197 research outputs found
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.
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
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
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