Quantum carpets woven by cold atoms in a laser field

Propagation of wave packets of cold two-level atoms in a standing-wave laser field can be interpreted in the dressed-state basis as motion in two optical potentials. The three distinct regimes of the wavepacket motion are specified by the ratio of the squared atom–laser detuning to the normalized Doppler shift. We calculate the momentum and position probability densities, which form patterns with minima and maxima of probability both in the momentum and the position spaces known as quantum carpets. At small and large detunings, the atomic motion is substantially adiabatic, and the quantum carpets have a simple form. At intermediate detunings, the wave packet moves nonadiabatically, splitting at each node of the standing wave, which causes a proliferation or branching of atomic trajectories with a single atom. Nonadiabatic transitions produce beautiful quantum carpets with a rich structure.     

Effects of atomic motion in a standing-wave laser field on the Rabi oscillations

We study the effects of the two-level-atom motion in a standing-wave laser field on the Rabi oscillations. In the presence of the resonance optical Stern–Gerlach effect, the atomic wave packet, centered initially at a node of the standing wave, is shown to evolve in such a way that the atomic population inversion remains zero when the initially de-excited atom moves between the nodes, then collapses to the ground level upon crossing the nodes, and practically returns to zero after that. This coherent population trapping is explained in the dressed-state picture. The Doppler–Rabi resonance, i.e., maximum Rabi oscillations at large values of the atom–field detuning, becomes possible if the detuning is equal to the Doppler shift. A simple formula for the population inversion is derived in the Raman–Nath approximation.     

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.     

Geometric optics with atomic beams scattered by a detuned laser standing wave

We report on a theoretical and numerical study of the propagation of atomic beams crossing a detuned standing-wave laser beam in the geometric-optics limit. The interplay between the external and internal atomic degrees of freedom is used to manipulate the atomic motion along the light optical axis. By adjusting the atom–laser detuning, we demonstrate how to focus, split, and scatter atomic beams in real experiments. The novel effect of chaotic scattering of atoms on a regular near-resonant standing wave is found numerically and explained qualitatively. Some applications of the effects found are discussed.     

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。     

Anomalous spatial concentration of atoms in the field of a standing light wave

The stationary momentum and coordinate distributions of two-level atoms in the field of a one-dimensional standing light wave have been studied. A qualitatively new effect—the predominant concentration of atoms outside of the minima of the optical potential—has been detected in the regime of moderate saturation of an atomic transition and red frequency detuning. This effect has been qualitatively interpreted. Calculations have been performed using the quantum kinetic equation for the atomic density matrix with the complete inclusion of recoil and localization effects in an arbitrary-intensity light field. In addition to theoretical significance, the results can be useful for atomic nanolithography and frequency standards based on optical gratings.     

Splitting of atomic beams by light for creation of high-resolution spatial structures in optical nanolithography

Diffraction of atomic wave packets from a standing laser wave with a Gaussian profile is studied theoretically and numerically in pursuing the aim of creating high-resolution spatial structures in optical nanolithography. To this end, we propose to use nonadiabatic transitions between two optical potentials which take place when square of the value of detuning off the resonance is approximately equal to the Doppler shift. In this case, atomic wave packets experience splitting at nodes of the standing wave, which allows creating atomic structures on a substrate with a period substantially smaller than the standard nanofabrication limit equal to half the wavelength of light. We propose a scheme of the experiment for the observation of nonadiabatic transitions and splitting of the wave of matter caused by them. A number of computer simulations with parameters corresponding to real atoms have been performed, which exhibit this effect in both momentum and coordinate spaces.     

Observation of collimation and decollimation of an atomic beam in a misaligned standing wave

This paper reports an experimental study on the collimation and decollimation of an atomic beam in a misaligned standing wave, in which the effective detuning caused by the Doppler effect is affected by the longitudinal velocity of the atomic beam. The experiment shows that in a strong field with red detuning between laser field and atomic transition frequency, laser heating in a normal standing wave becomes laser cooling in a misaligned standing wave for an approriate misalignment angle. For blue detuning, laser cooling in a standing wave can also become laser heating in a misaligned standing wave for an appropriate condition. These results ca be used in controling atomic motion.     

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.     

Localization and kinetics of an atom in the spectral filtration of its resonance fluorescence

It is shown that spectral filtration of a significant fraction of radiation of a resonantly fluorescing atom changes its kinetics. The effect of a spectral observation event on the behavior of an atom is demonstrated by two examples: localization of an atom at its flight through a region occupied by a standing light wave and translatory dynamics of an atom at its motion along a standing light wave. In the first case, localization probabilities are calculated in the absence of spontaneous emission events and for one photoemission event. The arising distribution over the atomic momentum, which is sensitive to spectral filtration, is also calculated for one photoemission event. In the second example, it is shown that spectral filtration of spontaneous emission leads to the occurrence of an anomalous additive to the force acting on an atom in the standing-wave field.     

Quantum instability in cavity QED

The stability and instability of quantum evolution are analyzed in the interaction of a two-level atom with a quantized-field mode in an ideal cavity with allowance for photon recoil, which is the basic model of cavity QED. It is shown that the Jaynes-Cammings quantum dynamics can be unstable in the regime of the random walk of the atom in the quantized field of a standing wave in the absence of any interaction with the environment. This instability is manifested in large fluctuations of the quantum entropy, which correlate with a classical-chaos measure, the maximum Lyapunov exponent, and in the exponential sensitivity of the fidelity of the quantum states of the strongly coupled atom-field system to small variations of resonance detuning. Numerical experiments reveal the sensitivity of the atomic population inversion to the initial conditions and to correlation between the quantum and classical degrees of freedom of the atom.     

Laser-Induced Climbing of Cold Atoms Against the Gravity

We demonstrate climbing of cold atoms against the gravity in a one-dimensional vertical laser standing wave. At an appropriately chosen laser–atom detuning, we show that freely falling atoms change the direction of motion and move upward. The effect is due to a tiny interplay between internal and external atomic degrees of freedom in a rigid optical lattice.     

Chaotic walking and fractal scattering of atoms in a tilted optical lattice

We consider analytically and numerically chaotic walking of cold atoms in a tilted optical lattice created by two counter-propagating running waves with an additional external field in the semiclassical and Hamiltonian approximations. The effect consists in random-like changing the direction of atomic motion in a rigid lattice under the influence of a constant force due to a specific behavior of the atomic dipole-moment component that changes abruptly in a random-like manner while atoms cross standing-wave nodes. Chaotic walking generates a fractal-like scattering of atoms that manifests itself in a self-similar structure of the scattering function in the atom?Cfield detuning in the position and momentum spaces. We show that the probability distribution function of the scattering time decays in a non-exponential way with a power-law tail.     

Atomic localization caused by the asymmetry of the Landau-Zener transitions

The motion of an atomic wave packet in a standing light wave can be described in terms of two periodic potentials. Single atom may perform Landau-Zener (LZ) transitions between these two energy states. In this Letter we have found regimes when atom is localized in the momentum space in the vicinity of its initial momentum. We argue that this localization is caused by the asymmetry of LZ transitions (i.e. probability of tunneling depends on its direction) due to the interference.     

A nanofiber-based optical conveyor belt for cold atoms

We demonstrate optical transport of cold cesium atoms over millimeter-scale distances along an optical nanofiber. The atoms are trapped in a one-dimensional optical lattice formed by a two-color evanescent field surrounding the nanofiber, far red- and blue-detuned with respect to the atomic transition. The blue-detuned field is a propagating nanofiber-guided mode while the red-detuned field is a standing-wave mode which leads to the periodic axial confinement of the atoms. Here, this standing wave is used for transporting the atoms along the nanofiber by mutually detuning the two counter-propagating fields which form the standing wave. The performance and limitations of the nanofiber-based transport are evaluated and possible applications are discussed.     

Atom localization via absorption spectrum

We propose a scheme to localize an atom in a three-level A-type configuration inside a classical standing wave field conditioned upon the measurement of frequency of a weak probe field. Inside the classical standing wave field, the interaction between 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. Localizing of an atom via absorption spectrum occurs during its motion inside the standing wave field. An investigation of the probe field frequency shows that the degree of localization depends on interaction parameters such as detuning, phase difference between applied fields, and Rabi frequency of the driving field.     

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.     

Chaotic motion of atom in the coherent field of a standing light wave

A new effect of chaotic motion of the center of mass of a cold atom in the coherent field of a standing light wave in a high-finesse Fabry-Pérot cavity is theoretically predicted and numerically implemented in the absence of any random fluctuations due to spontaneous emission. Numerical experiments demonstrate that the Hamiltonian chaos arises near resonance in the range of parameters characteristic of the strong coupling regime that was implemented in recent experiments. The effect is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.     

Reflection of thermal atoms by a pulsed standing wave

Reflection of thermal atoms by a pulsed standing wave with a duration in the nanosecond range is studied. The momentum distribution of the reflected atoms is determined by calculations based on the adiabatic atom-photon interactions. It is shown that with a proper choice of the field intensity and the pulse duration the standing-wave pattern functions as a row of independent atom mirrors. At an optimum choice of the parameter values, the fraction of the elastically reflected atoms is more than 20%. Furthermore, we show that the pulsed standing-wave mirror can be used to manipulate their final momentum distribution. When using laser pulses with an intensity of several tens of MW/cm², tens of thousands of atoms can be reflected by a single laser pulse. Received 3 December 1999 and Received in final form 25 April 2000     

Rectified momentum transport for a kicked Bose-Einstein condensate

We report the experimental observation of rectified momentum transport for a Bose-Einstein condensate kicked at the Talbot time (quantum resonance) by an optical standing wave. Atoms are initially prepared in a superposition of the 0 and -2hkl momentum states using an optical pi/2 pulse. By changing the relative phase of the superposed states, a momentum current in either direction along the standing wave may be produced. We offer an interpretation based on matter-wave interference, showing that the observed effect is uniquely quantum.