Bulletin of the American Physical Society
40th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics
Volume 54, Number 7
Tuesday–Saturday, May 19–23, 2009; Charlottesville, Virginia
Session Q5: Nonlinear Dynamics |
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Chair: John Delos, College of William and Mary Room: Clark Hall 107 |
Friday, May 22, 2009 8:00AM - 8:12AM |
Q5.00001: Some exactly solvable quantum-chaotic models Vladimir Yurovsky, Maxim Olshanii Exact analytical expressions are obtained for the wavefunctions of two atoms with a zero-range interaction in two types of the external potentials. The potential of first kind is a three-dimensional anisotropic harmonic oscillator; the second is a harmonic oscillator in two directions with periodic boundary conditions in the third direction. Neither of the two systems is known to possess a complete set of integrals of motion. The energy eigenvalues are roots of a transcendent equation and form a discrete spectrum. The energy spectrum statistics exhibits distinctive features of quantum-chaotic systems. [Preview Abstract] |
Friday, May 22, 2009 8:12AM - 8:24AM |
Q5.00002: Chaos Threshold and Failure of Chirikov's Criteria in Mean Field Bose-Hubbard Model Amy Cassidy, Vanja Dunjko, Maxim Olshanii We calculate the threshold for chaos in the one-dimensional mean-field Bose-Hubbard model. The threshold is found to depend on two parameters, the nonlinear coupling strength and total energy per particle, both of which survive in the thermodynamic limit [A.C. Cassidy, D. Mason, V. Dunjko, M. Olshanii, Phys. Rev. Lett. 102, 025302 (2009)]. The dependence on these parameters contradicts the predictions obtained by Chirkov's criterion of overlapping resonances. We study the influence of the conserved quantities of the nearby, fully integrable model of Ablowitz and Ladik. [Preview Abstract] |
Friday, May 22, 2009 8:24AM - 8:36AM |
Q5.00003: Chaotic Escape of Rays from a Vase-shaped Billiard: Simulations and Experiment Jaison Novick, Mathew Keeler, John Delos We study the escape of rays from a two dimensional, specularly-reflecting open vase-shaped cavity. The narrowest point of the vase's neck defines a dividing surface between rays that escape without return and those turned back into the cavity. Our simulations show that a point burst of rays emitted in all directions can contain both regular and chaotic scattering trajectories. The chaotic trajectories leak out in an infinitely long pulse train organized by a fractal. For escaping trajectories, we record the propagation time to escape and find that the fractal manifests itself in the escape time versus the launch angle. We have experimentally verified the early fractal structure. A two dimensional aluminum vase with reflective Teflon walls was constructed with an ultrasound transmitter as the point source. A microphone was placed at points along the vase's mouth. We find good agreement between measurements and classical simulations. [Preview Abstract] |
Friday, May 22, 2009 8:36AM - 8:48AM |
Q5.00004: Chaotic Ionization of a Rydberg Atom Subjected to Alternating Kicks Korana Burke, Kevin Mitchell The ionization of highly excited Rydberg atoms subjected to periodic electric field pulses has been the focus of a number of recent experimental studies. We present a theoretical analysis for such systems in the case of periodic alternating positive and negative kicks. Under such conditions, the electron dynamics is chaotic. Our analysis shows how the chaotic ionization process can be understood in terms geometric structures called homoclinic tangles, which form a kind of ``leaky'' separatrix in phase space. Using this geometric approach, we propose an experimental protocol to directly visualize the tangle structure within the ionization data. [Preview Abstract] |
Friday, May 22, 2009 8:48AM - 9:00AM |
Q5.00005: Strong Field Atomic Dynamics Driven by Shaped Ultrafast Laser Pulses Stephen Clow, Uvo Holscher, Carlos Trallero, Thomas Weinacht We demonstrate coherent control of atomic dynamics in strong laser fields including a phenomenon very similar to electromagnetically induced transparency (EIT) and population transfer in a multilevel system with multiphoton coupling between states. Ultrafast pulse shaping allows us to produce probe and coupling pulses for our EIT measurements with arbitrary intensities and time delays from a single ultrafast laser pulse. We compare our results to more traditional implementations of EIT. In our population transfer measurements we find that sequential population transfer is generally more efficient than adiabatic passage on ultrafast timescales with multiphoton coupling between states.~Behind these experiments lies a simple time domain picture which draws upon the atom-field phase evolution in strong fields. [Preview Abstract] |
Friday, May 22, 2009 9:00AM - 9:12AM |
Q5.00006: Controlling Material Transformation and Plasma Emission with Trains of Ultrafast Laser Pulses Robert J. Gordon, Sima Singha, Zhan Hu Trains of ultrafast laser pulses, generated by passing a 50 fs, 800 nm Ti:Sapphire pulse through a spatial light modulator, were used to ablate GaAs in air. The wavelength-resolved plasma emission was measured as a function of pulse spacing and fluence. For a pair of pulses, the plasma emission increased monotonically with spacing, with the fluorescence enhancement described by $A(1-e^{-t/\tau})$, where t is the pulse spacing and $\tau =$ 46 ps, at a total fluence of 12.3 J/cm$^2$. This behavior is explained by a mechanism in which the first pulse melts the surface and the second pulse interacts with the liquid phase, while the melt front propagates into the crystal (1, 2). Much more complex time and energy behavior was observed for a three-pulse train. The fluorescence enhancement at 450.8 nm displayed peaks at pulse spacings that correspond roughly to multiples of the LO phonon period of the crystal. This behavior suggests a mechanism involving coherent excitation of the crystal by the pulse train.\\[3pt] [1] Z. Hu, S. Singha, Y. Liu, and R. J. Gordon, Appl. Phys. Lett. 90, 131910 (2007).\\[0pt] [2] S. Singha, Z. Hu, and R. J. Gordon, J. Appl. Phys. 104, 113520 (2008). [Preview Abstract] |
Friday, May 22, 2009 9:12AM - 9:24AM |
Q5.00007: Monodromy matrix theory of Trojan wave packets on elliptical orbits Matt Kalinski The possibility of existence of so called Trojan wavepackets on elliptical orbits, nondispersing wave packets once predicted on cirular orbits while the Hydrogen atom is placed in the CP field has been predicted both theoretically [1] and after many years finally confirmed experimentally in recent microwave experiments. They are caused by so called population lock on the resonance with the infinite semi-harmonic but nonlinear spectrum. However no extension of harmonic theory has been given which simply explains the phenomenon as generalized concept of the Paul trap in the atom but for the single electron. Hereby we apply the monodromy matrix theory originally developed by Heller [2] to study such phenomenon. We define the instantaneous Hamiltonian for the electron an the elliptical orbit and surprisingly find out that it needs not to have real eigenvalues for all times of the circular motion while the packed motion is still nondispersing. Numerical simulations using split-operator method are also presented. [1] E. A. Shapiro, M. Kalinski, and J. H. Eberly, ``Non-circular Trojan-like wavepackets: quantum theory and application to quantum control,'' J. Phys. B {\bf 33}, 3079, (2000); [2] E. J. Heller, ``Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits,'' Phys. Rev. Lett. {\bf 53}, 1515 (1984). [Preview Abstract] |
Friday, May 22, 2009 9:24AM - 9:36AM |
Q5.00008: Three-dimensional solitons in Bose-Einstein condensates with Rydberg state mediated nonlocal interactions Mark Saffman, Stefan Skupin, Pavel Lushnikov, Wieslaw Krolikowski We analyze theoretically and numerically creation of stable three dimensional bright solitons in Bose-Einstein condensates by optical coupling of the condensate atoms to Rydberg levels. This gives an effective ground state potential that is dressed by the long range Rydberg interaction. Coupling to Rydberg $s-$ states provides an isotropic and attractive long range interaction, while coupling to $p-$ or $d-$ states provides an anisotropic but sign-definite attractive or repulsive interaction. We find stable three-dimensional solitons taking into account both the long range interaction and a short range contact interaction. Modulational instability of the condensate is observed for a repulsive long range interaction. [Preview Abstract] |
Friday, May 22, 2009 9:36AM - 9:48AM |
Q5.00009: High Degrees of Impulsive Alignment in Repetitively Excited $\mbox{N}_2$ at STP James Cryan, Ryan Coffee, Philip Bucksbaum \newcommand{\trace}[1]{\mbox{tr}\left( #1 \right)} We demonstrate a high degree of both transient and time-independent alignment in Nitrogen at STP resulting from multiple impulsive Raman excitations with linearly polarized light. The alignment is optimized by exploiting the structure of the density matrix, $\rho(J,m_J)$. Our experiment demonstrates a time-independent population alignment, defined as the time average of $\langle\cos^2\theta\rangle$, that exceeds the single pulse transient coherent alignment. We compare our experimental results to a quantum calculation, which suggests that transient alignment following multiple excitations can exceed $\langle\cos^2\theta\rangle\sim0.6$. Under impulsive excitation the entropy and quantum purity remain constant, but both the energy of the ensemble and the $J$-state distribution move markedly away from a thermal distribution. Transient alignment is related to rotational coherence $C_2 = \left(1 - \frac{ \trace{\mbox{diag}(\rho)^2}} { \trace{\rho^2} } \right)^{1/2}$. We show that this $C_2$ coherence grows monotonically with our train of eight impulses. [Preview Abstract] |
Friday, May 22, 2009 9:48AM - 10:00AM |
Q5.00010: Moyal phase-space analysis of nonlinear optical Kerr media Karl-Peter Marzlin, Tom Osborn The Moyal equation of a quantum observable corresponds to a phase space representation of its Heisenberg equation of motion. Because the latter has a close relation to the corresponding classical dynamics, the Moyal method is ideally suited to study the transition from classical to quantum behaviour in a system. The Moyal representation is related to the Wigner function like the Heisenberg picture is related to the Schr\"odinger picture. Unfortunately the Moyal equation is difficult to solve so that only few exact solutions are known. We have studied nonlinear optical self-phase modulation of Kerr type using the Moyal equation for a single optical field mode. An exact solution for the annihilation operator is found. The phase space representation of this operator is related to the classical field amplitude by a complex factor that shows characteristic singularities in time. We show that these singularities disappear in the classical limit and demonstrate how the uncertainty relation prevents that observable quantities are affected by it. [Preview Abstract] |
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