(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

It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

Wave propagation and group velocity

We review some basic techniques for laser-induced adiabatic population transfer between discrete quantum states in atoms and molecules.

Laser-induced population transfer by adiabatic passage techniques.

心臓病診療プラクティス 16. 心不全を癒す

We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.

/pdf/optimal-control-in-laser-induced-population-transfer-for-two-1c4906ml21.pdf

Optimal control in laser-induced population transfer for two- and three-level quantum systems

Considering the problem of the control of a two-state quantum system by an external field, we establish a general and versatile method allowing the derivation of smooth pulses which feature the properties of high fidelity, robustness, and low area. Such shaped pulses can be interpreted as a single-shot generalization of the composite pulse-sequence technique with a time-dependent phase.

Robust quantum control by a single-shot shaped pulse.

We report a direct nonintrusive observation of alignment and planar delocalization of ${\mathrm{C}\mathrm{O}}_{2}$ after an intense linearly polarized femtosecond laser pulse excitation. The effects are measured by a polarization technique involving a perturbative probe that itself does not induce appreciable alignment. We show that this technique allows one to measure a signal proportional to $⟨{cos﻿}^{2}\ensuremath{\theta}⟩\ensuremath{-}1/3$, with $\ensuremath{\theta}$ the angle between the molecular axis and the laser polarization. Simulations that support this analysis allow one to characterize the experimentally observed alignment and planar delocalization quantitatively.

Postpulse molecular alignment measured by a weak field polarization technique.

We present a method for optimization of the technique of adiabatic passage between two quantum states by composite sequences of frequency-chirped pulses with specific relative phases: composite adiabatic passage (CAP). By choosing the composite phases appropriately the nonadiabatic losses can be canceled to any desired order with sufficiently long sequences, regardless of the nonadiabatic coupling. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp. The accuracy of the CAP technique and its robustness against parameter variations make CAP suitable for high-fidelity quantum information processing.

/pdf/high-fidelity-adiabatic-passage-by-composite-sequences-of-3iws50o098.pdf

Stéphane Guérin

Papers

Optimal control in laser-induced population transfer for two- and three-level quantum systems

Robust quantum control by a single-shot shaped pulse.

Postpulse molecular alignment measured by a weak field polarization technique.

High-Fidelity Adiabatic Passage by Composite Sequences of Chirped Pulses

Control of Quantum Dynamics by Laser Pulses: Adiabatic Floquet Theory