The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it ha...

The Jaynes-Cummings Model

This Account discusses surface-enhanced Raman scattering at extremely high enhancement levels that can occur for molecules attached to silver and gold nanoclusters. Strongly enhanced and highly confined local optical fields enable surface-enhanced Stokes and anti-Stokes Raman spectroscopy of single molecules even under nonresonant excitation conditions as well as extremely large effective cross sections in two-photon excited Raman spectroscopy. The ability for very sensitive and spatially confined molecular structural probing makes gold and silver nanoclusters very promising tools for studies of small structures in biological materials, such as cellular compartments.

Surface-enhanced Raman scattering in local optical fields of silver and gold nanoaggregates-from single-molecule Raman spectroscopy to ultrasensitive probing in live cells.

We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.

http://export.arxiv.org/pdf/cond-mat/0301273

Chaos and the quantum phase transition in the Dicke model.

Presentation du probleme et des methodes theoriques de calcul des intensites. Application aux systemes moleculaires XY 2

Overtone frequencies and intensities in the local mode picture

The theory of reactive (rearrangement) scattering for three atoms in three physical dimensions using adiabatically adjusting, principal axes hyperspherical (APH) coordinates is given. The relationships of the APH coordinates to Delves and Jacobi coordinates are given, and the kinetic energy operator is shown to be relatively simple. Procedures for solving the equations via either an exact coupled channel (CC) method or an optimum centrifugal sudden (CSAPH) approximation are given as well as procedures for applying scattering boundary conditions. Surface functions of two angles are obtained using a finite element method with an optimized, nonuniform mesh, and the CC equations are solved using the efficient VIVAS method. Sample CC results are given for the H3 system. The present approach has the advantages that all arrangements are treated fully equivalently; it is a principal axis system, so that both axes and internal coordinates swing smoothly with the reactions; it is directly applicable to both symmetric and unsymmetric systems and mass combinations and all total angular momenta; it gives convenient mappings for visualization of potential energy surfaces and wave functions; only regular radial solutions are required; all coordinate matching is by simple projection; and the expensive parts of the calculation are energy independent, so that, once they are done, the scattering matrices can be rapidly generated at the large numbers of energies needed to map out reactive thresholds and resonances. Accurate reactive scattering calculations are now possible for many chemically interesting reactions that were previously intractable.

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory

The fundamental role of Eckart vectors and Eckart frames is demonstrated in the theort of the vibration--rotation Hamiltonian for a polyatomic molecule. (AIP)

Eckart vectors, Eckart frames, and polyatomic molecules

The problem of a collection of two-level atoms interacting with a single-mode classical electromagnetic field is considered. It is found that the model with an initial population inversion exhibits chaotic behavior that becomes stronger for higher atomic number density. The chaos is characterized by Fourier analysis and the maximal Lyapunov exponent. In the rotating-wave approximation, however, there is no prediction of chaos.

H. W. Galbraith

Papers

Eckart vectors, Eckart frames, and polyatomic molecules

Chaos in the Semiclassical N -Atom Jaynes-Cummings Model: Failure of the Rotating-Wave Approximation

Identification of the SF6 transitions pumped by a CO2 laser

Towards an explanation of collisionless multiple-photon laser dissociation of SF6

The ν3 Q branch of SF6 at high resolution: Assignment of the levels pumped by P(16) of the CO2 laser☆