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We study the analogue of optical frequency combs in driven nonlinear phononic systems, and present a new generation mechanism for phononic frequency combs via nonlinear resonances. The nonlinear resonance refers to the simultaneous excitation of a set of phonon modes by the external driving, and thereby generated frequency combs are characterized by an array of equidistant spectral lines in the spectrum of each nonlinearly excited phonon mode. Frequency combs via nonlinear resonance of different orders are investigated, and particularly we reveal the possibility for correlation tailoring in higher order cases. The investigation contributes to potential applications in various nonlinear acoustic processes, such as harvesting phonons and generating phonon entanglements, and can also be generalized to other nonlinear systems.
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The mechanical analog of optical frequency combs, phononic frequency combs, has recently been demonstrated in mechanical resonators and has been attributed to coupling between multiple phonon modes. This paper investigates the influence of mode structure on comb generation using a model of two nonlinearly coupled phonon modes. The model predicts that there is only one region within the amplitude-frequency space where combs exist, and this region is a subset of the Arnold tongue that describes a 2:1 autoparametric resonance between the two modes. In addition, the location and shape of the comb region are analytically defined by the resonance frequencies, quality factors, mode coupling strength, and detuning of the driving force frequency from the mechanical resonances, providing clear conditions for comb generation. These results enable comb structure engineering for applications in areas as broad as sensing, communications, and quantum information science.
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.
We investigate theoretically frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that appear as tilted resonances bifurcating from the spectrum of linear axial modes. We then study azimuthal modulational instability of these modes and show that families of 2D soliton states localized both azimuthally and axially bifurcate from them at critical pump frequencies. Depending on detuning, 2D solitons can be either stable, or form persistent breathers, chaotic spatio-temporal patterns, or exhibit collapse-like evolution.
We have developed the full theory of a synchronously pumped type I optical parametric oscillator (SPOPO). We derive expressions for the oscillation threshold and the characteristics of the generated mode-locked signal beam. We calculate the output quantum fluctuations of the device, and find that, in the degenerate case (coincident signal and idler set of frequencies), perfect squeezing is obtained when one approaches threshold from below for a well defined super-mode, or frequency comb, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.
Dynamic Nuclear Polarization (DNP) has enabled enormous gains in magnetic resonance signals and led to vastly accelerated NMR/MRI imaging and spectroscopy. Unlike conventional cw-techniques, DNP methods that exploit the full electron spectrum are appealing since they allow direct participation of all electrons in the hyperpolarization process. Such methods typically entail sweeps of microwave radiation over the broad electron linewidth to excite DNP, but are often inefficient because the sweeps, constrained by adiabaticity requirements, are slow. In this paper we develop a technique to overcome the DNP bottlenecks set by the slow sweeps, employing a swept microwave frequency comb that increases the effective number of polarization transfer events while respecting adiabaticity constraints. This allows a multiplicative gain in DNP enhancement, scaling with the number of comb frequencies and limited only by the hyperfine-mediated electron linewidth. We demonstrate the technique for the optical hyperpolarization of 13C nuclei in powdered microdiamonds at low fields, increasing the DNP enhancement from 30 to 100 measured with respect to the thermal signal at 7T. For low concentrations of broad linewidth electron radicals, e.g. TEMPO, these multiplicative gains could exceed an order of magnitude.
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