Mathematical modeling of the population dynamics of “dark” states of a three-level system

Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (??dark??). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.     

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.     

一维原子链局域等离激元的非线性激发

本文基于含时密度泛函理论, 研究了不同频率光脉冲场作用下一维钠原子链中电子的输运与等离激元共振之间的耦合规律. 在等离激元共振点附近约0.8 eV频率范围内的光脉冲场, 都可以激发体系的等离激元共振. 这些不同频率外场激发的等离激元共振强度大小在一个数量级. 外场频率越接近等离激元共振频率, 外场激起的等离激元振动的振幅越大. 对于线性原子链等离激元的非线性激发现象, 本文用经典谐振子模型给出了定性解释.     

Absorption notch in the spectrum of a transform limited pulse of small area

We consider the frequency distribution of the absorption when a short uncertainty broadened light pulse interacts with an atomic resonance sharp with respect to the spectral width of the pulse. We demonstrate theoretically that a sharp absorption notch within the frequency profile of an uncertainty broadened incident light pulse originates from destructive interference between the original pulse and the free induction tail of radiation of excited atoms. The notch is unambiguously observed for nanosecond pulses interacting with an atomic beam of sodium.     

Photon emission from a two-level atom moving in a cavity

The interaction of a two-level atom uniformly moving along a classical trajectory with a high-Q cavity quantum mode is analyzed. The dressed-state method is used to derive a recurrence formula for the transition probability of the atom with photon emission; the temporal dynamics of this probability qualitatively depends on the Doppler shift of the atomic transition frequency, on the Rabi frequency of the atom-field system, and on the detuning of the atomic transition frequency from the field mode frequency. The emission dynamics of a moving atom is very sensitive to the detuning. Rabi-type oscillations with a frequency equal to the Doppler shift can arise under certain conditions. At resonance, the emission probability of a moving atom can considerably exceed the emission probability of an atom at rest. A plane-parallel-mirror cavity and a confocal spherical-mirror cavity are considered. It is shown that the peculiarities of Doppler-Rabi oscillations must be taken into account in micromaser theory.     

Do Mie plasmons have a longer lifetime on resonance than off resonance?

The dynamics of laser-excited electrons in elliptically shaped silver nano-particles is studied using time-resolved two-photon photo-emission. By changing the polarization of the laser pulse at a fixed frequency, a different dynamics is observed near and far from resonance. To analyze these data, the effect of radiation damping on Mie plasmons of Ag nano-particles is studied as a function of laser frequency and polarization. It is shown that the off-resonance lifetime can be shorter or longer than the lifetime at resonance, depending on the incidence conditions of the laser light and on the depolarization factors characterizing the optical response of the nano-particles. Received: 28 August 2001 / Published online: 15 October 2001     

金刚石氮-空位色心的原子自旋声子耦合机理

金刚石氮-空位色心结构因在量子精密测量领域的高灵敏度优势而备受关注.本文引入耦合声子场对氮-空位色心原子自旋进行共振调控,以提高氮-空位色心的自旋跃迁效率.首先,基于波函数和晶格的点阵位移矢量关系,分析了声子与晶格能量交互作用,研究了基于声子共振调控的氮-空位色心的自旋跃迁机理,建立了基于应变诱导的能量转移声子-自旋交互耦合激发模型.其次,基于氮-空位色心晶格振动理论,引入满足布洛赫定理的系数矩阵,建立了不同轴向氮-空位色心第一布里渊区特征区域的声子谱模型.同时,基于德拜模型,考虑热膨胀效应,解析该声子共振系统的声子热平衡性质,并对其比热模型进行研究.最后,基于分子动力学仿真软件CASTEP和密度泛函理论进行第一性原理研究,构建了声子模式下不同轴向氮-空位色心的结构优化模型,并分析了其结构特性、声子特性和热力学特性.研究结果表明,系统声子模式的演化依赖于氮-空位的占位,声子模式强化伴随着热力学熵的降低.含氮-空位色心金刚石的共价键较纯净无缺陷金刚石更弱,热力学性质更不稳定.含氮-空位色心金刚石的声子主共振频段处于THz量级,次共振频率约为[800,1200]MHz.根据次共振频段设计叉指宽度为1.5μm的声表面波共振机构,其中心频率约为930 MHz.在该声子共振调控参数条件下,声子共振调控方法可有效增大氮-空位色心的自旋跃迁概率,实现氮-空位色心原子自旋操控效率的提高.     

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.     

原子力显微镜探针悬臂几何结构变化对高次谐波信息增强的研究

轻敲模式原子力显微镜高次谐波信号包含待测样品表面纳米力学特性等方面的信息, 但是传统原子力显微镜的高次谐波信号非常微弱. 里兹法证明在探针悬臂的特定位置打孔可以实现探针的内共振从而增强高次谐波信号强度. 本文通过有限元仿真计算获得探针第一共振频、第二共振频及其比值随着孔的尺寸和位置变化的规律. 在实验上通过聚焦离子束在探针悬臂上打孔使其第二共振频约为第一共振频的6倍, 提高了第6次谐波信号的信噪比, 并在实验室研制的高次谐波成像实验装置上获得了6次谐波图像. 关键词： 轻敲模式原子力显微镜 探针悬臂几何结构 高次谐波 聚焦离子束加工     

Damping of light in a weakly resonant inhomogeneous medium

On the basis of an expression obtained earlier for the permittivity in the form of a series in powers of the atomic polarizability, the mechanism of damping of light caused by the processes of reemission between two atoms is considered. It is shown that, on an increase in the polarizability, as a consequence of the light frequency approaching the resonance frequency, this mechanism leads to a sharp increase in the extinction coefficient. This effect is caused by the collective behavior of the atoms and is not connected with the natural absorption near the resonance.     

Proliferation of atomic wave packets at the nodes of a standing light wave

A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.     

The cumulative resonance in atomic ground state induced by modulated light field

The interaction of an atomic system with a light beam, intensity-modulated at the ground-state Zeeman frequency is analysed by the dressed-atom method. When the light field is resonant, this interaction produces a new type of degereracy of dressed-atom energy levels which is not of level crossing type. This gives rise to the cumulative resonance with a width depending on the light intensity.     

Dressed-atom model for optical pumping with modulated light

The interaction of an atomic system with the light modulated at the ground-state Zeeman frequency is analysed by the dressed atom method. The analogy between the magnetic resonance and optical pumping with modulated light is emphasized. The dependence of the effects expected in light absorption on the geometry of the experimental arrangement and light polarization is given.     

Quasiclassical dynamics of resonantly driven Rydberg states

We present a semiclassical analysis of the dynamics of Rydberg states of atomic hydrogen driven by a resonant microwave field of linear polarization. The semiclassical quasienergies of the atom in the field are found to be in very good agreement with the exact quantum solutions. The ionization rates of individual eigenstates of the atom dressed by the field reflect their quasiclassical dynamics along classical periodic orbits in the near integrable regime, but exhibit a transition to nonspecific rates when global chaos takes over in phase space. We concentrate both on the principal resonance where the unperturbed Kepler frequency is equal to the driving field frequency and on the higher primary resonance The latter case allows for the construction of nondispersive wave packets which propagate along Kepler ellipses of intermediate eccentricity. Received: 23 June 1998 / Accepted: 10 November 1998     

Effects of an applied low frequency field on the dynamics of a two-level atom interacting with a single-modefield

The effects of an applied low frequency field on the dynamics of a two-level atom interacting with a single-mode field are investigated. It is shown that the time evolution of the atomic population is mainly controlled by the coupling constants and the frequency of the low frequency field, which leads to a low frequency modulation function for the time evolution of the upper state population. The amplitude of the modulation function becomes larger as the coupling constants increase. The frequency of the modulation function is proportional to the frequency of the low frequency field, and decreases with increasing coupling constant.     

Superradiant resonant Rayleigh scattering of light by the Bose-Einstein condensate of rarified atomic gases

Based on the earlier model, the superradiant Rayleigh scattering of the high-intensity short light pulses by the Bose-Einstein condensate of rubidium vapor is studied. It is demonstrated that only six states with a certain momentum are filled when the resonance detuning is about the Rabi frequency. The first two states describe the atomic motion along the condensate due to absorption, whereas the remaining four states describe the atomic motions at angles of 45° and 135° to the condensate axis owing to the reemission of the photon. The condensate pulsations between the state with zero momentum and the last four states are revealed. The corresponding shape of the coherent Rayleigh pulse is found for various resonance detunings.     

Decoherence in the solvable dynamics of <Emphasis Type="Italic">N</Emphasis> strongly driven atoms coupled to a cavity mode

We present the exact solution of the dynamics of N two-level atoms strongly driven by an external coherent field and equally coupled on resonance to a cavity mode, in the presence of both cavity dissipation and atomic decay. Analytical results are presented for system and subsystem dynamics, showing how environment-induced decoherence leads the system from pure to mixed states. In the limit of negligible atomic decay, where the system is known to exhibit decoherence-free subspaces, we present a detailed discussion of the decoherence function that can be monitored by atomic population measurements.     

Collisional redistribution of radiation

The subject of this review is the collisional redistribution of resonance atomic radiation in dilute gases. The formation of scattered spectra in weak and intense fields is discussed and the formation that may be obtained from experiments is presented. The focus of recent work in the field is on radiative events taking place during collisions. Different aspects of the problem are presented using mainly the density matrix and correlation function approach. This work has shown what types of information on interatomic potentials and collision dynamics can be obtained using near-resonant light scattering from gases: this is highlighted in a discussion of light scattering in the presence of depolarizing collisions. We discuss the relationship of work on collisional redistribution to the various “half-collision” experiments that have recently come to the fore.     

Resonance beating of light stored using atomic spinor polaritons

We investigate the storage of light in atomic rubidium vapor using a multilevel-tripod scheme. In the system, two collective dark polariton modes exist, forming an effective spinor quasiparticle. Storage of light is performed by dynamically reducing the optical group velocity to zero. After releasing the stored pulse, a beating of the two reaccelerated optical modes is monitored. The observed beating signal oscillates at an atomic transition frequency, opening the way to novel quantum limited measurements of atomic resonance frequencies and quantum switches.