原子-场强度相关耦合时原子质心平移运动与内态布居的关系

基于原子与腔场共振相互作用及原子-场缀饰态,讨论了驻波腔场中两能级原子与场耦合强度相关时的原子质心的量子化平移运动对原子内态布居间的相互影响。结果表明原子平移运动敏感地依赖于原子的内态布居。特别地,当原子处于两内态等权重同位相迭加态时,平移运动呈现出很稳定的特征。     

高Q腔中原子内态布居对原子平移运动的影响

基于原子作双光子共振跃迁的原子－场缀饰态，讨论了驻波腔场中两能级原子的量子化平移运动与原子内态布居间的相互影响，结果表明原子平移运动敏感地依赖于原子的内态布居，特别当原子处于两内态等权重同相位叠加态时，平移运动呈现出很稳定的特征。     

The effect of atomic motion and two-quanta JCM on the information entropy

We study the interaction between a moving two-level atom and a single-mode field. The coupled atom-cavity system with atomic center-of-mass motion included is modeled by considering the dependence of the atomic motion along z-axis. At exact resonance between the internal atomic transition and the cavity eigenfrequency, an exact solution of the system is obtained and periodically modulated Rabi oscillations and regular translational motion are observed. We focused on the dynamics of both field Wehrl entropy and Wehrl phase distribution. The influence of the atomic motion on the evolution of von Neumann entropy and Wehrl entropy is examined. The results show that the atomic motion and the field-mode structure play important roles in the evolution of the von Neumann entropy, Wehrl entropy and Wehrl PD.     

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.     

Collective atomic motion in an optical lattice formed inside a high finesse cavity

We report on collective nonlinear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance linewidth. We observe bistability and self-induced squeezing oscillations resulting from the retroaction of the atoms upon the optical potential wells. We can well understand most of our observations within a simplified model assuming adiabaticity of the atomic motion. Nonadiabatic aspects of the atomic motion are reproduced by solving the complete system of coupled nonlinear equations of motion.     

Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice

A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.     

Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity

Localization to the ground state of axial motion is demonstrated for a single, trapped atom strongly coupled to the field of a high finesse optical resonator. The axial atomic motion is cooled by way of coherent Raman transitions on the red vibrational sideband. An efficient state detection scheme enabled by strong coupling in cavity QED is used to record the Raman spectrum, from which the state of atomic motion is inferred. We find that the lowest vibrational level of the axial potential with zero-point energy variant Planck's over 2 h omega a/2kB = 13 microK is occupied with probability P0 approximately 0.95.     

利用高阶拉盖尔-高斯横模精确测量法布里-珀罗腔内原子的运动轨迹

研究了冷原子与法布里-珀罗腔内拉盖尔-高斯横模强耦合相互作用体系的透射光谱, 分析了透射光谱与原子在腔中运动轨迹的关系. 结果表明, 与厄米特-高斯横模相比, 拉盖尔-高斯横模的腔场与原子的最大耦合系数几乎不随阶数的增加而变化, 使得探测光谱的对比度受模式阶数的影响较小. 在拉盖尔-高斯横模场分布的圆环边缘附近, 原子运动轨迹的微小偏移会引起透射光谱的很大变化, 因此在这些位置可以实现原子运动轨迹的高精度探测.     

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.     

Quantum feedback control of atomic motion in an optical cavity

We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies.     

Dynamics of a moving five-level atom interacting with cavity fields

We study the entanglement between a single five-level atom interacting with a one-mode cavity field in the case where the atomic motion is taken into account. The field entropy of this system is investigated under the nonresonant conditions. The effects of the detuning parameter and the atomic motion on the degree of entanglement are investigated. We show that both the detuning and atomic motion play important roles in the evolution of the von Neumann entropy and atomic populations.     

Quantum Entropy of a Nonlinear Two-level Atom with Atomic Motion

The wave function of a system governed by the time-dependent nonlinear Jaynes-Cummings (JC) model is obtained. We compute analytically the eigenvalues of the reduced field density operator by which the dynamics of the entropy of entanglement of the cavity field are analyzed. The influences of the atomic motion, the field-mode structure and the Kerr-like medium on this phenomenon are illustrated. The population dynamics of an excited atom is also discussed for the same set of parameters. The cavity field is assumed to be initially excited in either a Fock or a coherent states. The cavity excitation in a Fock state generates a class of an entanglement without death with fixed amplitude by adjusting the parameters of the atomic motion as well as the Kerr and the field-mode structure. In case of a coherent cavity, the only phenomenon to be noted is the periodical behavior of the dynamics under study when the atomic motion is considered. Although the Kerr medium affects the strength of the entanglement negatively, the entropy of entanglement loses its zeros where the Kerr is taken into consideration.     

Controlled generation of momentum states in a high-finesse ring cavity

A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons of a pump beam into counterpropagating cavity modes, populating a bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil linewidth allows to control the quantized atomic motion, selecting particular discrete momentum states and generating atom-photon entanglement. The semiclassical and quantum model for the 2D collective atomic recoil lasing (CARL) are derived and the superradiant and good-cavity regimes discussed. For pump incidence perpendicular to the cavity axis, the momentum lattice is symmetrically populated. Conversely, for oblique pump incidence the motion along the two recoil directions is unbalanced and different momentum states can be populated on demand by tuning the pump frequency.     

Feedback control of a single atom in an optical cavity

We discuss feedback control of the motion of a single neutral atom trapped inside a high-finesse optical cavity. Based on the detection of single photons from a probe beam transmitted through the cavity, the position of the atom in the trap is estimated. Following this information, the trapping potential is switched between a high and a low value in order to counteract the atomic motion. This allowed us to increase the storage time by about one order of magnitude. Here, we describe the technical implementation of the feedback loop and give a detailed analysis of its limitations as deduced from Monte-Carlo simulations. We also discuss different strategies to further improve the performance of the feedback.     

原子质心运动对Λ型三能级原子动力学行为的影响

研究了由单模腔场驱动的质心做谐振运动的Λ型三能级原子系统,考察了腔场、原子内态及其质心运动线性熵的演化特征,结果表明原子质心运动不仅影响腔场与原子内态线性熵的演化规律而且能够有效地改变两者的关系. 关键词： 原子质心运动 Λ型三能级原子 线性熵     

单个二能级超冷原子在多个单模腔场间的共振隧穿和光子辐射

考虑单个二能级超冷原子穿过多个空间分离的单模腔场，研究原子质心运动的动能、腔长和腔间距对原子透射率和光子辐射率的影响.在腔间距等于原子质心运动de Broglie波的半波长整数倍时，结果表明，原子透射率和光子辐射率在多腔系统中出现多共振峰结构.这一结果说明，可以通过一系列腔的安排在宏观上实现对超冷原子质心运动波函数的调制. 关键词： 超冷原子 单模腔场 共振隧穿     

Squeezing and entangling atomic motion in cavity QED via quantum nondemolition measurement

We propose a scheme for preparing the squeezing of an atomic motion and an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated trapped atoms. The scheme utilizes the quantum nondemolition measurements with interaction between the cavity field and the motional state of the trapped atom in cavity QED. By illuminating the atoms with bichromatic light, the interaction Hamiltonian of the cross-Kerr effect between the cavity and atomic motion is generated to implement quantum nondemolition measurements.Received: 5 February 2003, Published online: 17 July 2003PACS: 03.67.Hk Quantum communication - 32.80.Lg Mechanical effects of light on atoms, molecules, and ions - 42.50.-p Quantum optics     

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.     

Effect of Moving Mass Center on Atomic Transition Probability in a Single-Mode Cavity

By considering a two-level atom coupling with a single-mode cavity field which is prepared in three different initial states respectively, the influence of spatial motion of the atomic centre of mass on the atomic transition probability is studied. It is shown that the oscillation with collapse and revival in atomic transition probability may be suppressed due to Doppler effect.