蒙特卡罗模拟四极阱中原子的参变激发

在中性原子的磁囚禁实验中,磁阱线圈的电流噪声会激发磁阱中的原子运动,势必对原子团的温度和寿命产生不可忽视的影响。对于非简谐阱,这种激发具有能量选择特性,它又取决于电流噪声的频谱分布。选择了实验中常用的四极阱为研究对象,用直接模拟蒙特卡罗方法来模拟四极阱中原子运动的参变激发现象,得到了原子温度与原子数损失随激发频率的变化关系,并进一步计算了两个共振峰处原子温度随调制时间和调制深度的变化曲线。此外,还研究了弹性碰撞速率对参变激发过程中原子温度上升的影响。这些结果对四极阱参变激发的实验有较好的参考价值。     

Faraday patterns in bose-Einstein condensates

Temporal periodic modulation of the interatomic s-wave scattering length in Bose-Einstein condensates is shown to excite subharmonic patterns in the atom density through a parametric resonance. The dominant wavelength of the spatial structures is primarily selected by the excitation frequency but also affected by the depth of the spatial modulation via a nonlinear resonance. These phenomena represent analogues of the Faraday patterns excited in vertically vibrated liquids.     

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.     

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.     

Spin dynamics of magnetic resonance with parametric modulation in a potassium vapor cell

A typical magnetic-resonance scheme employs a static bias magnetic field and an orthogonal driving magnetic field oscillating at the Larmor frequency, at which the atomic polarization precesses around the static magnetic field. Here we demonstrate both theoretically and experimentally the variations of the resonance condition and the spin precession dynamics resulting from the parametric modulation of the bias field. We show that the driving magnetic field with the frequency detuned by different harmonics of the parametric modulation frequency can lead to resonance as well. Also, a series of frequency sidebands centered at the driving frequency and spaced by the parametric modulation frequency can be observed in the precession of the atomic polarization. We further show that the resonant amplitudes of the sidebands can be controlled by varying the ratio between the amplitude and the frequency of the parametric modulation. These effects could be used in different atomic magnetometry applications.     

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.     

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.     

Direct measurement of the oscillation frequency in an optical-tweezers trap by parametric excitation

We demonstrate a novel technique for direct measurement of the oscillation frequency in an optical-tweezers trap. The technique uses the phenomenon of parametric resonance in an oscillator when the stiffness of the trapping potential is modulated. The trapped particle is a strongly damped oscillator; hence, the signature of parametric resonance is not an increase in the amplitude but an increase in the size of Brownian fluctuations. The trap frequency is measured with an accuracy of 0.1%, which is better than previous techniques and thus opens up new possibilities in experiments with optical tweezers.     

Cooling induced by parametric resonance in a magnetic quadrupole trap

It is demonstrated experimentally that the anharmonic property of the quadrupole trap can be exploited to cool trapped atoms by modulating the trap potential anisotropically.This cooling effect arises from the energy-selective removal of the most energetic trapped atoms and the thermal equilibrium of the remaining atoms.The frequency dependences of the temperature and the fraction of the atoms left in the trap after the modulation are explored.It is also demonstrated that the cooling induced by parametric resonance can also increase the phase space density of the trapped atoms.     

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.     

Individual and center-of-mass resonances in the motional spectrum of an electron cloud in a Penning trap

We have examined experimentally the motional spectrum of an electron cloud confined in a Penning trap. When the axial oscillation is excited by a radio frequency field the resonance exhibits a double structure. Both components depend differently on the number of trapped electrons and have different shape and width. We conclude that one of them corresponds to the excitation of the individual electrons while the other is the center-of-mass mode of the cloud. The threshold behaviour of the center-of-mass resonance suggests that it is a parametric instability of a Mathieu type equation of motion. Received 11 July 2001 and Received in final form 12 November 2001     

低密等离子体通道中的非共振激光直接加速

在低密等离子体通道中, 横向有质动力可以有效调制电子的横向振荡过程. 一方面, 横向有质动力可以向外推动电子, 增大电子横向振荡振幅, 减小失相率, 使电子获得能量增益; 另一方面, 横向有质动力也可以通过对失相率的非线性调制来降低失相率, 在电子横向振荡振幅很小的情况下导致激光直接加速. 横向有质动力调制的大小由等离子体密度、激光强度和束宽共同决定. 三维模型结果也证实可以通过参数放大实现激光直接加速, 弥补了准二维模型的局限性.     

基于垂直引线和调制电流的三线环形磁导引

提出了一种在单层原子芯片上实现闭合且导引中心无磁场零点的环形磁导引的新方案. 芯片表面刻蚀的导线结构由同心等距三环线构成, 三环线的电流引线垂直于芯片表面. 加载直流电流后, 这种构型即可在芯片表面附近产生闭合的环形磁导引. 交流调制三环线电流后, 环形磁导引的势能极小值附近不再存在磁场零点且其磁场起伏小. 这种方案可用于基于物质波干涉的原子芯片陀螺仪研究.     

Stability regions for Mathieu equation with imperfect periodicity

We consider a mean square stability for Mathieu equation with a random phase modulation in parametric excitation. An efficient numerical scheme is proposed for obtaining the stability charts for this equation. The influence of the random phase modulation on the shape of parametric resonance regions is studied. It is found that this influence can lead to stabilization under some conditions. A comparison with a case of Gaussian parametric excitation is presented.     

Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory

In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.     

Quasi-energy of single quantum particles and a Bose-Einstein condensate in a dynamical trap

The quasi-energy states have been found analytically for single quantum particles and an atomic Bose-Einstein condensate in a trap with periodically oscillating walls with a small modulation depth. A resonance is shown to exist as the modulation frequency approaches the difference of the frequencies corresponding to the levels in the unperturbed problem. Quasi-energy splitting and, accordingly, beats with a periodic population exchange between two levels in resonance have been found in the resonant case. Bistability of the response to trap size modulation, when the sustenance (depending on the initial conditions) of various quasi-energy states is possible under the same conditions, has been found for a Bose-Einstein condensate under resonance conditions.     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

Difference-frequency ultrasound generation from microbubbles under dual-frequency excitation

The difference-frequency (DF) ultrasound generated by using parametric effect promises to improve detection depth owing to its low attenuation, which is beneficial for deep tissue imaging. With ultrasound contrast agents infusion, the harmonic components scattered from the microbubbles, including DF, can be generated due to the nonlinear vibration. A theoretical study on the DF generation from microbubbles under the dual-frequency excitation is proposed in formula based on the solution of the RPNNP equation. The optimisation of the DF generation is discussed associated with the applied acoustic pressure, frequency, and the microbubble size. Experiments are performed to validate the theoretical predictions by using a dual-frequency signal to excite microbubbles. Both the numerical and experimental results demonstrate that the optimised DF ultrasound can be achieved as the difference frequency is close to the resonance frequency of the microbubble and improve the contrast-to-tissue ratio in imaging.     

[Russian Text Ignored]

The stability of the electromagnetic plasma confinement by powerful external s-polarized pump waves is considered. The parametric excitation of standing electromagnetic waves along the plasma boundary with frequencies close to the frequency of the pump wave leads to a periodic density modulation of the plasma boundary. The density disturbances along the direction of the external wave field are connected to the excitation of transverse p-polarized surface waves while the modulation in the direction perpendicular to the pump field are created by the parametric interaction between the external wave and s-polarized trapped leaking oscillations. Only when the leaking waves are excited the scale length of the modulation is larger than half the free space wave length of the incident radiation.     

Universal quantum control based on parametric modulation in superconducting circuits

As superconducting quantum circuits are scaling up rapidly towards the noisy intermediate-scale quantum(NISQ)era, the demand for electronic control equipment has increased significantly. To fully control a quantum chip of N qubits,the common method based on up-conversion technology costs at least 2 × N digital-to-analog converters(DACs) and N IQ mixers. The expenses and complicate mixer calibration have become a hinderance for intermediate-scale quantum control.Here we propose a universal control scheme for superconducting circuits, fully based on parametric modulation. To control N qubits on a chip, our scheme only requires N DACs and no IQ mixer, which significantly reduces the expenses. One key idea in the control scheme is to introduce a global pump signal for single-qubit gates. We theoretically explain how the universal gates are constructed using parametric modulation. The fidelity analysis shows that parametric single-qubit(two-qubit) gates in the proposed scheme can achieve low error rates of 10~(4), with a gate time of about 60 ns(100 ns).