Approximation rotating-wave

Here the oscillatory terms like e2,ta> and e 2lt<0 have been ignored, which is called the rotating wave approximation (RWA). Linear susceptibility yl et) is defined by... 

The theory has been generalized by us to finite temperatures and to qubits driven by an arbitrary time-dependent field, which may cause the failure of the rotating-wave approximation (RWA) [11]. It has also been extended to the analysis of multilevel systems, where quantum interference between the levels may either inhibit or accelerate the decay [19]. 

Eq. (6.26) is the TDSE in the Schrodinger picture. In general, it proves more convenient to discuss the time evolution of the driven system in a rotating frame, such as the frame rotating with the laser carrier frequency q- After transformation into the carrier frequency picture and application of the rotating wave approximation (RWA), the TDSE takes the form [92]... 

On the other hand, there are many instances when the rotating wave approximation cannot be used. For example, in order to find the energy levels of a molecule placed in a strong microwave field, it is necessary to diagonalize a large piece of the full Floquet matrix involving multiple n-states and multiple eigenstates of Hq, as discussed in Section 8.3.4. 

This reduces to (2.3) if one supposes (c) the rotating wave approximation terms with ana0 and 44 may be omitted. They are associated with the high frequencies Q + con and therefore negligible in most applications. For our present case this approximation was not indispensable, but simplified the algebra. 

Adopting the rotating-wave approximation (RWA) and introducing the detuning frequency Ao= Ujk-yjk and the Rabi frequency Mjk -we find... 

Figure 1- Liouville space diagram corresponding to the only term that contributes to the spontaneous light emission from a two-level system within the rotating-wave approximation [Eq. (2.7)]. Here ]g) and e) denote the ground and the excited states, respectively.

After transformation into the interaction picture and application of the rotating-wave approximation [46, SO, 54] the population dynamics can be calculated numerically by solving the time-dependent three-level Schrodinger equation or (if phenomenological relaxation rates are considered) by solving the density matrix equation (3) for the molecular system. The density matrix equation is given by... 

For a three-level system the Hamiltonian in the interaction picture //, in Rotating Wave Approximation is given in matrix representation by... 

A. E. Kondo, V. M. Blokker, and W. J. Meath,/. Chem. Phys., 96, 2544 (1992). Permanent Dipole Moments and Two-Colour Multi-Photon Resonances in the Two-Level Molecule Rotating Wave Approximation Versus Exact Results. 

For uifi > 0 (absorption) the first term is usually much smaller than the second one and therefore it is neglected (rotating wave approximation). The reverse holds for < 0 (stimulated emission). Within this approximation the time-dependent probability for making a transition from initial state Fj) to final state Ff) under the influence of the photon beam... 

Let the laser field be expressed as s(t) — o(t) sin(coLt), where o(t) is the pulse envelope function, including polarization, and col is the central frequency. For simplicity, consider a 8 function excitation. In the rotating wave approximation, the field is expressed as e(t) = S(t) exp(—icoLt) with field strength sq. Integration over t in Eq. (25) gives... 

Moreover, within the rotating wave approximation, which is usual in the quantum theory of damping, the terms corresponding to double excitations or desexcita-tions in Eq. (104) are neglected. Thus, within this approximation, Eq. (104) reduces to... 

As a consequence, using the Bosons description and performing the rotating wave approximation lead us to write the effective Hamiltonians (102) and (103) describing the H-bond bridge coupled to the thermal bath as follows ... 

Consider then excitation of this mixed state with a Gaussian pulse, within the rotating wave approximation. The pulse is of the form... 

Equation (8.16), in the rotating wave approximation, is then given by... 

The coupled channels expansion can be further simplified by introducing the (number state) rotating-wave approximation (RWA), valid only when the field is jjsfif moderate intensity and the system is near resonance. As pointed out above, igtyen an initial photon number state [JVf), the components of E, n, N — 1") of. . greatest interest for a one-photon transition are (JV, , n",JV, —1 ) and y (Nj dt l[Ji, n, Nj — 1 ). If [ , ) is the ground material state, then the (Nj+m,... 

We now consider this scenario in detail by first writing the CPT (radiatiod + matter) Hamiltonian in the rotating wave approximation as... 

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