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

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

Oscillator tunneling dynamics in the Rabi model

The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, continues to produce rich and surprising physics when the coupling strength becomes comparable to the individual subsystem frequencies. We construct approximate solutions for the regime in which the oscillator frequency is small compared to that of the two-level system and the coupling strength matches or exceeds the oscillator frequency. Relating our fully quantum calculation to a previous semi-classical approximation, we find that the dynamics of the oscillator can be considered to a good approximation as that of a particle tunneling in a classical double-well potential, despite the fundamentally entangled nature of the joint system. We assess the prospects for observation of oscillator tunneling in the context of nano- or micro-mechanical experiments and find that it should be possible if suitably high coupling strengths can be engineered.Comment: 25 pages, 5 figures, preprint forma

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