squeezing in Two-Species Bose-Einstein Condensate

We investigate spin squeezing dynamics of a system of two-species Bose-Einstein condensate with weak nonlinear interatomic interactions and Josephson-like tunneling. Numerical analysis of spin squeezing is presented. It is shown that spin squeezing is independent of Josephson-like coupling and the increasing total atomic number causes weaker spin squeezing and shorter squeezing time.

Does economic growth and financial development spur energy consumption in Tunisia?

A physical background is derived for the generation of 1/f fluctuations that are observed ubiquitously in energy partition in quasi-harmonic oscillators that exchange energy through weak nonlinear interactions. Weak three-mode coupling terms in the unperturbed Hamiltonian bring no net transfer of energy between oscillators, but four-mode coupling terms bring about irreversible energy transfer between unperturbed oscillators as well as 1/f fluctuations in energy partition in which the reaction of energy transfer plays a crucial role. Oscillation (vibration) modes in material media are accompanied by nonlinear coupling of modes, and 1/f energy fluctuations are always observed in each oscillation mode. This is the main reason for the ubiquitous existence of this kind of fluctuation. The power spectral density of fractional 1/f energy fluctuations is simply given by (1/n)(1/f), where n is the number of quasi-oscillators involved in the generation of 1/f fluctuations. The present theoretical formula allows estimation of the number of quasi-harmonic oscillators involved in the generation of observed 1/f spectra, and this approach is applicable to oscillation phenomena from the nanometer to the astronomical scale. The origin of 1/ffluctuations in biological rhythm is possibly attributed to vibrations of ion channel conductance. Key words: Heart rate, 1/f fluctuations, nonlinearity, harmonic oscillators, biological rhythm.