Is a Circular Orbit Possible According to General Relativity?

A new parameter space is used to classify circular orbits in the Schwarzschild metric.Comment: 12 pages, no figures, no tables. In this version we consider a broader parameter space for the orbits than in the original versio

Analytically solvable driven time-dependent two-level quantum systems

Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions. Any function satisfying these constraints yields an exact analytical solution. We demonstrate this method by presenting several new exact solutions to the time-dependent Schrodinger equation. Our general method and many of the new solutions we present are particularly relevant to qubit control in quantum computing applications.Comment: 4.5 pages, 4 figures, PRL versio

Cavity state preparation using adiabatic transfer

We show how to prepare a variety of cavity field states for multiple cavities. The state preparation technique used is related to the method of stimulated adiabatic Raman passage or STIRAP. The cavity modes are coupled by atoms, making it possible to transfer an arbitrary cavity field state from one cavity to another, and also to prepare non-trivial cavity field states. In particular, we show how to prepare entangled states of two or more cavities, such as an EPR state and a W state, as well as various entangled superpositions of coherent states in different cavities, including Schrodinger cat states. The theoretical considerations are supported by numerical simulations.Comment: 11 pages, 9 figures. Accepted in Phys. Rev.

Stimulated Raman adiabatic passage in a multi-level atom

We present a general formalism for describing stimulated Raman adiabatic passage in a multi-level atom. The atom is assumed to have two ground state manifolds a and b and an excited state manifold e, and the adiabatic passage is carried out by resonantly driving the a-e and b-e transitions with time-dependent fields. Our formalism gives a complete description of the adiabatic passage process, and can be applied to systems with arbitrary numbers of degenerate states in each manifold and arbitrary couplings of the a-e and b-e transitions. We illustrate the formalism by applying it to both a simple toy model and to adiabatic passage in the Cesium atom.Comment: 14 pages, 2 figure

Characterizing Planetary Orbits and the Trajectories of Light

Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can be associated with different characteristics of the orbits. The boundaries for these regions are clearly defined. Observational data can be directly associated with points in the regions. A possible extension of these considerations with an additional parameter for the case of Kerr geometry is briefly discussed.Comment: 49 pages total with 11 tables and 10 figure

Semiclassical Analysis of Quasi-Exact Solvability

Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that are central to quasi-exact solvability. These two properties define a new class of semiclassically quasi-exactly solvable potentials.Comment: 12 pages, ReVTe