Number states multimode

Despite the fact that the matrix element of /V2(r, t) resembles the product of two classical fields, neither the number state nor the wave-packet themselves have classical analogs in the sense that these states are eigenstates of the A operator. A state that fulfills this criteria is a highly excited multimode coherent state [27],... 

It will be of interest to explore the connections between scaling theories (163) of energy flow in quantum number state-space with detailed computational results on specific systems. Interesting results have recently been obtained for model lattices (164), but the question remains as to how useful these approaches will be for more complex multimode systems. 

In this work we have attempted to model the available experimental data for CaO Cu2+ using a variety of parameter sets taken from the literature. We conclude that only O Brien s multimode model [7], for which hw 216 cm 1 and jX/hoy 8, can satisfactorily account for all the data. These systems are particularly attractive to both the theoretician and experimentalist fascinated by Jahn-Teller funny business in that the states pertaining to j = 1/2 and 3/2 span just a few wave numbers. We have demonstrated how a number of modem physical techniques can be employed to elucidate further the low-lying vibronic structure. In particular it should be possible to obtain a direct measure of the tunnelling splitting from a high-held, high-frequency EPR experiment. 

Provided that ( C 1, one can always find a specific number of excitations in the cell that allows conditional production of number-squeezed atomic states. For instance, if ( 0.1, the optimal Q is found to be — 0.5 in both multimode and monomode cases. This indicates that highly nonclassical states (Q < 0) can be produced with parameters in the range of our current experimental. 

The time dependence of Nj(x) in Eq. (104) resembles that of the pump field, if DpjL characteristic time of the change of pump-field intensity). This means that one-photon multimode Fock-state fields with a given mean-photon-number time dependence can be generated for suitably chosen pump-field-intensity profiles. For instance, if the pump field consists of two femtosecond pulses of the same duration and one has no chirp whereas the other one is highly chirped, the overall pump field as well as Nj(t) have a peaked structure (see Fig. 17). 

State calculations. With the extensions provided, the method can be applied to the full Watson Hamiltonian [51] for the vibrational problem. The efficiency of the method depends greatly on the nature of the anharmonic potential that represents couphng between different vibrational modes. In favorable cases, the latter can be represented as a low-order polynomial in the normal-mode displacements. When this is not the case, the computational effort increases rapidly. The Cl-VSCF is expected to scale as or worse with the number N of vibrational modes. The most favorable situation is obtained when only pairs of normal modes are coupled in the terms of the polynomial representation of the potential. The VSCF-Cl method was implemented in MULTIMODE [47,52], a code for anharmonic vibrational spectra that has been used extensively. MULTIMODE has been successfully applied to relatively large molecules such as benzene [53]. Applications to much larger systems could be difficult in view of the unfavorable scalability trend mentioned above. 

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