The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

The Physics of Quantum Information

This Review article provides an overview of the fundamental origins and important applications of the main spin–orbit interaction phenomena in modern optics that play a crucial role at subwavelength scales. Light carries both spin and orbital angular momentum. These dynamical properties are determined by the polarization and spatial degrees of freedom of light. Nano-optics, photonics and plasmonics tend to explore subwavelength scales and additional degrees of freedom of structured — that is, spatially inhomogeneous — optical fields. In such fields, spin and orbital properties become strongly coupled with each other. In this Review we cover the fundamental origins and important applications of the main spin–orbit interaction phenomena in optics. These include: spin-Hall effects in inhomogeneous media and at optical interfaces, spin-dependent effects in nonparaxial (focused or scattered) fields, spin-controlled shaping of light using anisotropic structured interfaces (metasurfaces) and robust spin-directional coupling via evanescent near fields. We show that spin–orbit interactions are inherent in all basic optical processes, and that they play a crucial role in modern optics.

Spin-orbit interactions of light

Tables of integrals

We study the classical and quantum dynamics of a Fermi accelerator realized by an atom bouncing off a modulated atomic mirror. We find that in a window of the modulation amplitude, dynamical localization occurs in both position and momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. 74, 4972 (1995)] shows that this system can be implemented experimentally.

http://arxiv.org/pdf/quant-ph/9809040.pdf

Fermi accelerator in atom optics

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. \ifmmode \acute{S}\else \'{S}\fi{}liwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schr\"odinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schr\"odinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of the Maxwell equations with embedded vortex lines are given. Vortex lines in the Laguerre-Gaussian beams are treated in some detail.

Vortex lines of the electromagnetic field

We study nonlinear wave equations of the Schroedinger-Pauli and Klein-Gordon type. We show that from a class of nonlinearities the logarithmic nonlinearity is distinguished by several interesting physical properties. Wave equations with such a nonlinearity have stable, localized, soliton-like solutions in any number of dimensions.

Wave Equations with Logarithmic Nonlinearities

Coherent dynamics of N-level atoms and molecules. II. Analytic solutions

We show that the change of the phase of the wave function of a free relativistic spinning particle under the action of the Poincar\'e group is described by a certain universal connection in momentum space. This connection determines the parallel transport of the spin during the motion of the particle through external fields. In the special case of photons we reproduce the formula for Berry's phase calculated recently by Chiao and Wu.

Iwo Bialynicki-Birula

Papers

Fermi accelerator in atom optics

Vortex lines of the electromagnetic field

Wave Equations with Logarithmic Nonlinearities

Coherent dynamics of N-level atoms and molecules. II. Analytic solutions

Berry's phase in the relativistic theory of spinning particles.