Nonlinear Sideband Research Articles

Nonlinear Sideband Cooling to a Cat State of Motion.

The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.

Nonlinear Sideband Thermocapillary Instability of a Thin Film Coating the Inside of a Thick Walled Cylinder with Finite Thermal Conductivity in the Absence of Gravity

The nonlinear sideband thermocapillary instability of a thin liquid film coating the inside of a heated cylinder in the absence of gravity is investigated. It is shown that for a newtonian fluid and under the approximation of small wavenumber and large radius of the cylinder, the axial and all azimuthal modes with wavenumber kmax > 0 have the same linear maximum growth rate, in the same way as in a previous papers for flow outside the cylinder. Here, this indeterminacy of the linear problem is resolved nonlinearly looking for the parameters’ range where the axial mode prevails and where it is unstable against the first azimuthal mode of thermocapillary instability.

Sideband thermocapillary instability of a thin film flowing down the outside of a thick walled cylinder with finite thermal conductivity

The sideband thermocapillary instability of a thin liquid film flowing down the outside of a hot vertical cylinder is investigated. The wall of the cylinder is thick and has finite thermal conductivity. In contrast to previous work, it is shown that the presence of a main flow represented by the Reynolds number promotes the linear axial instability mode as the most unstable one. Thermocapillarity excites the appearance of linear azimuthal modes but it is not able to make them the most unstable when the wavenumber is small but finite. Only when the wavenumber tends to zero the growth rate of the azimuthal modes is larger than that of the axial mode. It is found that the thickness and thermal conductivity of the wall have an important influence on the stability. Even though the linear axial mode is the most unstable one, azimuthal modes are observed in the experiment. Therefore, it is of interest here to investigate the nonlinear sideband instability of the flow to find out the parameters region where the first azimuthal mode is able to prevail. It was possible to group for the first time the Reynolds, surface tension and Marangoni numbers with wall effect in only one parameter.

A mobile crack detection system for plate-like structure based on non-linear ultrasonic fibre Bragg grating

Many researchers have highlighted the fact that non-linear ultrasonic technology is more suitable than linear ultrasonic technology for detecting micro-cracks. In most existing non-linear ultrasonic detection systems, piezoelectric patches are pasted directly onto specimens and used to detect ultrasonics. In this paper, a fibre Bragg grating (FBG) was adopted for sensing ultrasonics because FBGs possess many advantages over piezoelectric patches. Non-linear ultrasonic technology was combined with FBG sensing technology to detect cracks in thin aluminium plates. This study proposed a mobile system in which the excitation and monitoring points were easily moved on the surface of a specimen because piezoelectric patches and FBGs were glued to acrylic plates and placed in contact with the specimen surface using industrial ultrasonic couplants. The influence of acrylic plate thicknesses on the characteristics of mobile piezoelectric patches (MPPs) and FBGs was discussed. This mobile system was more flexible than traditional systems, in which piezoelectric patches and FBGs are fixed to the structures, and it did not destroy the surface of the specimen. Experimental results showed that the mobile system can detect non-linear sideband signals caused by cracks at every excitation and sensing point. The factors influencing sideband amplitude, including excitation amplitude and frequency, and the relative positions of two excitations and a FBG were studied.

Nonlinear optomechanics with gain and loss: amplifying higher-order sideband and group delay

We study the nonlinear optomechanically induced transparency (OMIT) with gain and loss. We find that (i) for a single active cavity, significant enhancement can be achieved for the higher-order sidebands, including the transmission rate and the group delay; (ii) for active–passive-coupled cavities, hundreds of microsecond of optical delay or advance are attainable for the nonlinear sideband pulses in the parity-time-symmetric regime. The active higher-order OMIT effects, as firstly revealed here, open up the way to make a low-power optomechaical amplifier, which can amplify both the strength and group delay of not only the probe light but also its higher-order sidebands.

Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

Nonlinearly driven second harmonics of Alfvén cascades

In recent experiments on Alcator C-Mod [J. A. Snipes et al., Phys. Plasmas 12, 056102 (2005)], measurements of density fluctuations with phase contrast imaging through the plasma core show a second harmonic of the basic Alfvén cascade (AC) signal. The present paper presents a theory that describes the second-harmonic perturbation as a nonlinear sideband produced by the AC eigenmode via quadratic terms in the magnetohydrodynamic equations. It is shown that in a low-pressure plasma the nonlinear coupling to compressional Alfvén and acoustic perturbations can be neglected when calculating the second-harmonic density. The derived expressions for this density perturbation can potentially be used together with experimental measurements to determine the AC amplitude inside the plasma, rather than just at the edge as with magnetic probes.

Nonlinear acoustic detection of weathered, low compliance landmines

Two potential impediments to acoustic landmine detection are soil weathering processes and low compliance landmines. To bury landmines, the soil within a mine diameter is removed and replaced such that bulk density, compression, and shear strength all decrease, leaving an acoustic scar detectable with the linear acoustic measurement technique. After a few soil wetting and drying cycles, this contrast is reduced. Linear acoustic mine detection measurements were made on a low impedance contrast landmine before the first rainfall on several occasions over the subsequent 5 years. During this period of time, both the spatial and frequency resolution had to be increased to maintain an on/off target velocity ratio that allowed detection. In some cases, the landmine remains undetectable. To address this, two-tone nonlinear acoustic measurements have been made on these landmines. When the landmine is detectable with linear acoustics, two tones are broadcast at the frequency where the on/off target velocity ratio is the largest. For the cases when the landmine is undetectable, a two-tone sweep is performed and the operator observes the real-time velocity FFT, noting nonlinear sidebands. Next, two-tone tests are conducted at these sidebands to determine nonlinear velocity profiles. [Work supported by U.S. Army RDECOM, NVESD.]

Influence of rf waves on interchange modes in HANBIT mirror plasmas

A study is conducted on the influence of radio frequency (rf) waves upon interchange stability in HANBIT mirror plasmas. An emphasis is put on the interchange stability near the resonance region, ω0 ≃ Ωi, where ω0 (Ωi) is the angular frequency of the applied rf wave (ion cyclotron frequency). A strong nonlinear interaction between the rf wave and the interchange mode has been observed with the generation of sideband waves. A theory of rf-interchange mode interaction keeping effects of both the equilibrium ponderomotive force and the nonlinear sideband wave coupling is applied to interpret HANBIT experimental results, resulting in good agreement. Results have shown that the nonlinear coupling process is responsible for the rf stabilization of interchange modes near the resonance region.

Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in non-linear optics

The vector Maxwell equations of non-linear optics coupled to a single Lorentz oscillator and with instantaneous Kerr non-linearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore the properties of Maxwell’s equations in non-linear optics, without resorting to the commonly used non-linear Schrödinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to non-linear sideband wave interactions. This is important in femto-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field E, in terms of the canonical variables, with possible multiple real roots for E. In order to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether’s theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr non-linearity, are shown to reduce to a single ordinary differential equation for the variable y= E 2, where E is the electric field intensity. The differential equation has solutions y= y( ξ), where ξ= z− st is the traveling wave variable and s is the velocity of the wave. These solutions exhibit new phenomena not obtainable by the NLS approximation. The characteristics of the solutions depends on the values of the wave velocity s and the energy integration constant ϵ. Both smooth periodic traveling waves and non-smooth solutions in which the electric field gradient diverges (i.e. solutions in which | E ξ |→∞ at specific values of E, but where | E| is bounded) are obtained. The traveling wave solutions also include a kink-type solution, with possible important applications in femto-second technology.

Quasienergy Spectroscopy of Excitons

We theoretically study nonlinear optics of excitons under intense THz irradiation. In particular, the linear near infrared absorption and resonantly enhanced nonlinear sideband generation are described. We predict a rich structure in the spectra which can be interpreted in terms of the quasienergy spectrum of the exciton, via a remarkably transparent expression for the susceptibility, and show that the effects of strongly avoided quasienergy crossings manifest themselves directly, both in the absorption and transmitted sidebands.

Nonlinear sidebands of two powerful waves at closely spaced frequencies in the ionosphere

Observations of nonlinearly produced sidebands in the ionospherically reflected wave, using two powerful incident HF waves at closely spaced frequencies, are described. The sidebands are separated by multiples of the difference frequency of the incident waves. A theory for the production of the sidebands is proposed in terms of a modulation of the phase of the reflected wave at the difference frequency. The results of this theory are in reasonable agreement with the observations.

Single beam, single detector diagnostic for plasma density profiles across a magnetic field gradient

A scheme is proposed whereby the density profile of a tokamak or mirror plasma is mapped to nonlinear sidebands of a diagnostic wave, so that the sideband frequency spectrum is an image of the density profile traversed by the wave. The diagnostic relies on a monochromatic, high-frequency (ω≳ωce), pulsed wave source to determine the density profile across a magnetic field gradient. In principle, the technique offers time-dependent direct density profiles having high spatial resolution. However, the feasibility of the diagnostic is limited by the intense power and the rapid rise time required of the pulsed diagnostic wave. For parameters relevant to fusion plasmas, and for the particular scattering geometry suggested here, the technique requires, roughly, 30 mJ pulses of 2 nsec duration. The required power can be reduced by a factor of roughly 104 by applying signal averaging techniques. The rise time of the pulsed source must be short in comparison to one period of the diagnostic wave.

A nonlinear theory of sideband stability in ducted whistler mode waves

This paper is concerned with large amplitude ducted VLF waves (> 1.5pT) in the Earth's magnetosphere. The waves are excited by nonlinear cyclotron resonance with a continuous distribution of energetic electrons. The nonlinear sideband stability of such VLF waves is investigated. In addition the paper looks at wave particle interaction effects in waveflelds consisting of multiple sidebands, discrete waves plus hiss bands, or intense band limited hiss. The treatment is non-selfconsistent. The wavefield is specified a priori and the nonlinear resonant particle current is directly computed. The wavefield and current are spatially DFT'd, and the nonlinear growth rate is calculated as a function of frequency. Sideband stability behaviour is controlled by the magnitude and sign of the inhomogeneity. The magnetic field strength provides a parabolic inhomogeneity, and it was found that under these circumstances the upper sideband was unstable and the lower sideband damped. In band limited signals the uppermost frequencies get the most power, and intermediate frequencies are usually relatively damped. The computations lead directly to a nonlinear theory of quiet band, and also suggest a mechanism for PLHR line drift. Results with intense band limited hiss suggest that nonlinear wave particle interactions may cause a broadband spectrum to become spectrally structured. Assuming strong nonlinearity, constant inhomogeneity and weak sidebands, an analytic theory of sideband stability is developed. This is found to agree well with both computations and the experimental results from the Siple station.