The von Neumann picture: A new representation for ultrashort laser pulses

Optics Express

Volumn 15, Issue 23, 2007, Pages 15387-15401

  Fechner, Susanne ^a   Dimler, Frank ^a   Brixner, Tobias ^a   Gerber, Gustav ^a   Tannor, David J ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; GAUSSIAN DISTRIBUTION; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

DISCRETE LATTICES; VON NEUMANN REPRESENTATION;

ULTRASHORT PULSES;

EID: 36248940829     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.15.015387     Document Type: Article

References (25)

1. E. Wigner, "On the Quantum Correction For Thermodynamic Equilibrium," Phys. Rev. 40, 749-759 (1932).
2. K. Husimi, "Some Formal Properties of the Density Matrix," Proc. Phys. Math. Soc. Jpn. 22, 264-314 (1940).
3. R. Kosloff, S. A. Rice, P. Gaspard, S. Tersigni, and D. J. Tannor, "Wavepacket Dancing - Achieving Chemical Selectivity By Shaping Light-Pulses," Chem. Phys. 139(1), 201-220 (1989).
4. D. J. Tannor and Y Jin, Mode, selective Chemistry, chap. Design of Femtosecond Pulse Sequences to Control Photochemical Products, pp. 333-345 (Kluwer Academic Publishers, 1991).
5. J. Paye, "The Chronocyclic Representation of Ultrashort Light Pulses," IEEE J. Quantum. Electronics 28, 2262-2272 (1992).
6. J. Paye, "Space-Time Wigner functions and their application to the analysis of a pulse shaper," J. Opt. Soc. Am. B 12, 1480-1490 (1995).
7. G. Vogt, P. Nuernberger, R. Selle, F. Dimler, T. Brixner, and G. Gerber, "Analysis of femtosecond quantum control mechanisms with colored double pulses," Phys. Rev. A 74(3), 033413 (2006).
8. B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, "Coherent control using adaptive learning algorithms," Phys. Rev. A 6306(6), 063412 (2001).
9. T. C. Weinacht and P. H. Bucksbaum, "Using feedback for coherent control of quantum systems," J. Opt. B: Quantum. Semiclass. Opt. 4(3), R35-R52 (2002).
10. B. Amstrup, G. J. Tóth, G. Szabó, H. Rabitz, and A. Lörincz, "Genetic Algorithm With Migration On Topology Conserving Maps For Optimal-Control of Quantum-Systems," J. Phys. Chem. 99(14), 5206-5213 (1995).
11. T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, "Liquid-phase adaptive femtosecond quantum control: Removing intrinsic intensity dependencies," J. Chem. Phys. 118(8), 3692-3701 (2003).
12. S. Mukamel, C. Ciordas-Ciurdariu, and V. Khidekel, "Wigner spectrograms for femtosecond pulse-shaped heterodyne and autocorrelation measurements," IEEE J. Quantum Electron. 32(8), 1278-1288 (1996).
13. B. Schäfer-Bung, R. Mitrić, V. Bonačić- Koutecký, A. Bartelt, C. Lupulescu, A. Lindinger, V. Vajda, S. M. Weber, and L. Wöste, "Optimal control of ionization processes in NaK: Comparison between theory and experiment," J. Phys. Chem. A 108(19), 4175-4179 (2004).
14. K.-H. Hong, J.-H. Kim, Y. Kang, and C. Nam, "Time-frequency analysis of chirped femtosecond pulses using Wigner distribution function," Appl. Phys. B 74, 231-236 (2002).
15. D. Lalović, D. M. Davidović, and N. Bijedić, "Quantum mechanics in terms of non negative smoothed Wigner functions," Phys. Rev. A 46, 1206-1212 (1992).
16. H.-W. Lee, "Generalized antinormal ordered quantum phase-space distribution functions," Phys. Rev. A 50, 2746-2749 (1994).
17. J. von Neumann, "Die Eindeutigkeit der Schrödingerschen Operatoren," Math. Ann. 104, 570 (1931).
18. M. Boon and J. Zak, "Discrete coherent states on the von Neumann lattice," Phys. Rev. B 18, 6744-6751 (1978).
19. M. J. Davis and E. J. Heller, "Semiclassical Gaussian basis set method for molecular vibrational wave functions," J. Chem. Phys. 71, 3383 (1979).
20. D. J. Tannor, Introduction to Quantum Mechanics A Time-Dependent Perspective (Palgrave Macmillan, 2007).
21. R. Kosloff, "Time-Dependent Quantum-Mechanical Methods for Molecular Dynamics," J. Phys. Chem. 92, 2087 (1988).
22. R. Kosloff, Numerical Grid Methods and Their Application, to Schrodinger's Equation, chap. The Fourier Method, 1st ed.(Springer-Verlag GmbH, 1993-09-00 1993-09) pp. 175-194.
23. A. M. Perelomov, "On the Completeness of a System of Coherent States," Theor. Math. Phys. 11, 156 (1971).
24. W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, 2001).
25. S. S. Mizrahi, "Quantum mechanics in the Gaussian wave-packet phase space representation," Physica A 127, 241-264 (1984).