Atom localization of a two-level pump-probe system via the absorption spectrum

We propose a scheme to localize a two-level atom inside a classical standing wave field conditioned upon the measurement of the frequency of a weak probe field at resonance excitation of a two-level atomic system. Inside the classical standing wave field, the interaction between the atom and the field is position-dependent due to the Rabi frequency of the driving field; hence, as the absorption frequency of the probe field is measured, the position of an atom inside the classical standing wave field will be determined. The effects of atomic parameters on atom localization are then discussed.     

三能级三模量子系统中探测场的增益研究

研究了三能级原子与多模光场相互作用的量子系统，从系统的密度矩阵运动方程出发讨论了无粒子数反转探测场的增益条件，发现当驱动场拉比频率取5，探测场拉比频率取1，非相干抽运取3，驱动场失谐量取3时，系统可以在偏离共振的两端获得粒子数无反转而相应的探测场获得了增益，即实现了无粒子数反转激光，其在光通信方面具有重要的应用价值。     

Absorption and dispersion by a multiple driven two-level atom

We investigate the absorption and dispersion properties of a two-level atom driven by a polychromatic field. The driving field is composed of a strong resonant (carrier) frequency component and a large number of symmetrically detuned sideband fields (modulators). A rapid increase in the absorption at the central frequency and the collapse of the response of the system from multiple frequencies to a single frequency are predicted to occur when the Rabi frequency of the modulating fields is equal to the Rabi frequency of the carrier field. These are manifestations of the undressing or a disentanglement of the atomic and driving field states, that leads to a collapse of the atom to its ground state. Our calculation permits consideration of the question of the undressing of the driven atom by a multiple-modulated field and the predicted spectra offer a method of observing undressing. Moreover, we find that the absorption and dispersion spectra split into multiplets whose structures depend on the Rabi frequency of the modulating fields. The spectral features can jump between different resonance frequencies by changing the Rabi frequency of the modulating fields or their initial phases, which can have potential applications as a quantum frequency filter. Received 23 October 2001 and Received in final form 31 January 2002     

Superposition of Stationary Wave Fields Via Atom Microscopy

We investigate one-dimensional position microscopy of a three-level atom moving through a stationary wave region under the condition of electromagnetically induced transparency.The precise position information of an atom is observed on the resonance absorption and dispersion distribution spectrum of a weak probe field.Single and multiple localization peaks are observed in specific directions of the corresponding wave numbers and phase of the standing wave fields.The strength of space-independent Rabi frequency reduces the position uncertainty in the localized peaks without disturbing the probability of the atom.In a hot atomic medium the localized probability of an atom is reduced which depends upon the temperature of that medium.Our results provide useful applications in the development of laser cooling,atom nanolithography and Bose-Einstein condensation.     

Coherent scattering of an atom in the field of a standing wave under conditions of initial quantum correlation of subsystems

Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.     

倒Y型四能级量子系统中亚光速和超光速传播现象的转换研究

研究了探测场、耦合场和驱动场三场作用下倒Y型四能级量子系统的光学特性,利用数值模拟的方法探讨了外加相干驱动场的拉比频率和失谐量变化时系统对探测光场吸收特性的影响. 通过绘制三维立体图,发现了探测光场的群速度在电磁诱导透明窗口处的变化规律,并且选择合适的驱动场拉比频率和失谐量,可以在理论上实现亚光速和真空光速以及超光速传播之间的转换. 关键词： 倒Y型四能级 群速度 超光速传播 亚光速传播     

Nonstationary parametric amplification of polychromatic radiation propagating in an extended absorbing resonant medium

An experimental and theoretical study of the two-wave interaction (of a probe wave and a pumping wave) of wide-band multimode laser pulses with an optically dense extended resonant medium (metastable neon atoms in a positive glow-discharge column) is presented. Depending on the pumping power and characteristics of the medium, various regimes of interaction between the field and the matter, leading to qualitatively different types of amplification spectra, are realized: a cooperative interaction regime at low pumping powers corresponds to amplification spectra consisting of two peaks, which lie on both sides of the absorption line; in the regime of nonstationary Rabi oscillations (Rabi flopping), the amplification appears in the form of an isolated peak at a frequency close to the resonance in the substance; under certain interaction conditions, a dispersive shape of amplification spectra is observed. A significant gain in the probe field (by several times at a length of 10 cm) is obtained as a result of a nonstationary population inversion upon rotation of the Bloch vector of the resonant medium under the action of a strong pumping field in the course of propagation of the two waves.     

驻波场中原子的跃迁速率与所受辐射压力的关系

从二能级原子的密度矩阵运动方程出发,研究了原子在驻波场中的受激吸收速率、受激辐射速率和辐射压力的对应关系,提出了在驻波场中原子所受的辐射压力由受激吸收力和受激辐射力构成。此观点可以推广至N个行波场和原子相互作用的情况。     

电磁诱导下Y型四能级原子系统的左手效应

采用了一个闭合的Y型四能级原子系统,在多模光场的作用下,利用量子相干技术使其实现介质的左手效应,使介质具备左手材料特性. 在相互作用表象下,考虑偶极近似和旋转波近似,利用密度矩阵方程并结合相关条件下的有关公式进行理论计算. 数值模拟结果显示：在合适的参量条件下,介质的相对介电常量和相对磁导率可以同时出现负值,产生了左手效应,相应的介质转化为左手材料.在弱探测场条件下,当探测光的拉比频率增加时,介质实现左手效应的频率范围减小并且与之相对应的折射率和吸收系数也发生变化. 通过讨论在左手效应成立的条件下介质对光场的吸收和增益问题,结果表明：在弱探测场条件下,利用电磁诱导的方法也可以实现介质的左手效应,使得左手材料在实验上的实现也得到了进一步的扩展,同时也扩展了电磁诱导的应用领域.     

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.     

Deflection and internal dynamics of atoms dressed by a resonant standing wave

A unitary transformation to dress a two-level atom by the field of a resonant standing wave is shown to yield in a very simple way the main results of previous theories of deflection without using explicit analytical or numerical solutions of the Schrödinger equation. A generalization of Rabi precession induced by an inhomogeneous standing wave is obtained.     

Preparation of steady-state entanglement via a laser-excited resonant interaction

In this paper we propose a scheme in which two-mode entanglement in a steady state is produced by using two lasers to resonantly drive a single four-level atom embedded inside a two-mode optical cavity.In this scheme,atomic coherence induced by a classical laser plays an important role in the process of preparing the entangled state.With the coupling of a strong control field,direct two-photon transition is generated and the relatively weak pump field induces the parametric interaction between two photons,which makes them entangle with each other.By numerical calculation,we find that the degree of entanglement depends strongly on the Rabi frequencies of the classical laser fields and the cavity losses.     

Dynamics of spontaneous radiation of atoms scattered by a resonance standing light wave

The scattering of atoms by a resonance standing light wave is considered under conditions when the lower of two resonance levels is metastable, while the upper level rapidly decays due to mainly spontaneous radiative transitions to the nonresonance levels of an atom. The diffraction scattering regime is studied, when the Rabi frequency is sufficiently high and many diffraction maxima are formed due to scattering. The dynamics of spontaneous radiation of an atom is investigated. It is shown that scattering slows down substantially the radiative decay of the atom. The regions and characteristics of the power and exponential decay are determined. The adiabatic and nonadiabatic scattering regimes are studied. It is shown that the wave packets of atoms in the metastable and resonance excited states narrow down during scattering. A limiting (minimal) size of the wave packets is found, which is achieved upon nonadiabatic scattering in the case of a sufficiently long interaction time.     

Gain without population inversion in a two-level atom damped by a broadband squeezed vacuum

We study the absorption spectrum of a two-level atom driven by a resonant laser field and damped by a broadband squeezed vacuum. We show that for some values of the Rabi frequency of the driving field the central component of the absorption spectrum can switch from absorption to amplification. We find that the presence of the squeezed vacuum field is essential for the gain at the central component. Moreover, the gain is not attributed to any population inversion in both the atomic bare states and in the dressed atomic states. We show that the gain originates from the coherent population oscillations, which are significantly enhanced when the atom is damped by a broadband squeezed vacuum.     

Interaction Dynamics of the External and Internal Degrees of Freedom of an Atom in the Resonant Field of a Standing Light Wave

The theory of the dynamic interaction of the external (translational) and internal (electronic) degrees of freedom of a twolevel atom in the field of a standing light wave in a perfect cavity of the Fabry–Perot type was developed. The theory describes the energy exchange between three subsystems, namely, translational, electronic, and field subsystems, as opposed to the theories of the parametric interaction (in the approximations of Raman–Nath and/or large resonance detuning) and of the atomic motion in free space. In the semiclassical approximation, the corresponding Heisenberg equations of motion were shown to form a closed Hamiltonian dynamic system with two degrees of freedom, namely, translational and collective electron–field degrees of freedom. This system is integrated in terms of the elliptic Jacobian functions in the resonance limit. The solutions obtained describe the effects of trapping of an atom in the periodic potential of the standing light wave, and its cooling and heating, as well as the effect of the dynamic Rabi oscillations. The latter is caused by the interaction of the internal and external atomic degrees of freedom through the radiation field.     

准Λ型四能级原子系统在弱场中的增益及电磁感应透明

利用数值模拟的方法讨论了稳态下准型四能级原子与两光场相互作用系统对探测场的增益以及与粒子数布居规律之间的关系。结果表明即使在场较弱的情况下,随着探测场和它所对应能级间跃迁频率失谐量的变化,系统在所有拉比频率相位为零时对探测光总会同时呈现三个增益峰和两个固定的产生电磁感应透明(EIT)现象的位置,并且当系统呈现电磁感应透明的同时,探测场所对应的高能级粒子数为零;而拉比频率相位的变化则会导致系统对探测光既有吸收也有增益,并且也呈现电磁感应透明现象,但仅仅相位的变化并不影响高能级的粒子数分布。值得注意的是该结果均在精确求解下所得。     

准A型四能级原子系统中的烧孔和光学双稳现象

研究了准A型四能级原子与两光场相互作用系统中的量子干涉效应．发现在弱探测场下系统驱动场拉比频率改变时，其色散曲线会呈现出烧孔现象，吸收增益曲线会出现全增益区以及宽而平坦的电磁感应透明窗口．另外，色散曲线随探测场拉比频率相位的演化会呈现出光学双稳态效应．     

Chimera states in an ensemble of linearly locally coupled bistable oscillators

Effects of quantum deviation of a two-level atom at coherent scattering on an inhomogeneous optical potential created by crossed electromagnetic fields are considered. The region of interaction is formed by a lowfrequency quantized standing wave from a micromaser and a coherent traveling optical wave generated by an optical fiber located inside a cavity. The atom interacts with both fields under the conditions of two-photon two-wave resonance. It is shown that two effects of quantum deviation of translational motion of the atom can be observed. Interaction with the standing wave is caused under these conditions by a harmonic potential the character of scattering of the atom on which depends significantly on the initial conditions of preparation of the atom and quantized mode. The other effect—deviation of the atom by the classical traveling wave—is also completely quantum mechanical under these conditions and is produced by the noncommutative contribution of the kinetic energy operator of the atom and the interaction energy.     

Ξ型三能级原子玻色-爱因斯坦凝聚体单模光场系统中双模原子激光的压缩性质

研究了Ξ型三能级原子玻色-爱因斯坦凝聚体单模光场系统中双模原子激光的压缩性质.结果表明:双模原子激光能被周期性压缩,并且具有量子Rabi振荡和崩塌-回复现象两种形式的振荡.最大压缩深度和崩塌-回复振荡频率主要依赖于光场与原子间相互作用强度,量子Rabi振荡频率主要由光场圆频率决定.     

Nonlinear coherent dynamics of an atom in an optical lattice

We consider a simple model of the lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. The internal dynamics of the atom is governed by the laser field, which is treated as classical with a large number of photons. The center-of-mass classical atomic motion is governed by the optical potential and the internal atomic degrees of freedom. The resulting Hamilton-Schrö dinger equations of motion are a five-dimensional nonlinear dynamical system with two integrals of motion, and the total atomic energy and the Bloch vector length are conserved during the interaction. In our previous papers, the motion of the atom has been shown to be regular or chaotic (in the sense of exponential sensitivity to small variations of the initial conditions and/or the system’s control parameters) depending on the values of the control parameters, atom-field detuning, and recoil frequency. At the exact atom-field resonance, the exact solutions for both the external and internal atomic degrees of freedom can be derived. The center-of-mass motion does not depend in this case on the internal variables, whereas the Rabi oscillations of the atomic inversion is a frequency-modulated signal with the frequency defined by the atomic position in the optical lattice. We study analytically the correlations between the Rabi oscillations and the center-of-mass motion in two limiting cases of a regular motion out of the resonance: (1) far-detuned atoms and (2) rapidly moving atoms. This paper is concentrated on chaotic atomic motion that may be quantified strictly by positive values of the maximal Lyapunov exponent. It is shown that an atom, depending on the value of its total energy, can either oscillate chaotically in a well of the optical potential, or fly ballistically with weak chaotic oscillations of its momentum, or wander in the optical lattice, changing the direction of motion in a chaotic way. In the regime of chaotic wandering, the atomic motion is shown to have fractal properties. We find a useful tool to visualize complicated atomic motion-Poincaré mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincaré mappings are constructed using the translational invariance of the standing laser wave. We find common features with typical nonhyperbolic Hamiltonian systems-chains of resonant islands of different sizes imbedded in a stochastic sea, stochastic layers, bifurcations, and so on. The phenomenon of the atomic trajectories sticking to boundaries of regular islands, which should have a great influence on atomic transport in optical lattices, is found and demonstrated numerically.