Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.Comment: 22 pages, 7 figure

Controlling Molecular Scattering by Laser-Induced Field-Free Alignment

We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbow-like features in the distribution of the scattering angle. Moreover, by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. We provide quantum and classical treatment of the deflection process. The effects of strong deflecting field on the scattering of rotating molecules are considered by the means of the adiabatic invariants formalism. This new control scheme opens new ways for many applications involving molecular focusing, guiding and trapping by optical and static fields

Squeezing of Atoms in a Pulsed Optical Lattice

We study the process of squeezing of an ensemble of cold atoms in a pulsed optical lattice. The problem is treated both classically and quantum-mechanically under various thermal conditions. We show that a dramatic compression of the atomic density near the minima of the optical potential can be achieved with a proper pulsing of the lattice. Several strategies leading to the enhanced atomic squeezing are suggested, compared and optimized.Comment: Latex, 9 pages, 10 figures, submitted to PR

Orientation and Alignment Echoes

We present what is probably the simplest classical system featuring the echo phenomenon - a collection of randomly oriented free rotors with dispersed rotational velocities. Following excitation by a pair of time-delayed impulsive kicks, the mean orientation/alignment of the ensemble exhibits multiple echoes and fractional echoes. We elucidate the mechanism of the echo formation by kick-induced filamentation of phase space, and provide the first experimental demonstration of classical alignment echoes in a thermal gas of CO_2 molecules excited by a pair of femtosecond laser pulses

Superrevivals in the quantum dynamics of a particle confined in a finite square well potential

We examine the revival features in wave packet dynamics of a particle confined in a finite square well potential. The possibility of tunneling modifies the revival pattern as compared to an infinite square well potential. We study the dependence of the revival times on the depth of the square well and predict the existence of superrevivals. The nature of these superrevivals is compared with similar features seen in the dynamics of wavepackets in an anharmonic oscillator potential.Comment: 8 pages in Latex two-column format with 5 figures (eps). To appear in Physical Review

Echo in Optical Lattices: Stimulated Revival of Breathing Oscillations

We analyze a stimulated revival (echo) effect for the breathing modes of the atomic oscillations in optical lattices. The effect arises from the dephasing due to the weak anharmonicity being partly reversed in time by means of additional parametric excitation of the optical lattice. The shape of the echo response is obtained by numerically simulating the equation of motion for the atoms with subsequent averaging over the thermal initial conditions. A qualitative analysis of the phenomenon shows that the suggested echo mechanism combines the features of both spin and phonon echoes.Comment: 13 pages, 3 figure

Quantum resonances in selective rotational excitation of molecules with a sequence of ultrashort laser pulses

We investigate experimentally the effect of quantum resonance in the rotational excitation of the simplest quantum rotor - a diatomic molecule. By using the techniques of high-resolution femtosecond pulse shaping and rotational state-resolved detection, we measure directly the amount of energy absorbed by molecules interacting with a periodic train of laser pulses, and study its dependence on the train period. We show that the energy transfer is significantly enhanced at quantum resonance, and use this effect for demonstrating selective rotational excitation of two nitrogen isotopologues, $^{14}N_2$ and $^{15}N_2$. Moreover, by tuning the period of the pulse train in the vicinity of a fractional quantum resonance, we achieve spin-selective rotational excitation of para- and ortho-isomers of $^{15}N_2$.Comment: 5 pages, 4 figure

Fractional Echoes

We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes which appear periodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses

Extended Gaussian wave packet dynamics

We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found, and relationships are explored between the squeezed system, Gaussian wave packet dynamics, the time dependent harmonic oscillator, and wave packet dynamics in a Gauss-Hermite basis. Expressions are given for the matrix elements of the potential in some simple cases. Several examples are given, including the propagation of a non-Gaussian initial state in a Morse potential

Coherent Manipulation of Quantum Delta-kicked Dynamics: Faster-than-classical Anomalous Diffusion

Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system parameters and over long time scales, is shown to display energy absorption that is significantly faster than that associated with the underlying classical anomalous diffusion. The results are of interest to both areas of quantum chaos and quantum control.Comment: 6 pages, 4 figures, to appear in Physical Review