45 research outputs found
Two-state system driven by imperfect pi pulses: an estimate of the error accumulation in bang-bang control methods
The evolution of a two-state system driven by a sequence of imperfect pi
pulses (with random phase or amplitude errors) is calculated. The resulting
decreased fidelity is used to derive a plausible limit on the performance of
"bang-bang" control methods for the suppression of decoherence.Comment: 9 pages, 3 figures; submitted to Journal of Modern Optic
University Physics I: Classical Mechanics
This is a textbook for the first semester of University Physics for scientists and engineers. It covers classical mechanics, and a brief introduction to thermodynamics. The presentation and approach are similar to Mazur’s “The Principles and Practice of Physics,” in that conservation laws are introduced before forces, and one-dimensional systems thoroughly covered before moving to two dimensions. Although the course is “calculus based,” the book has been written with the understanding that many students may be taking calculus simultaneously as a corequisite, so the use of calculus is relatively sparse.
This revised version (Fall 2019) takes into account a number of student suggestions. it has more worked out examples, and also a few more problems; the material in Chapters 8 and 9 has been slightly rearranged, so that now rotational kinematics is part of Chapter 8 (“Motion in two dimensions”); and the chapters on gravity and waves, 10 and 12, have been simplified a bit (particularly 12). Some of the more advanced examples from the first version have now been labeled “Advanced Topics,” so students should know that they can skip them if they want to. Several typos have been corrected as well.https://scholarworks.uark.edu/oer/1002/thumbnail.jp
Impossibility of large phase shifts via the "giant Kerr effect" with single-photon wavepackets
An approximate analytical solution is presented, along with numerical
calculations, for a system of two single-photon wavepackets interacting via an
ideal, localized Kerr medium. It is shown that, because of spontaneous emission
into the initially unoccupied temporal modes, the cross-phase modulation in the
Schrodinger picture is very small as long as the spectral width of the
single-photon pulses is well within the medium's bandwidth. In this limit, the
Hamiltonian used can be derived from the "giant Kerr effect" for a four-level
atom, under conditions of electromagnetically-induced transparency; it is shown
explicitly that the linear absorption in this system increases as the pulse's
spectral width approaches the medium's transparency bandwidth, and hence, as
long as the absorption probability remains small, the maximum cross-phase
modulation is limited to essentially useless values. These results are in
agreement with the general, causality- and unitarity-based arguments of Shapiro
and co-workers.Comment: 8 pages, 2 figures, to be submitted to Physical Review
Reply to "Comment on "Some implications of the quantum nature of laser fields for quantum computations''''
In this revised reply to quant-ph/0211165, I address the question of the
validity of my results in greater detail, by comparing my predictions to those
of the Silberfarb-Deutsch model, and I deal at greater length with the beam
area paradox. As before, I conclude that my previous results are an
(order-of-magnitude) accurate estimate of the error probability introduced in
quantum logical operations by the quantum nature of the laser field. While this
error will typically (for a paraxial beam) be smaller than the total error due
to spontaneous emission, a unified treatment of both effects reveals that they
lead to formally similar constraints on the minimum number of photons per pulse
required to perform an operation with a given accuracy; these constraints agree
with those I have derived elsewhere.Comment: A reply to quant-ph/0211165. Added more calculations and discussion,
removed some flippanc