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arXiv:1010.3627 · Journal of Modern Physics

Study of the Double Nonlinear Quantum Resonances in Diatomic Molecules

Gustavo V. López, J. G. T. Zanudo

Published Jan 1, 2011• 1 citation
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Abstract

We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear reso-nances associated to the vibrational and rotational motion. We solve the Schrödinger equation associated with the wave function expanded in term of proper stationary states, |n> |lm> (vibrational angular momentum states). Looking for quantum-classic correspondence, we consider the Liouville dynamics in the two dimensional phase space defined by the coherent-like state of vibrational states. We consider the rela-tionship between the overlapping of the classical resonances and the mixing of the quantum states, and it is found some similarities when the quantum dynamics is pictured in terms of number and phase operators.

DOI
10.4236/jmp.2011.26057

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We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear reso-nances associated to the vibrational and rotational motion. We solve the Schrödinger equation associated with the wave function expanded in term of proper stationary states, |n> |lm> (vibrational angular momentum states). Looking for quantum-classic correspondence, we consider the Liouville dynamics in the two dimensional phase space defined by the coherent-like state of vibrational states. We consider the rela-tionship between the overlapping of the classical resonances and the mixing of the quantum states, and it is found some similarities when the quantum dynamics is pictured in terms of number and phase operators.
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Optical pumping of the electronic ground state of molecules has been investigated under conditions of plane, elliptically, and circularly polarized light broadband excitation. The analysis has been performed assuming arbitrary angular momentum values, and applying the apparatus of polarization moments, the latter forming the coefficients in the expansion of the density matrix over irreducible tensor operators, including simplifications due to asymptotic limits for large momentum values. In addition to accounting for the external magnetic field, attention has been also given to the dynamical Stark effect arising from the absence of coincidence between the centers of the exciting line and the absorption line. An alternative classical description is also proposed using multiple moments as coefficients of the expansion of a classical quasidensity of states over spherical harmonics. The equivalence of both approaches of description in the limit of infinitely large angular moments is demonstrated, and the meaning of the origin of coherence is clarified, as well as its destruction by the magnetic field in the classical description of the system.
The quantum dynamics of a coherently driven nonlinear oscillator are studied by solving the Schrödinger equation numerically. The results are used to examine the effect of increasingly strong driving on the mean number, squeezing, the second-order correlation function and the general behaviour of the Q function. For comparison, the corresponding quantities for the classical Liouville dynamics are also computed. It is found that while the dynamics do maintain some quantum aspects as the strength of the driving is increased, the spectacular quantum features of the undriven nonlinear oscillator are in fact progressively lost.