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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Studies of shock focusing and nonlinear resonance in shock tubes

Some current problems in noise pollution which involve the dynamics of weak shock waves can be succesfully investigated using shock tubes and shock-tube techniques. Two examples presently under study are discussed; in one case the experiments are carried out in a large, conventional shock tube originally designed for studies of rarefied gasdynamics, while in the other case the experimental facility is a less conventional 'repeating' shock tube.

Sturtevant, B.↗
NASA NTRS1994

Nonlinear Resonances in the Solar System

Orbital resonances are ubiquitous in the Solar system. They play a decisive role in the long term dynamics, and in some cases the physical evolution, of the planets and of their natural satellites, as well as the evolution of small bodies (including dust) in the planetary system. The few-body gravitational problem of hierarchical planetary-type systems allows for a complex range of dynamical timescales, from the fast orbital periods to the very slow orbit precession rates. The interaction of fast and slow degrees of freedom produces a rich diversity of resonance phenomena. Weak dissipative effects - such as tides or radiation drag forces - also produce unexpectedly rich dynamical behaviors. This paper provides a mostly qualitative discussion of simple dynamical models for the commonly encountered orbital resonance phenomena in the Solar system.

Malhotra, Renu↗
NASA NTRS1994

Resonantly driven nonlinear density waves in protostellar disks

Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance, and that the propagation distance (and therefore the region of the disk to which angular momentum is redistributed) is set by the distance at which the wavelength becomes comparable to the disk thickness.

Yuan, Chi↗
DOE OSTI2024

Latched detection of zeptojoule spin echoes with a kinetic inductance parametric oscillator

When strongly pumped at twice their resonant frequency, nonlinear resonators develop a high-amplitude intracavity field, a phenomenon known as parametric self-oscillations. The boundary over which this instability occurs can be extremely sharp and thereby presents an opportunity for realizing a detector. Here, we operate such a device based on a superconducting microwave resonator whose nonlinearity is engineered from kinetic inductance. The device indicates the absorption of low-power microwave wavepackets by transitioning to a self-oscillating state. Using calibrated pulses, we measure the detection efficiency to zeptojoule energy wavepackets. We then apply it to measurements of electron spin resonance, using an ensemble of 209 Bi donors in silicon that are inductively coupled to the resonator. We achieve a latched readout of the spin signal with an amplitude that is five hundred times greater than the underlying spin echoes.

42 ENGINEERING↗
DOE OSTI2023

Nonlinear nanomechanical resonators approaching the quantum ground state

It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Universal control in bosonic systems with weak Kerr nonlinearities

Resonators with weak single-photon self-Kerr nonlinearities can theoretically be used to prepare Fock states in the presence of a loss much larger than their nonlinearities. Two necessary ingredients are large displacements and a two-photon (parametric) drive. Here, in this study, we find that these systems can be controlled to achieve any desired gate operation in a finite-dimensional subspace (whose dimensionality can be chosen at will). Moreover, we show that the two-photon driving requirement can be relaxed and that full controllability is achievable with only one-photon (linear) drives. We make use of both Trotter-Suzuki decompositions and gradient-based optimization to find control pulses for a desired gate, which reduces the computational overhead by using a small blockaded subspace. We also discuss the infidelity arising from input power limitations in realistic settings, as well as from corrections to the rotating-wave approximation. Our universal control protocol opens the possibility for quantum information processing using a wide range of lossy systems with weak nonlinearities.

Yuan, Ming [Univ. of Chicago, IL (United States)] ↗
DOE OSTI2020

Two-frequency sub-Doppler spectroscopy of the caesium D{sub 1} line in various configurations of counterpropagating laser beams

Sub-Doppler resonances in caesium vapours are studied in a laser field produced by counterpropagating two-frequency light beams with mutually orthogonal linear polarisations. The beams are in resonance with optical transitions in the D{sub 1} line, the frequency difference of the field spectral components being equal to the hyperfine ground-state splitting in the Cs atom (∼9.2 GHz). It has already been shown that in this configuration, the hypercontrast effect can be observed for sub-Doppler resonances, which makes this configuration promising for the employment in new-generation miniature optical frequency standards. In the present work, two different two-frequency configurations are compared with each other and with the single-frequency configuration widely used in practice for observing saturated absorption resonances. The parameters of nonlinear resonances are measured at various temperatures of caesium vapours and at different optical field intensities. The results of the investigations performed make it possible to find an optimal two-frequency scheme for exciting nonlinear resonances and to estimate a potential of the scheme for its applications in quantum metrology. (laser spectroscopy of atoms)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Peterson, Lee D.↗
NASA NTRS2006

Microwave Oscillators Based on Nonlinear WGM Resonators

Optical oscillators that exploit resonantly enhanced four-wave mixing in nonlinear whispering-gallery-mode (WGM) resonators are under investigation for potential utility as low-power, ultra-miniature sources of stable, spectrally pure microwave signals. There are numerous potential uses for such oscillators in radar systems, communication systems, and scientific instrumentation. The resonator in an oscillator of this type is made of a crystalline material that exhibits cubic Kerr nonlinearity, which supports the four-photon parametric process also known as four-wave mixing. The oscillator can be characterized as all-optical in the sense that the entire process of generation of the microwave signal takes place within the WGM resonator. The resonantly enhanced four-wave mixing yields coherent, phase-modulated optical signals at frequencies governed by the resonator structure. The frequency of the phase-modulation signal, which is in the microwave range, equals the difference between the frequencies of the optical signals; hence, this frequency is also governed by the resonator structure. Hence, further, the microwave signal is stable and can be used as a reference signal. The figure schematically depicts the apparatus used in a proof-of-principle experiment. Linearly polarized pump light was generated by an yttrium aluminum garnet laser at a wavelength of 1.32 microns. By use of a 90:10 fiber-optic splitter and optical fibers, some of the laser light was sent into a delay line and some was transmitted to one face of glass coupling prism, that, in turn, coupled the laser light into a crystalline CaF2 WGM disk resonator that had a resonance quality factor (Q) of 6x10(exp 9). The output light of the resonator was collected via another face of the coupling prism and a single-mode optical fiber, which transmitted the light to a 50:50 fiber-optic splitter. One output of this splitter was sent to a slow photodiode to obtain a DC signal for locking the laser to a particular resonator mode. The other output of this splitter was combined with the delayed laser signal in another 50:50 fiber-optic splitter used as a combiner. The output.of the combiner was fed to a fast photodiode that demodulated light and generated microwave signal. In this optical configuration, the resonator was incorporated into one arm of a Mach-Zehnder interferometer, which was necessary for the following reasons: It was found that when the output of the resonator was sent directly to a fast photodiode, the output of the photodiode did not include a measurable microwave signal. However, when the resonator was placed in an arm of the interferometer and the delay in the other arm was set at the correct value, the microwave signal appeared. Such behavior is distinctly characteristic of phase-modulated light. The phase-modulation signal had a frequency of about 8 GHz, corresponding to the free spectral range of the resonator. The spectral width of this microwave signal was less than 200 Hz. The threshold pump power for generating the microwave signal was about 1 mW. It would be possible to reduce the threshold power by several orders of magnitude if resonators could be made from crystalline materials in dimensions comparable to those of micro-resonators heretofore made from fused silica.

Maleki, Lute↗
DOE OSTI2023

Controllable branching of robust response patterns in nonlinear mechanical resonators

In lieu of continuous time active feedback control in complex systems, nonlinear dynamics offers a means to generate desired long-term responses using short-time control signals. This type of control has been proposed for use in resonators that exhibit a plethora of complex dynamic behaviors resulting from energy exchange between modes. However, the dynamic response and, ultimately, the ability to control the response of these systems remains poorly understood. Here, we show that a micromechanical resonator can generate diverse, robust dynamical responses that occur on a timescale five orders of magnitude larger than the external harmonic driving and these responses can be selected by inserting small pulses at specific branching points. We develop a theoretical model and experimentally show the ability to control these response patterns. Hence, these mechanical resonators may represent a simple physical platform for the development of springboard concepts for nonlinear, flexible, yet robust dynamics found in other areas of physics, chemistry, and biology.

42 ENGINEERING↗
NASA NTRS1982

Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

Tkalcevic, S.↗
NASA NTRS1972

Nonlinearity of Helmholtz resonators

Consideration of the nonlinear damping of pressure oscillations by means of acoustic liners consisting of a perforated plate communicating with a volume or of individual Helmholtz resonators. A nonlinear analysis leads to a modified first-order theory; in particular, some second-order damping effects (due to the formation of jets through the orifices) are considered, while other less important damping effects (of second order) are neglected. The effect of the vena contracta in the orifice flow is also taken into account, and the conditions of maximum damping are discussed. A determination is made of the orifice velocity, the cavity pressure, the admittance coefficient, the resistance, and the reactance, and good agreement is found between the theoretically determined resistance and orifice velocity and the pertinent experimental data.

Sirignano, W. A.↗