Showing papers on "Parametric oscillator published in 2007"

Widely tunable parametric amplifier based on a superconducting quantum interference device array resonator

Abstract: The authors create a Josephson parametric amplifier from a transmission line resonator whose inner conductor is made from a series of superconducting quantum interference device (SQUID) array. By changing the magnetic flux through the SQUID loops, they are able to adjust the circuit’s resonance frequency and the center of the amplified band between 4 and 7.8GHz. They observe that the amplifier has gains as large as 28dB and infers that it adds less than twice the input vacuum noise.

A widely tunable parametric amplifier based on a SQUID array resonator

Abstract: We create a Josephson parametric amplifier from a transmission line resonator whose inner conductor is made from a series SQUID array. By changing the magnetic flux through the SQUID loops, we are able to adjust the circuit's resonance frequency and, consenquently, the center of the amplified band, between 4 and 7.8 GHz. We observe that the amplifier has gains as large as 28 dB and infer that it adds less than twice the input vacuum noise.

Gravitational wave production at the end of inflation.

Abstract: We consider gravitational wave production due to parametric resonance at the end of inflation, or ``preheating.'' This leads to large inhomogeneities that source a stochastic background of gravitational waves at scales inside the comoving Hubble horizon at the end of inflation. We confirm that the present amplitude of these gravitational waves need not depend on the inflationary energy scale. We analyze an explicit model where the inflationary energy scale is $\ensuremath{\sim}{10}^{9}\text{ }\text{ }\mathrm{GeV}$, yielding a signal close to the sensitivity of Advanced Laser Interferometer Gravitational Wave Observatory and Big Bang Observer. This signal highlights the possibility of a new observational ``window'' into inflationary physics and provides significant motivation for searches for stochastic backgrounds of gravitational waves in the Hz to GHz range, with an amplitude on the order of ${\ensuremath{\Omega}}_{\mathrm{gw}}(k){h}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}11}$.

Observation of Faraday Waves in a Bose-Einstein Condensate

Abstract: Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

Observation of Faraday Waves in a Bose-Einstein Condensate

Abstract: Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances

Abstract: In this paper, the nonlinear planar vibration of a pipe conveying pulsatile fluid subjected to principal parametric resonance in the presence of internal resonance is investigated. The pipe is hinged to two immovable supports at both ends and conveys fluid at a velocity with a harmonically varying component over a constant mean velocity. The geometric cubic nonlinearity in the equation of motion is due to stretching effect of the pipe. The natural frequency of the second mode is approximately three times the natural frequency of the first mode for a range of mean flow velocity, resulting in a three-to-one internal resonance. The analysis is done using the method of multiple scales (MMS) by directly attacking the governing nonlinear integral-partial-differential equations and the associated boundary conditions. The resulting set of first-order ordinary differential equations governing the modulation of amplitude and phase is analyzed numerically for principal parametric resonance of first mode. Stability, bifurcation, and response behavior of the pipe are investigated. The results show new zones of instability due to the presence of internal resonance. A wide array of dynamical behavior is observed, illustrating the influence of internal resonance.

Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method

Abstract: This paper applies He's energy balance method to determine the frequency-amplitude relation of the Duffing-harmonic oscillator, which gives a good estimate for the angular frequency.

Picosecond optical parametric oscillator pumped synchronously, intracavity, by a mode-locked Nd:YVO4 laser

Abstract: The operation of a picosecond synchronously intracavity pumped optical parametric oscillator (OPO) is reported. A magnesium doped lithium niobate crystal (MgO:PPLN), periodically poled, is used as the optical parametric oscillator crystal coupling the pump and the resonant signal cavities. The active medium of the pump cavity is a a diode pumped passively mode-locked Nd:YVO4 crystal. Continuous mode-locked operation was achieved, tunable from 1531 to 1554 nm by adjusting the OPO crystal from 31 to 55°C. The spectral width of the generated radiation was 2 nm.

Parametric resonance of optically trapped aerosols

Abstract: The Brownian dynamics of an optically trapped water droplet are investigated across the transition from over- to underdamped oscillations. The spectrum of position fluctuations evolves from a Lorentzian shape typical of overdamped systems (beads in liquid solvents) to a damped harmonic oscillator spectrum showing a resonance peak. In this later underdamped regime, we excite parametric resonance by periodically modulating the trapping power at twice the resonant frequency. The power spectra of position fluctuations are in excellent agreement with the obtained analytical solutions of a parametrically modulated Langevin equation.

Faraday waves in Bose-Einstein condensates

Abstract: Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement. We offer a fully analytical explanation of the observed parametric resonance, based on a Mathieu-type analysis of the non-polynomial Schr\"odinger equation. The theoretical prediction for the pattern periodicity versus the driving frequency is directly compared to the experimental data, yielding good qualitative and quantitative agreement between the two. These results are corroborated by direct numerical simulations of both the one-dimensional non-polynomial Schr\"odinger equation and of the fully three-dimensional Gross-Pitaevskii equation.

A novel harmonic balance analysis for the Van Der Pol oscillator

Abstract: This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge–Kutta) methods.

2:1 Resonance in the delayed nonlinear Mathieu equation

Abstract: We investigate the dynamics of a delayed nonlinear Mathieu equation: $$\ddot{x}+(\delta+\varepsilon\alpha\,\cos t)x +\varepsilon\gamma x^3=\varepsilon\beta x(t-T)$$ in the neighborhood of δ = 1/4. Three different phenomena are combined in this system: 2:1 parametric resonance, cubic nonlinearity, and delay. The method of averaging (valid for small ɛ) is used to obtain a slow flow that is analyzed for stability and bifurcations. We show that the 2:1 instability region associated with parametric excitation can be eliminated for sufficiently large delay amplitudes β, and for appropriately chosen time delays T. We also show that adding delay to an undamped parametrically excited system may introduce effective damping.

Theory of parametric amplification in superlattices.

Abstract: We consider a high-frequency response of electrons in a single miniband of superlattice subject to dc and ac electric fields. We show that Bragg reflections in miniband result in a parametric resonance which is detectable using ac probe field. We establish theoretical feasibility of phase-sensitive THz amplification at the resonance. The parametric amplification does not require operation in conditions of negative differential conductance. This prevents a formation of destructive domains of high electric field inside the superlattice.

Continuous-variable entanglement in a nondegenerate three-level laser with a parametric oscillator

Abstract: We consider a nondegenerate three-level cascade laser with a subthreshold nondegenerate parametric oscillator coupled to a vacuum reservoir. Applying the pertinent master equation, we analyze the squeezing and entanglement properties of the two-mode light produced by this quantum optical system inside and outside the cavity. We also determine the normalized second-order correlation function for the two-mode light as well as for individual mode. We find that the light generated by this system is in a two-mode squeezed state and the state of the system is strongly entangled at steady state. Moreover, the presence of the parametric oscillator leads to an increase in the degree of squeezing and entanglement. We also find that the intermode correlation decreases as the injected atomic coherence decreases in the system.

Frequency calibration for a monolithic clock generator and timing/frequency reference

Abstract: Exemplary embodiments of the invention provide a system, method and apparatus for frequency calibration of a free-running, reference harmonic oscillator. An exemplary system comprises the harmonic oscillator, a frequency divider, a comparator, and a reactance modulator. The reference harmonic oscillator includes a plurality of switchable reactance modules controlled by corresponding coefficients, and provides an oscillation signal having an oscillation frequency, which is divided or multiplied by the frequency divider to provide an output signal having an output frequency. The comparator compares the output frequency to an externally supplied reference frequency using first and second predetermined levels of discrimination, and provides first or second comparison signals when the output frequency is higher or lower than the reference frequency. The reactance modulator determines a plurality of coefficients to control switching of the plurality of switchable reactance modules to increase or decrease a reactance of the oscillator in response to the first and second comparison signals.

A 30-GHz Self-Injection-Locked Oscillator Having a Long Optical Delay Line for Phase-Noise Reduction

Abstract: We demonstrate a millimeter-wave self-injection-locked (SIL) oscillator having a long optical delay line as a feedback route. In the SIL oscillator, a part of output signal is self-injected into the oscillator after passing through a long optical delay line, resulting in locked oscillation and phase-noise reduction. By controlling the self-injection power, we achieve 30-GHz oscillation with a sidemode suppression ratio larger than 50 dB and about 18-dB phase-noise reduction at 10-kHz frequency offset.

Narrow-band single photons from a single-resonant optical parametric oscillator far below threshold

Abstract: We present a single-resonant optical parametric oscillator pumped far below threshold as a source for narrow-band single photons. Spontaneous generation of single photons via parametric downconversion is modified and follows the cavity transfer function. Cross-correlation measurements between signal and idler beams show a cavity bandwidth of 62MHz. As the main improvement to prior realizations, our cavity is locked to the pump beam via the Hansch-Couillaud method and therefore allows the continuous generation of heralded single photons with long-term stability.

Parametric resonance for solitons in the nonlinear Schrödinger equation model with time-dependent harmonic oscillator potential

Abstract: The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schrodinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose–Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered.

Precise frequency estimation in a microelectromechanical parametric resonator

Abstract: The authors report here on precise resonant frequency estimation using the nonlinear spectral features of parametric resonance. Demonstration of 100 parts per 109 frequency resolution at room temperature is accompanied by a technique to observe the phase trajectories of escape in bistable parametrically resonant systems. The system offers an expanded dynamic range over similar linear resonators. Precise frequency estimation has implications in resonant mass sensing.

High spectral purity and tunable operation of a continuous singly resonant optical parametric oscillator emitting in the red.

Abstract: Continuous-wave oscillation of a singly resonant optical parametric oscillator operating from 619to640 nm has been obtained. Parametric gain is created in a MgO-doped periodically poled stoichiometric lithium tantalate crystal pumped at 532 nm. 100 mW of single-frequency red light have been generated. The signal frequency is tunable, and its frequency stabilization on an external reference has been achieved.

Principal parametric resonances of a slender cantilever beam subject to axial narrow-band random excitation of its base

Abstract: The non-linear integro-differential equations of motion for a slender cantilever beam subject to axial narrow-band random excitation are investigated. The method of multiple scales is used to determine a uniform first-order expansion of the solution of equations. According to solvability conditions, the non-linear modulation equations for the principal parametric resonance are obtained. Firstly, The largest Lyapunov exponent which determines the almost sure stability of the trivial solution is quantificationally resolved, in which, the modified Bessel function of the first kind is introduced. Results show that the increase of the bandwidth facilitates the almost sure stability of the trivial response and stabilizes the system for a lower acceleration oscillating amplitude but intensifies the instability of the trivial response for a higher one. Secondly, the first and second order non-trivial steady state response of the system is obtained by perturbation method and the corresponding amplitude–frequency curves are calculated when the bandwidth is very small. Results show that the effective non-linearity of whether the amplitude expectation of the first order steady state response or the amplitude expectation of the second order steady state response is of the hardening type for the first mode, whereas for the second mode the effective non-linearity of whether the amplitude expectation of the first order steady state response or the amplitude expectation of the second order steady state response is of the softening type. Finally, the stochastic jump and bifurcation is investigated for the first and second modal parametric principal resonance. The basic jump phenomena indicate that, under the conditions of system parameters with a smaller bandwidth, the most probable motion is around the non-trivial branch of the amplitude response curve, whereas with a higher bandwidth, the most probable motion is around the trivial one of the amplitude response curve. However, the stochastic jump is sometimes more sensitive to the change of the bandwidth, in other words, a small change of bandwidth may induce a series of stochastic jump and bifurcation.

Controllability of the coupled spin- 1 2 harmonic oscillator system

Abstract: We present a control-theoretic analysis of a system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that, by applying external fields with just two resonant frequencies, any desired unitary operator can be generated.

Higher-dimensional periodic and chaotic oscillations for viscoelastic moving belt with multiple internal resonances

Abstract: In this paper, higher-dimensional periodic and chaotic oscillations for a parametrically excited viscoelastic moving belt with multiple internal resonances are investigated for the first time The external damping and internal damping of the material for the viscoelastic moving belt are considered simultaneously First, the nonlinear governing equation of planar motion for the viscoelastic moving belt with the external damping is given Then, the transverse nonlinear oscillations of the viscoelastic moving belt are considered The method of multiple scales and the Galerkin approach are applied directly to the governing partial differential equation of motion for the viscoelastic moving belt to obtain an eight-dimensional averaged equation for the case of 1:2:3:4 internal resonances for the first-, the second-, the third- and the fourth-order modes and primary parametric resonance of the first-order mode Finally, numerical method is used to investigate higher-dimensional periodic and chaotic motions of the viscoelastic moving belt The results of numerical simulation demonstrate that there exist the period, period 2, period 4, multiple period and chaotic motions of the viscoelastic moving belt The multipulse chaotic motions of the viscoelastic moving belt are observed from numerical simulations

Dual-Harmonic Oscillator for Quartz Crystal Resonator Sensors

Abstract: An oscillator circuit is proposed that simultaneously excites and tracks two harmonic resonances in a piezoelectric resonant sensor that, in particular, can be a quartz crystal resonator (QCR) sensor. By probing the resonator at two harmonic modes at the same time, enhanced sensing capabilities can be conveniently achieved because a larger set of parameters can be measured with a single sensor, thereby increasing the information content and accuracy. The principle and circuit architecture can be extended from QCRs to a larger class of piezoelectric microresonator sensors. The oscillator was tested with AT-cut crystals simultaneously operated at the fundamental and third harmonic, both in air and in contact with liquid. The results show an excellent agreement between the oscillator readings and reference measurements taken with an impedance analyzer.

High-fidelity transfer of an arbitrary quantum state between harmonic oscillators

Abstract: It is shown that by switching a specific time-dependent interaction between a harmonic oscillator and a transmission line (a waveguide, an optical fiber, etc.) the quantum state of the oscillator can be transferred into that of another oscillator coupled to the distant other end of the line, with a fidelity that is independent of the initial state of both oscillators. For a transfer time $T$, the fidelity approaches 1 exponentially in $\ensuremath{\gamma}T$ where $\ensuremath{\gamma}$ is a characteristic damping rate. Hence, a good fidelity is achieved even for a transfer time of a few damping times. Some implementations are discussed.

Nonlinear optics with two trapped atoms

Abstract: We show theoretically that two atomic dipoles in a resonator constitute a nonlinear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We identify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics might be observed as a result of self-organization of laser-cooled atoms in resonators.