Standing-wave Laser Research Articles

Boundary-Dependent Chaotic Regions for a Bose–EinsteinCondensate Interacting with Laser Field

Spatial chaos of a Bose–Einstein condensate perturbed by a weak laserstanding wave and a weak laser δ pulse is studied. By using theperturbed chaotic solution we investigate the new type of Melnikovchaotic regions, which depend on an integration constant c0determined by the boundary conditions. It is shown that when the |c0|values are small, the chaotic region corresponds to small values oflaser wave vector k, and the chaotic region for the larger k valuesis related to the large |c0| values. The result is confirmednumerically by finding the chaotic and regular orbits on thePoincaré section for the two different parameter regions. Thus, fora fixed c0 the adjustment of k from a small value to large valuecan transform the chaotic region into the regular one or on thecontrary, which suggests a feasible method for eliminating or generatingMelnikov chaos.

Manifestation of quantum resonances and antiresonances in a finite-temperature dilute atomic gas

We investigate the effect of temperature on resonant and antiresonant dynamics in a dilute atomic gas kicked periodically by a standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and show that the atomic dynamics are highly sensitive to the initial momentum width of the gas. We explain this sensitivity by examining the time evolution of individual atomic center-of-mass momentum eigenstates with varying quasimomentum, and we determine analytic expressions for the evolution of the second-order momentum moment to illustrate the range of behaviors.

Analysis of Aberrations in Laser-Focused Nanofabrication

Based on the semi-classical model,we analyse the motion equation of chromium atoms in the laserstanding wave field under the condition of low intensity light fieldusing fourth-order Adams–Moulton algorithm. The trajectory of theatoms is obtained in the standing wave field by analytical simulation.The image distortion coming from aberrations is analysedand the effects on focal beam features are also discussed. Besidesthese influences, we also discuss the effects on contrast as well asthe feature width of the atomic beam due to laser power and laser beamwaist. The simulation results have shown that source imperfection,especially the transverse velocity spread, plays a critical role inbroadening the feature width. Based on these analyse, we present somesuggestions to minimize these influences.

Dynamics of Two-Level Trapped Ion in a Standing WaveLaser in Noncommutative Space

We study the dynamics of a two-level trapped ion in a standingwave electromagnetic field in two-dimensional (2D) noncommutativespaces in the Lamb–Dicke regime under the rotating waveapproximation. We obtain the explicit analytical expressions forthe energy spectra, energy eigenstates, unitary time evolutionoperator, atomic inversion, and phonon number operators. The Rabioscillations, the collapse, and revivals in the average atomicinversion and the average phonon number are explicitly shown tocontain the information of the parameter of the spacenoncommutativity, which sheds light on proposing new schemes basedon the dynamics of trapped ion to test the noncommutativity.

Fast scheme for generating quantum-interference states and GHZ state of N trapped ions

We propose a fast scheme to generate the quantum-interference states of N trapped ions. In the scheme the ions are driven by a standing-wave laser beam whose carrier frequency is tuned such that the ion transition can take place. We also propose a simple and fast scheme to produce the GHZ state of N hot trapped ions and this scheme is insensitive to the heating of vibrational motion, which is important from the viewpoint of decoherence.

Localization of atomic ensembles via superfluorescence

The sub-wavelength localization of an ensemble of atoms concentrated to a small volume in space is investigated. The localization relies on the interaction of the ensemble with a standing wave laser field. The light scattered in the interaction of standing wave field and atom ensemble depends on the position of the ensemble relative to the standing wave nodes. This relation can be described by a fluorescence intensity profile, which depends on the standing wave field parameters, the ensemble properties, and which is modified due to collective effects in the ensemble of nearby particles. We demonstrate that the intensity profile can be tailored to suit different localization setups. Finally, we apply these results to two localization schemes. First, we show how to localize an ensemble fixed at a certain position in the standing wave field. Second, we discuss localization of an ensemble passing through the standing wave field.

The preliminary result of laser- focused Cr atomic deposition for fabricating nanostructure

The technology of laser-focused atomic deposition can be used to develop the nanostrucrure transfer standard of length. When the frequency of laser standing wave is higher than the resonant frequency of atoms, the atoms will be focused on the wave node of the standing wave. The collimated Cr atoms are focused by a standing-wave laser field as they are deposited on a silicon substrate. Atomic force microscopy measurements shows a spacing of 215nm.

Distilling two-atom distance information from intensity-intensity correlation functions

The intensity-intensity correlation function of the resonance fluorescence light of two two-level atoms driven by a resonant standing-wave laser field is examined. Our aim is to gain information on the distance between the two atoms from observables accessible in experiments. For this, we numerically solve the time-evolution equations of the system and calculate the steady-state intensity-intensity correlation by using the Laplace transform and quantum regression theory. By varying the interatomic distance from about half a wavelength down to small fractions of a wavelength, we show that the correlation function exhibits characteristic properties for different distance ranges. Based on these results, we propose a scheme to obtain interatomic distance information from the power spectrum of the correlation function, which allows us to extract the desired distance information over a wide range of distances with high accuracy.

High-speed geometric quantum phase gates for trapped ions in thermal motion

We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.

Bose-Einstein-condensate interferometer with macroscopic arm separation

A Michelson interferometer using Bose-Einstein condensates is demonstrated with coherence times of up to 44 ms and arm separations up to 0.18 mm. This arm separation is larger than that observed for any previous atom interferometer. The device uses atoms weakly confined in a magnetic guide and the atomic motion is controlled using Bragg interactions with an off-resonant standing wave laser beam.

Light Diffraction by a Strong Standing Electromagnetic Wave

The nonlinear quantum interaction of a linearly polarized x-ray probe beam with a focused intense standing laser wave is studied theoretically. Because of the tight focusing of the standing laser pulse, diffraction effects arise for the probe beam as opposed to the corresponding plane wave scenario. A quantitative estimate for realistic experimental conditions of the ellipticity and the rotation of the main polarization plane acquired by the x-ray probe after the interaction shows that the implementation of such vacuum effects is feasible with future X-ray Free Electron Laser light.

Motional Quantum-State Engineering and Implementation of aQuantum Phase-Gate for Multiple TrappedIons

We propose a scheme to generate a superposition of motionalcoherent states with arbitrary coefficients on a line in phasespace and implement a quantum controlled phase-gate for multipletrapped ions with a single standing-wave laser pulse whose carrierfrequency is tuned to the ions transition. In the scheme each iondoes not need to be exactly positioned at the node of the standingwave, which is very important from viewpoint of experiment.Furthermore, our scheme may allow the generation of asuperposition of coherent states with large mean phonon number fora large number of trapped ions in a fast way by choosing suitablelaser intensity. We show that it can also be used to generatemaximally entangled states of multiple trapped ions.

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-Schro 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-Poincare mapping of atomic trajectories in an effective three-dimensional phase space onto planes of atomic internal variables and momentum. The Poincare 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.

Measurement of the separation between atoms beyond diffraction limit

Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a standing wave laser field. The information is extracted from the collective resonance fluorescence spectrum, relying entirely on far-field imaging techniques. Both the interatomic separation and the positions of the two particles can be measured with fractional-wavelength precision over a wide range of distances from about $\ensuremath{\lambda}∕550$ to $\ensuremath{\lambda}∕2$.

Kondensati Boze – Ejnshtejna v pole lazernogo izlucheniya

The properties of Bose–Einstein condensates in an external potential produced by a laser light field are discussed. Considered are the condensates embedded in periodic lattices produced by standing laser waves and the condensates confined within 'optical traps' near the focus of a traveling wave. Observations of the Mott transition in a periodic lattice are described, as are experiments on atoms near the Feshbach resonance and experiments on the condensates in a double potential well, which permit investigating the tunnel dynamics of condensate phases.

Nonlinear Jaynes-Cummings model of a trapped ion and the evolution of the ion population inversion

Starting from the Jaynes-Cummings (J-C) model describing the interaction of a trapped ion with a standing-wave laser field, we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excitated resonantly with 1-quantum vibrational mode. After solving the time-dependent states of this model, we study the evolution of population inversion for the ion numerically. It is shown that the period of the quantum collapse and revival of the population inversionis related with the Lamb-Dick parameter and the position of the ion in the standing-wave laser field. With the increasing of the parameter, it will decrease the period of the collapse and revival. When moving the ion from the node of the standing-wave laser to the antinode, the period of the collapse and revival becomes longer.

Theory of Atom Optics: Feynman’s Path Integral Approach

The present theory of atom optics is established mainly on the Schrodinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.

Publisher's Note: Relativistic reversal of the ponderomotive force in a standing laser wave [Phys. Rev. A72, 043401 (2005)

Publisher's Note: Relativistic reversal of the ponderomotive force in a standing laser wave [Phys. Rev. A<b>72</b>, 043401 (2005)

Relativistic reversal of the ponderomotive force in a standing laser wave

Effect of relativistic reversal of the ponderomotive force (PF), reported earlier for a collinear configuration of electron and laser standing wave [A. E. Kaplan and A. L. Pokrovsky, Phys. Rev. Lett., 95, 053601 (2005)], is studied here theoretically for various types of polarizations of the laser beam. We demonstrated that the collinear configuration, in which the laser wave is linearly polarized with electric field $\stackrel{P\vec}{E}$ parallel to the initial electron momentum ${\stackrel{P\vec}{p}}_{0}$, is the optimal configuration for the relativistic reversal. In that case, the transverse PF reverses its direction when the incident momentum is ${p}_{0}=mc$. The reversal effect vanishes in the cases of circular and linear with $\stackrel{P\vec}{E}\ensuremath{\perp}{\stackrel{P\vec}{p}}_{0}$ polarizations. We have discovered, however, that the counter-rotating circularly polarized standing waves develop attraction and repulsion areas along the axis of laser, in the laser field whose intensity is homogeneous in that axis, i.e., has no field gradient.

Harmonic generation from laser-driven vacuum

We investigate the feasibility that, in the field of a superstrong standing laser wave, high-order harmonics of the pumping laser are generated from vacuum. Analytical calculations employing adiabatic perturbation theory show that, for laser electric fields larger than ${E}_{\mathrm{cr}}={m}^{2}{c}^{3}/\ensuremath{\hbar}e=1.3\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\mathrm{V}/\mathrm{cm}$, high-order harmonics are generated. The harmonic spectrum shows a wide plateau followed by a cutoff. The cutoff starts approximately at photon energies $\ensuremath{\hbar}{\ensuremath{\omega}}_{M}\ensuremath{\sim}\sqrt{\ensuremath{\hbar}ec{E}_{L}}$, with ${E}_{L}$ being the amplitude of the laser field. In the opposite limit ${E}_{L}\ensuremath{\ll}{E}_{\mathrm{cr}}$, the emission of high harmonics is very unlikely. In this case, a feasibility analysis for the experimental observation of the photon-photon scattering process using x-ray free electron lasers shows that the requirements are much less restrictive than those required to observe electron-positron pair creation.