Parametric resonance and cooling on an atom chip

This paper observes the parametric excitation on atom chip by measuring the trap loss when applying a parametric modulation. By modulating the current in chip wires, it modulates not only the trap frequency but also the trap position. It shows that the strongest resonance occurs when the modulation frequency equals to the trap frequency. The resonance amplitude increases exponentially with modulation depth. Because the Z-trap is an anharmonic trap, there exists energy selective excitation which would cause parametric cooling. We confirm this effect by observing the temperature of atom cloud dropping.     

Theorie der Erzeugung der Differenzfrequenz zwischen Signal- und Idlerwelle eines optisch-parametrischen Oszillators außerhalb eines Resonators

Theory of Difference Frequency Generation between Signal and Idler Waves of an Optical Parametric Oscillator outside a Resonator The difference frequency generation between signal and idler wave of an optical parametric oscillator taking place outside a resonator is investigated theoretically. The efficiency of frequency transformation in the stationary state is computed. It is shown that the efficiency is determined by the resonance type of the parametric oscillator, by its relative excitation and by the nonlinear crystals used. An efficiency of difference frequency generation of 100% is attainable by using a doubly resonant oscillator with a ring resonator.     

Monte Carlo Simulation of Cooling Induced by Parametric Resonance

We demonstrate that the parametric resonance in a magnetic quadrupole trap can be exploited to cool atoms by using Bird＇s method. In our programme the parametric resonance was realized by anisotropically modulating the trap potential. The modulation frequency dependences of temperature and fraction of the trapped atoms are explored. Furthermore, the temperature after the modulation as functions of the modulation amplitude and the mean elastic collision time are also studied. These results are valuable for the experiment of parametric resonance in a quadrupole trap.     

High-order resonances in a parametrically excited magneto-optical trap

We present analytical and numerical study of high-order parametric resonance in a driven magneto-optical trap of cold atoms. We have obtained the general solutions for parametric resonance of arbitrary order. In particular, the amplitude and phase of atomic limit-cycle motion is expressed as a function of the modulation amplitude and frequency. Moreover, the atomic dynamics for high-order parametric resonance is investigated in terms of the Hamiltonian approach, which is useful in studying transitions between attractors. We find that the analytical results are in good agreement with the numerical calculations.     

双KTP晶体倍频过程的实验研究(二)——光学参量振荡腔内串接倍频

按第一部分指出的串接方位,将串接的双KTP晶体置于光学参量振荡腔中,并采用控温方式补偿程差,实现双模共振,使倍频效率较内腔单模起振提高近30倍,理论分析与实验结果基本符合。     

色噪声参激和周期调制噪声外激联合驱动的分数阶线性振子的共振行为

研究了色噪声参激和周期调制噪声外激联合驱动的分数阶线性振子及其共振行为, 利用Laplace变换和Shapiro-Loginov公式, 推导出了系统响应的一阶矩及稳态响应振幅的解析表达式. 讨论了系统阶数、摩擦系数、周期驱动力频率、色噪声强度和相关率等参数对系统稳态响应的影响, 发现系统稳态响应振幅具有非单调变化的特点, 即出现了广义随机共振现象. 并且在适当参数下, 稳态响应振幅还存在具有双峰的广义随机共振现象.     

Nonequilibrium dynamics of parametrically excited cold atoms via magnetic field-gradient modulation

We propose that the driven cold atomic system whose trap potential is periodically perturbed via parametric modulation of the magnetic field-gradien is a novel system to investigate the complex dynamics in nonlinear dynamical systems. We calculate the atomic trajectories and basins of attraction by varying the modulation amplitude and the modulation frequency. The calculation results show parametric resonance similar to those in Kim et. al.'s work [Opt. Commun. 236 (2004) 349] on cold atoms under parametric modulation of trap laser intensities in the case of small modulation amplitude or low modulation frequency. As the modulation amplitude or the modulation frequency is increased, the nonlinear effects are enhanced so that the dynamics of the system shows a wide variety of nonlinear behaviors, such as period doubling and chaos. We experimentally demonstrate the parametric resonance when the magnetic field gradient is parametrically modulated, which evidences the realization of the proposed system. We expect that this system is useful for understanding the stochastic phenomena occurring between complex basins of attraction, such as fluctuation induced transitions across the complex basin boundaries.     

Sensitive wavelength-modulated photoacoustic spectroscopy with a pulsed optical parametric oscillator

With a laser-excited acoustic wave as the carrier wave and by modulation of the light wavelength of a multikilohertz-repetition-rate optical parametric oscillator at a lower frequency than the acoustic frequency, we demonstrate a wavelength-amplitude double-modulation technique and achieve an enhancement factor of 35 in sensitivity in photoacoustic trace gas detection with the technique.     

Nonadiabatic pattern formation in optical parametric oscillators

A nonadiabatic mechanism for pattern formation in parametrically forced systems subjected to a slow periodic modulation of the excitation frequency is proposed and discussed in detail for the case of an optical parametric oscillator. It is demonstrated that nonautonomous dynamics may induce nonadiabatic off-axis emission of down-converted photons even when the signal field is blueshifted from the nearby cavity resonance.     

Two cold atoms in a time‐dependent harmonic trap in one dimension

We analyze the dynamics of two atoms with a short‐ranged pair interaction in a one‐dimensional harmonic trap with time‐dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non‐interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occurs we find that the interaction can significantly reduce the rate of energy increase. The implications for applications of our findings to cool or heat the system are also discussed.     

Bifurcation and resonance in a fractional Mathieu-Duffing oscillator

The bifurcation and resonance phenomena are investigated in a fractional Mathieu-Duffing oscillator which contains a fast parametric excitation and a slow external excitation. We extend the method of direct partition of motions to evaluate the response for the parametrically excited system. Besides, we propose a numerical method to simulate different types of local bifurcation of the equilibria. For the nonlinear dynamical behaviors of the considered system, the linear stiffness coefficient is a key factor which influences the resonance phenomenon directly. Moreover, the fractional-order damping brings some new results that are different from the corresponding results in the ordinary Mathieu-Duffing oscillator. Especially, the resonance pattern, the resonance frequency and the resonance magnitude depend on the value of the fractional-order closely.     

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.     

Parametric instability of quantum oscillator

It is shown that the dynamic symmetry group of an oscillator with variable frequency is the line or group SL(2, R). Classical and quantum oscillators are described respectively by two-dimensional representations of this group. The conditions for the appearance of parametric resonance are investigated. For the case of periodic frequency modulation, nonspreading coherent states are constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–12, May, 1979.     

Parametric resonance of optically trapped aerosols

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.     

Combination of a continuous-wave optical parametric oscillator and a femtosecond frequency comb for optical frequency metrology

We combined a tunable continuous-wave optical parametric oscillator and a femtosecond Ti:sapphire laser frequency comb to provide a phase-coherent bridge between the visible and the mid-infrared spectral ranges. As a first demonstration of this new technique we performed a direct frequency comparison between an iodine-stabilized Nd:YAG laser at 1064 nm and an infrared methane optical frequency standard at 3.39 microm.     

Squeezing in the audio gravitational-wave detection band

We demonstrate the generation of broadband continuous-wave optical squeezing from 280 Hz-100 kHz using a below-threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise, and detuning fluctuations, present in optical parametric amplifiers, have negligible effect on squeezing produced by a below-threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational-wave detectors.     

Widely tunable photonic crystal fiber Fabry-Perot optical parametric oscillator

We present a widely tunable low-threshold chi(3) optical parametric oscillator. The oscillator cavity is formed by butt coupling dichroic mirrors to either end of a highly nonlinear index-guiding photonic crystal fiber. This yields a singly resonant Fabry-Perot oscillator with a high feedback fraction for the resonant parametric sideband. The tuning range of the output parametric sideband stretches from 23 to 164 THz above the pump frequency. The threshold power of the oscillator is only 15 W.     

Parametric frequency transformation in a superconducting waveguide line with an integrated Josephson oscillator

The parametric frequency division in a coplanar waveguide line with an integrated single-contact rf SQUID (Josephson oscillator) is discussed. It is assumed that the oscillator is excited by pump pulses whose carrier frequency can be a multiple of the plasma frequency of the oscillator. It is shown that the Josephson oscillator excited at the pump frequency can induce frequency division by emitting subharmonics that are multiples of the fundamental frequency (fractional resonances). Parameters for which parametric frequency transformation occurs are determined. The possible generalization of this effect to the quantum case in which correlated microwave photons (entangled photon states) can be generated is discussed.     

Pulsed degenerate optical parametric oscillator based on a nonlinear-fiber Sagnac interferometer

We report operation of an all-fiber degenerate optical parametric oscillator that employs a nonlinear-fiber Sagnac interferometer as a parametric amplifier. Synchronous pumping with 3.9-ps pulses at 1544 nm yields 0.83-ps output pulses. The wide bandwidth of the fiber parametric amplifier causes the oscillator to act as a pulse compressor. The output signal pulses exhibit improved spectral symmetry and a reduced time-bandwidth product compared with the pump pulses. Currently, the net group-velocity dispersion in the passive section of the fiber cavity limits the signal-pulse bandwidth and hence the minimum-obtainable pulse width. This experiment suggests the possibility of frequency conversion by operation of a similar pulsed parametric oscillator away from degeneracy.     

Broadband optical frequency comb generation with a phase-modulated parametric oscillator

We introduce a novel broadband optical frequency comb generator consisting of a parametric oscillator with an intracavity electro-optic phase modulator. The parametric oscillator is pumped by 532-nm light and produces near-degenerate signal and idler fields. The modulator generates a comb structure about both the signal and the idler. Coupling between the two families of modes results in a dispersion-limited comb that spans 20 nm (5.3 THz). A signal-to-noise ratio of >30 dB in a 300-kHz bandwidth is observed in the beat frequency between individual comb elements and a reference laser.