(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 discuss the effects of resonances in driven quantum systems within the context of quantum averaging techniques in the Floquet representation. We consider in particular iterative methods of KAM type and the extensions needed to take into account resonances. The approach consists in separating the coupling terms into resonant and nonresonant components at a given scale of time and intensity. The nonresonant part can be treated with perturbative techniques, which we formulate in terms of KAM-type unitary transformations that are close to the identity. These can be interpreted as averaging procedures with respect to the dynamics defined by effective uncoupled Hamiltonians. The resonant parts are treated with a different kind of unitary transfomations that are not close to the identity, and are adapted to the structure of the resonances. They can be interpreted as a renormalization of the uncoupled Hamiltonian, that yields an effective dressed Hamiltonian, around which a perturbation expansion can be developed. The combination of these two ingredients provides a strongly improved approximation technique.

Quantum averaging for driven systems with resonances

This chapter is partly based on results and discussions published in Ref. (Sala et al., J. Chem. Phys., 140:194309, 2014, [1]). This material is reproduced with permission. Copyright [2014] AIP Publishing LLC.

Laser control of the radiationless decay in pyrazine using the dynamic Stark effect.

We describe analytically and numerically the process of population transfer by stimulated Raman adiabatic passage through a bright state when the pulses propagate in a medium. Limitations of the adiabaticity are analyzed and interpreted in terms of reshaping of the pulses. We find parameters for the pulses for which the population transfer is nearly complete over long distances.

http://www.iap.tu-darmstadt.de/fileadmin/nlq/publications/047.theory_b_STIRAP.PRA.2009.pdf

Theory of the bright-state stimulated Raman adiabatic passage

We developed single-shot shaped pulses for ultrahigh (UH)-fidelity population transfer on a three-level quantum system in $\mathrm{\ensuremath{\Lambda}}$ configuration. To ensure high fidelity, we use the Lewis-Riesenfeld (L-R) method to derive a family of solutions leading to an exact transfer, where the solutions follow a single dynamical mode of the L-R invariant. Among this family, we identify a tracking solution with a single parameter to control simultaneously the fidelity of the transfer, the population of the excited state, and robustness. We define a measure of the robustness of an UH-fidelity transfer as the minimum percentile deviation on the pulse areas at which the infidelity rises above ${10}^{\ensuremath{-}4}$. The robustness of our shaped pulses is found to be superior to that of Gaussian and adiabatically optimized pulses for moderate pulse areas.

Stéphane Guérin

Papers

Quantum averaging for driven systems with resonances

Laser control of the radiationless decay in pyrazine using the dynamic Stark effect.

Theory of the bright-state stimulated Raman adiabatic passage

Robust stimulated Raman exact passage using shaped pulses

Field-free quantum cogwheel by shaping of rotational wave packets