Coherent states photon exchange

Number of Exchanged Photons in Adiabatic Passage with Photons in Coherent States... 

In the preceding sections we have taken the limit h —> oo in which the coherent states become a 8i/2(0 — 9o) function. For the discussion of the exchanged photons we consider a large but finite h, such that the coherent state is represented by a sharply peaked function that can be written as a superposition (64). Under this condition, the relations (62) and (63) imply that the initial condition... 

We can explain these features by considering the equations of motion (96) for the density matrix elements. When A = 0, and the laser is tuned to the middle of the upper levels splitting the states 1) and 3) are equally driven by the laser and the coherences p12 and p32 oscillate in phase with frequency A/. The coherences are directly coupled by the cross-damping term I ) 2. However, for a strong driving field (fl 3> F) the Rabi oscillations dominate over the spontaneous exchange of photons, resulting in independent oscillations of the atomic dipole moments. 

The situation is different when A / 0. In this case the coherences oscillate with opposite phases indicating that there is an exchange of photons between the states 1) and 3), which prevents photons being emitted from the atomic levels. The coherences oscillate with A/2, which introduces the modulation of the Rabi oscillations, seen in Fig. 15. The exchange of photons between the atomic levels is better seen in the basis of the symmetric and antisymmetric states (107) and (108). In terms of these states, setting Ti=r2=r for simplicity, the equations of motion for the populations... 

QED [17] where energy is coherently exchanged between the internal state and single-photon radiation field. The first blue sideband, at 8 = +co drives transitions between states 11, n) 11, n+l) with Rabi frequency 2 +i = gTi(n+l) . ... 

A real nanometric material is composed not only of electrons but also of a crystal lattice. In this case, after a dressed photon is generated on an illuminated nanometric particle, its energy can be exchanged with the crystal lattice, as shown by the Feynman diagram of Fig. 1.3a. By this exchange, the crystal lattice can excite the vibration mode coherently, creating a coherent phonon state. As a result, the dressed photon and the coherent phonon can form a coupled state, as is schematically explained by Fig. 1.3b. The creation operator a] of this novel form of elementary excitation is expressed as... 

Fig. 1.3 Feynman diagrams representing the coupling of a dressed photon with phonons, (a) Generation of a dressed photon and exchange with the crystal lattice, (b) A coupled state of a dressed photon and a coherent phonon...

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