This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Regular and Chaotic Dynamics

An important development in modern physics is the emerging capability for investigations of dynamical processes for open quantum systems in a regime of strong coupling for which individual quanta play a decisive role. Of particular significance in this context is research in cavity quantum electrodynamics which explores quantum dynamical processes for individual atoms strongly coupled to the electromagnetic field of a resonator. An overview of the research activities in the Quantum Optics Group at Caltech is presented with an emphasis on strong coupling in cavity QED which enables exploration of a new regime of nonlinear optics with single atoms and photons.

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Strong interactions of single atoms and photons in cavity QED

Quantum wave packet revivals

1. General introduction 2. The separation of nuclear and electronic motion 3. The electronic hamiltonian 4. Interactions arising from nuclear magnetic and electric moments 5. Angular momentum theory and spherical tensor algebra 6. Electronic and vibrational states 7. Derivation of the effective hamiltonian 8. Molecular beam magnetic and electric resonance 9. Microwave and far-infrared magnetic resonance 10. Pure rotational spectroscopy 11. Double resonance spectroscopy Appendices.

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1878342

Rotational Spectroscopy of Diatomic Molecules

The ability to control the shape and motion of quantum states1,2 may lead to methods for bond-selective chemistry and novel quantum technologies, such as quantum computing. The classical coherence of laser light has been used to guide quantum systems into desired target states through interfering pathways3,4,5. These experiments used the control of target properties — such as fluorescence from a dye solution6, the current in a semiconductor7,8 or the dissociation fraction of an excited molecule9 — to infer control over the quantum state. Here we report a direct approach to coherent quantum control that allows us to actively manipulate the shape of an atomic electron's radial wavefunction. We use a computer-controlled laser to excite a coherent state in atomic caesium. The shape of the wavefunction is then measured10 and the information fed back into the laser control system, which reprograms the optical field. The process is iterated until the measured shape of the wavefunction matches that of a target wavepacket, established at the start of the experiment. We find that, using a variation of quantum holography11 to reconstruct the measured wavefunction, the quantum state can be reshaped to match the target within two iterations of the feedback loop.

Controlling the shape of a quantum wavefunction

Semiclassical catastrophes in the dynamics of a quantum rotor (molecule) driven by a strong time-varying field are considered. We show that for strong enough fields, a sharp peak in the rotor angular distribution can be achieved via a time-domain focusing phenomenon, followed by the formation of rainbowlike angular structures. A strategy leading to the enhanced angular squeezing is proposed that uses a specially designed sequence of pulses. The predicted effects can be observed in many processes, ranging from molecular alignment (orientation) by laser fields to heavy-ion collisions, and the trapping of cold atoms by a standing light wave.

Angular Focusing, Squeezing, and Rainbow Formation in a Strongly Driven Quantum Rotor

We introduce and demonstrate a general wave packet method for laser isotope separation. In this scheme, laser excited molecular (or atomic) wave packets of differing isotopes become {ital spatially} separated in the course of their long-time free evolution. In order to overcome the quantum spreading of wave packets, we make use of the phenomenon of revivals. We demonstrate experimentally, with mixed {sup 79}Br{sub 2}/{sup 81}Br{sub 2} isotopes, that significant control over the isotope ratio can be achieved in a single shot. {copyright} {ital 1996 The American Physical Society.}

http://faculty.chem.queensu.ca/people/faculty/stolow/Publications/PDF_Publications/isotope.pdf

Wave Packet Isotope Separation.

The rotational Doppler frequency shift is observed for a circularly polarized lightwave propagating through a gas of synchronously spinning molecules by using a linearly polarized pulsed laser beam to align diatomic molecules and a linearly polarized pulse to induce concerted unidirectional rotation.

Observing Molecular Spinning via the Rotational Doppler Effect

Spectroscopy aims at extracting information about matter through its interaction with light. However, when performed on gas and liquid phases as well as solid phases lacking long-range order, the extracted spectroscopic features are in fact averaged over the molecular isotropic angular distributions. The reason is that light–matter processes depend on the angle between the transitional molecular dipole and the polarization of the light interacting with it. This understanding gave birth to the constantly expanding field of “laser-induced molecular alignment”. In this paper, we attempt to guide the readers through our involvement (both experimental and theoretical) in this field in the last few years. We start with the basic phenomenon of molecular alignment induced by a single pulse, continue with selective alignment of close molecular species and unidirectional molecular rotation induced by two time-delayed pulses, and lead up to novel schemes for manipulating the spatial distributions of molecular samples through rotationally controlled scattering off inhomogeneous fields and surfaces.

Molecular Alignment Induced by Ultrashort Laser Pulses and Its Impact on Molecular Motion

We introduce a new scheme for controlling the sense of molecular rotation. By varying the polarization and the delay between two ultrashort laser pulses, we induce unidirectional molecular rotation, thereby forcing the molecules to rotate clockwise/counterclockwise under field-free conditions. We show that unidirectionally rotating molecules are confined to the plane defined by the two polarization vectors of the pulses, which leads to a permanent anisotropy in the molecular angular distribution. The latter may be useful for controlling collisional cross-sections and optical and kinetic processes in molecular gases. We discuss the application of this control scheme to individual components within a molecular mixture in a selective manner.

https://iopscience.iop.org/article/10.1088/1367-2630/11/10/105039/pdf

Ilya Sh. Averbukh

Papers

Angular Focusing, Squeezing, and Rainbow Formation in a Strongly Driven Quantum Rotor

Wave Packet Isotope Separation.

Observing Molecular Spinning via the Rotational Doppler Effect

Molecular Alignment Induced by Ultrashort Laser Pulses and Its Impact on Molecular Motion

Controlling the sense of molecular rotation