(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

When one extends the conventional stimulated Raman adiabatic passage method of population transfer; involving a pump pulse preceded by a Stokes pulse, to situations in which the pump ~or pump and Stokes! interaction involves a two-photon transition, there occur unavoidable dynamic Stark shifts which prevent maintenance of the relevant resonance conditions. Such shifts can prevent the desired population transfer. We show, through numerical modeling and analytic considerations, that the detrimental effects of dynamic shifts can be compensated by a suitable choice of ~static! detunings of the carrier frequencies of the two pulses, so that population transfer can be achieved. We present simple analytic expressions for bounding the range of detunings for which population transfer can occur, and we present numerical results supporting the simple picture of the two-step linewidth. We illustrate these remarks by considering specific examples. @S1050-2947~98!09311-1#

Stimulated hyper-Raman adiabatic passage. II. Static compensation of dynamic Stark shifts

We discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.

Stimulated hyper-Raman adiabatic passage. I. The basic problem and examples

A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.

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Adiabatic approximation for quantum dissipative systems: Formulation, topology, and superadiabatic tracking

We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, along with several other models, such as a Gaussian model and a Landau-Zener model with a pulsed coupling.

Stéphane Guérin

Papers

Stimulated hyper-Raman adiabatic passage. II. Static compensation of dynamic Stark shifts

Stimulated hyper-Raman adiabatic passage. I. The basic problem and examples

Adiabatic approximation for quantum dissipative systems: Formulation, topology, and superadiabatic tracking

Uniform analytic description of dephasing effects in two-state transitions

Dynamical resonances and the topology of the multiphoton adiabatic passage