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arXiv:quant-ph/0507082 · Physical Review A

Mesoscopic superposition and sub-Planck-scale structure in molecular wave packets

Suranjana Ghosh, Aravind Chiruvelli, J. Banerji, Prasanta Kumar Panigrahi

Published Jan 30, 2006• 38 citations
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Abstract

We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopic-quantum-superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.

DOI
10.1103/physreva.73.013411

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We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopic-quantum-superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.
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Quantum sensitivity is an important issue in the field of quantum metrology where sub-Planck scale structures play a crucial role in the Heisenberg limited measurement. We investigate the mesoscopic superposition structures, particularly for well-known catlike and compasslike states, in the rotating Morse system where sub-Planck scale structures originate in the dynamics of a suitably constructed SU(2) coherent state. A detail study of the sensitivity analysis reveals that rotational coupling in the vibrational wave packet can be used as a probe to enhance the sensitivity limit in a diatomic molecule. The maximum sensitivity limit is identified with the rotational amendment, and a quantitative measure of the angle of rotation for different rotational levels is also given. The correspondence of the numerical result with the angle of rotation is also delineated in phase-space Wigner representation.
Abstract We study the temporal dynamics of a photon-added SU(2) coherent state, involving vibrational bound states of an iodine molecule. The nonclassicality of Schrödinger cat-like and compass-like photon-added states of this anharmonic potential is explored through the Mandel Q parameter and the negative region in their phase spaces. The Wigner phase space distribution is thoroughly studied for the photon-added molecular state and displayed for cat- and compass-like states. Generation and control of the sub-Planck interference structures become intriguing with photon addition. We ensure that the photon addition helps to improve the quantum sensitivity for a diatomic molecular system by comparing it between photon-added and photon-subtracted states. The detailed study of quantum sensitivity reveals that one can use a photon-added molecular wave packet as a probe to attain sensitivity to displacement that greatly exceeds the standard quantum limit. We also report that the nature of variation of the quantum sensitivity becomes qualitatively commensurate with that of the Wigner-negativity.
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This paper presents the time evolution of a quantum wave packet bound in the Morse potential. The quantum wave packet is the superposition of vibrational energy levels of a diatomic molecule in an anharmonic potential. The probability density function, auto-correlation function, and various time scales have been used to explore the revival pattern of this wave packet. The dynamics of the wave packet with respect to time shows a series of collapses and the subsequent revivals. The results are presented for CO molecule.