The quantum transitions probability as paths-integral in energy states space

A. A. Biryukov ; M. A. Shleenkov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 2, pp. 221-240.

Résumé

By the use of the functional integration approach (paths integral approach) we present a non-perturbative method for dynamics of multi-levels quantum systems (such as atoms, molecules and nanosystems) interacting with high-intensity laser field describing. The probability of transitions between investigated quantum system states under electromagnetic field action is written as functional integral in energy representation (in investigated quantum system energy states space). In this approach we calculate probabilities of diatomic molecules transition between rotating quantum states under the ultrashort laser pulses train action by the use of numerical simulations. We investigate the dynamics of rotating quantum states population for $^{14}\mathrm N_2$ and $^{15}\mathrm N_2$ molecules interacting with a train of picoseconds laser pulses with different train period and intensity. We show for some train periods there are resonances of population transfer from low rotating quantum states of investigated molecules to high states. We study these resonances for various laser field intensities and pulses train periods. We note that in resonance case the parameters of laser field are different for $^{14}\mathrm N_2$ and $^{15}\mathrm N_2$ molecules. Obtained results indicate on the possibility of molecules rotating states selective exitation by ultrashort laser pulses train. Our numerical results are in agreement with results of experimental studies [Phys. Rev. Lett., 2012, vol. 109, 043003].

Détail

Keywords: the path integral approach, non-resonance processes, the energy representation, dinitrogen molecules, ultrashort laser pulses, non-linear interaction, rotating states selective excitation.
Mots-clés : multiphoton processes

Bibliographie

[1] Biryukov A. A., Shleenkov M. A., “The quantum transitions probability as paths-integral in energy states space”, The 4nd International Conference “Mathematical Physics and its Applications”, Book of Abstracts and Conference Materials, eds. I. V. Volovich; V. P. Radchenko, Samara State Technical Univ., Samara, 2014, 87 (In Russian)

[2] Sweatlock L. A., Maier S. A., Atwater H. A., Penninkhof J. J., Polman A., “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles”, Phys. Rev. B, 2005:23, 235408 | DOI

[3] Hao E., Schatz G. C., “Electromagnetic fields around silver nanoparticles and dimers”, J. Chem. Phys., 120:1 (2004), 357–369 | DOI

[4] Govorov A. O., “Semiconductor-metal nanoparticle molecules in a magnetic field: Spin-plasmon and exciton-plasmon interactions”, Phys. Rev. B, 82:15 (2010), 155322 | DOI

[5] Koshlyakov P. V., Chesnokov E. N., Gorelik S. R., Petrov A.K., “Infrared multiphoton dissociation of $\mathrm{SiF_3CH_3}$”, Khim. Fiz., 25:6 (2006), 22–32 (In Russian)

[6] Ursrey D., Anis F., Esry B. D., “Multiphoton dissociation of $\text{HeH}^{+}$ below the $\text{He}^+(1s) + \text{H}(1s)$ threshold”, Phys. Rev. A, 85:2, 023429, arXiv: [physics.atom-ph] 1112.3688 | DOI

[7] Wellers Ch., Borodin A., Vasilyev S., Offenberg D., Schiller S., “Resonant IR multi-photon dissociation spectroscopy of a trapped and sympathetically cooled biomolecular ion species”, Phys. Chem. Chem. Phys., 13:42 (2011), 18799–809 | DOI

[8] Richter M., Amusia M. Ya., Bobashev S. V., Feigl T., Juranić P. N., Martins M., Sorokin A. A., Tiedtke K., “Extreme Ultraviolet Laser Excites Atomic Giant Resonance”, Phys. Rev. Let., 102:16 (2009), 163002 | DOI

[9] Farrell J. P., Petretti S., Förster J., McFarland B. K., Spector L. S., Vanne Y. V., Decleva P., Bucksbaum P. H., Saenz A., Gühr M., “Strong Field Ionization to Multiple Electronic States in Water”, Phys. Rev. Let., 107:8 (2011), 083001, arXiv: [physics.atom-ph] 1103.4423 | DOI

[10] Goodsell A., Ristroph T., Golovchenko J. A., Hau L. V., “Field Ionization of Cold Atoms near the Wall of a Single Carbon Nanotube”, Phys. Rev. Let., 104:13 (2010), 133002, arXiv: [physics.atom-ph] 1004.2644 | DOI

[11] Raynaud M., Kupersztych J., “Ponderomotive effects in the femtosecond plasmon-assisted photoelectric effect in bulk metals: Evidence for coupling between surface and interface plasmons”, Phys. Rev. B., 76:24 (2007), 241402(R) | DOI

[12] Raynaud M., Kupersztych J., “Anomalous Multiphoton Photoelectric Effect in Ultrashort Time Scales”, Phys. Rev. Let., 95:14 (2005), 147401 | DOI

[13] Zhdanovich S., Bloomquist C., Floß J., Averbukh I. Sh., Hepburn J. W., Milner V., “Quantum Resonances in Selective Rotational Excitation of Molecules with a Sequence of Ultrashort Laser Pulses”, Phys. Rev. Lett., 109:4 (2012), 043003, arXiv: [quant-ph] 1201.3151 | DOI | MR

[14] Floß J., Fishman Shm., Averbukh I. Sh., “Anderson localization in laser-kicked molecules”, Phys. Rev. A, 88:2 (2013), 023426 | DOI

[15] Floß J., Averbukh I. Sh., “Quantum resonance, Anderson localization, and selective manipulations in molecular mixtures by ultrashort laser pulse”, Phys. Rev. A, 86:2 (2013), 021401(R), arXiv: [quant-ph] 1110.3509 | DOI

[16] Feynman R. P., Hibbs A. R., Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965 | Zbl

[17] Biryukov A. A., Shleenkov M. A., “The quantum system transitions probability as a paths integral of real functionals”, Teoreticheskaia fizika, 13 (2012), 8–42 (In Russian)

[18] Biryukov A., Shleenkov M., Path integral approach to the problem of rotational excitation of molecules by an ultrashort laser pulses sequence, 2014, 6 pp., arXiv: [quant-ph] 1407.3893

[19] Scully M. O., Zubairy M. S., Quantum Optics, Cambridge University Press, Cambridge, 1997, xxii+630 pp. | DOI

[20] Ryazanov G. V., “Quantum-mechanical probability as a sum over path”, JETP, 35:1 (1958), 121–131 | Zbl

[21] Landau L. D., Lifshitz E. M., Course of Theoretical Physics, v. 3, Quantum mechanics. Non-relativistic theory, Pergamon Press Ltd., London, New York, Paris, Los Angeles, 1958, xii+515 pp. | MR | Zbl | Zbl

[22] Irikura K., “Experimental Vibrational Zero-Point Energies: Diatomic Molecules”, J. Phys. Chem. Ref. Data, 36:2 (2007), 389–397 | DOI

[23] NIST Computational Chemistry Comparison and Benchmark Database, ed. Russell D. Johnson III, Release 16a, August 2013 http://cccbdb.nist.gov