Abstract
Availability of short, femtosecond laser pulses has recently made feasible the probing of phases in an atomic or molecular wave-packet (superposition of energy eigenstates). With short duration excitations the initial form of the wave-packet is an essentially real “doorway state,” and this develops phases for each of its component amplitudes as it evolves. It is suggested that these phases are hallmarks of a time arrow and irreversibility that are inherent in the quantum mechanical processes of preparation and evolution. To display the non-triviality of the result, we show under what conditions it would not hold; to discuss its truth, we consider some apparent contradictions. We propose that (in time-reversal invariant systems) the preparation of “initially” complex wave-packets needs finite times to complete, i.e., is not instantaneous.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. S. Davydov, Quantum Mechanics (Pergamon, Oxford, 1965), Sec. 108.
H. D. Zeh, The Physical Basis of the Direction of Time (Springer, Berlin, 1992).
J. L. Lebowitz, “Boltzmann's entropy and time's arrow,” Physics Today 46, 32 (Sep. 1993) [Various responses in Physics Today 47, 11 and following (Nov. 1994)].
L.S. Schulman, Time Arrows and Quantum Measurement (University Press, Cambridge, 1997)
A. Bohm, “Time asymmetric quantum physics,” Phys. Rev. A 60, 861 (1999).
A. Bohm, I. Antoniou, and P. Kielanowski, “The preparation-registration arrow of time in quantum mechanics,” Phys. Lett. A 189, 442 (1994).
T.C. Weinacht, J. Ahn, and P. H. Buchsbaum, “Measurement of amplitude and phase of a sculpted Rydberg wave packet,” Phys. Rev. Lett. 80, 5508 (1998).
I. S. Averbukh, M. Shapiro, C. Leichtle, and W. P. Schleich, “Reconstruction of wave packets by quantum state holography,” Phys. Rev. A 59, 2163 (1999).
A. Zucchetti, W. Vogel, D.-G. Welsch, and I. A. Walmsley, “Heterodyne measurement of vibrational wave packets of diatomic molecules,” Phys. Rev. A 60, 2716 (1999). [This reference has come to our attention after completing our research. Eq. (73) in it is equivalent to our Eq. (9).]
M. Kaku, Quantum Field Theory (University Press, Oxford, 1993).
J. Schwinger, “The theory of quantized fields. I and II,” Phys. Rev. 82, 914 (1951); 91, 713 (1953).
S. Weinberg, The Quantum Theory of Fields, Vol. 1 (University Press, Cambridge, 1995).
H. Feshbach, K. Kerman, and R.H. Lemmer, “Intermediate structure and doorway states in nuclear reactions,” Ann. Phys. (NY) 41, 230 (1967).
J. Jortner and S. Mukamel, “Radiationless transitions,” Intern. Rev. Sci. Theoret. Chem., Phys. Chem. (A. D. Buckingham and C.A. Coulson, eds.), Ser. 2, Vol.1 (1975, Butterworth, London), p. 327.
R. Englman, Non-Radiative Decay of Ions and Molecules in Solids (North-Holland, Amsterdam, 1979), p. 155.
W. Rhodes, “The nature of molecular excited states produced by weak light sources,” Chem. Phys. Lett. 11, 179 (1971).
A. Nitzan and J. Jortner, “Preparation of molecular states by optical excitation,” Chem. Phys. Lett. 14, 177 (1972).
I. Sh. Averbukh and N. F. Perel'man, “The dynamics of wave packets of highly excited states of atoms and molecules,” Sov. Phys. Usp. 34, 572 (1991). [Usp. Fiz. Nauk. 161, 41 (1991)].
K. F. Freed, “Irreversible electronic relaxation in polyatomic molecules,” J. Chem. Phys. 52, 1345 (1970).
R. Loudon, Quantum Theory of Light (University Press, Oxford, 1983).
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (University Press, Cambridge, 1995) Sec. 3.1.
R. Englman and A. Yahalom, “Reciprocity between moduli and phases in time-dependent wave-functions,” Phys. Rev. A 60, 1890 (1999).
P. Brumer and M. Shapiro, “Control of unimolecular reactions using coherent light,” Chem. Phys. Lett. 126, 541 (1986); “Laser control of molecular processes,” Ann. Rev. Phys. Chem. 43, 257 (1992).
M. Shapiro, “A uniform theory of preparation, dissociation and product formation in the decay of overlapping resonances,” J. Phys. Chem. A 102, 9570 (1998).
S. Husimi, “Miscellenea in elementary quantum mechanics,” Prog. Theor. Phys. 9, 381 (1953).
E.J. Heller, “Time-dependent approach to semiclassical dynamics,” J. Chem. Phys. 62, 1544 (1975); “Frozen Gaussians: a very simple semiclassical approximation,” ibid. 75, 2923 (1981).
G. Herzberg, Molecular spectra and molecular structure, Vol. 1 (Van Nostrand, Princeton, 1950).
P. W. Anderson, “Brainwashed by Feynman?,” Physics Today 53, 11 (Feb. 2000). “The essential step in a derivation of Feynman diagrams, or in fact of any other form of diagrammatic perturbation theory, is to imagine turning on the interactions gradually and to assume that nothing discontinuous happens as we do. But bound states don't form continuously. Therefore there are usually serious difficulties in perturbative treatments of scattering when bound states are present.” (Quote from p. 11.)
L. A. Khalfin, “Contribution to the decay theory of a quasi stationary state,” Soviet Physics JETP 6, 1053 (1958) [J. Exp. Teor. Fyz. (USSR) 33, 1371 (1957)].”... “we could use an experiment with the formation of an artificial, short lived isotope, fixing the initial moment of time t = 0 by having a' pulse' of particles bombard a stable nucleus, a product of which is an artificial short lived isotope. In this same experiment, we could observe the departure of the decay law from the exponential.” The formula (4.15) of Khalfin for the phase N (t) can also be used in the suggested experiment to determine the phases (including their sign!) of the decay products under suitable conditions. (Quote from p. 1063.)
T. D. Lee, “A theory of spontaneous T violation,” Phys. Rev. D 8, 1226 (1973); “CP non-conservation and a spontaneous symmetry breaking,” Phys. Rep. 9, 143 (1974).
D. Kharzeev, R. D. Pisarski, and M. H. G. Tytgat, “Possibility of spontaneous parity violation in hot QCD,” Phys. Rev Lett. 81, 512 (1998); “More on the history of P, CP, T violation in strong interactions,” Phys. Today 53, 76 (Feb. 2000).
G. Lubkin, “Going for the gold: first collisions at RHIC are set for December,” Phys. Today 52, 20 (Oct. 1999): “In QCD [the authors of [31]] don't understand why there is both P and C conservation. The ground state of [their] theory is a vacuum, which would have P and CP is even. But close to the transition, a metastable state could be produced that would be odd under both P and CP. Once you excited such states, you could observe parity odd correlations of the product particles. At least one of the RHIC detector groups, STAR, will search for P and T violations.” (Quote from p. 23.)
Y. Aharonov, P. G. Bergmann, and J. L. Leibowitz, “Time asymmetry in the quantum process of measurement,” Phys. Rev. B 134, 1410 (1964).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Engelman, R., Yahalom, A. “TIME ARROW” IN WAVE-PACKET EVOLUTION. Found Phys Lett 13, 329–343 (2000). https://doi.org/10.1023/A:1007867410417
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1007867410417