Dressed Coherent States of the Anharmonic Oscillator

D. Enzer; G. Gabrielse

doi:10.1103/PhysRevLett.78.1211

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Dressed Coherent States of the Anharmonic Oscillator

D. Enzer and G. Gabrielse

Department of Physics, Harvard University, Cambridge, Massachusetts 02138

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Phys. Rev. Lett. 78, 1211 – Published 17 February, 1997

DOI: https://doi.org/10.1103/PhysRevLett.78.1211

Abstract

Driving a damped, anharmonic oscillator produces stable, steady-state excitations according to the familiar classical description. A quantum mechanical description, however, shows the surprising result that such excitations are intrinsically unstable, and can be much smaller than classical expectations. We illustrate by calculating the motion of one electron in a magnetic field. This physically realizable system is among the simplest of nonlinear systems, being anharmonic because of special relativity and being damped by the spontaneous emission of synchrotron radiation.

References (18)

G. Milburn and C. Holmes, Phys. Rev. Lett. 56, 2237 (1986).
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L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon Press, New York, 1976), 3rd ed.
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G. Gabrielse, H. Dehmelt, and W. Kells, Phys. Rev. Lett. 54, 537 (1985).
G. Gabrielse and H. Dehmelt, Phys. Rev. Lett. 55, 67 (1985).
R. J. Glauber, in Quantum Optics and Electronics, Les Houches 1964, C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.
G. J. Milburn, Phys. Rev. A 33, 674 (1986).
D. Enzer, Ph.D. thesis, Harvard University, 1996.
M. Mallalieu and C. R. Stroud, Jr., Phys. Rev. A 49, 2329 (1994).
H. Dehmelt, F. Palmer, and R. Mittleman, Proc. Natl. Acad. Sci. U.S.A. 89, 5203 (1992).
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D. Enzer and G. Gabrielse (to be published).
S. Peil and G. Gabrielse (unpublished).

[c1] G. Milburn and C. Holmes, Phys. Rev. Lett. 56, 2237 (1986).

[c2] D. Daniel and G. Milburn, Phys. Rev. A 39, 4628 (1989).

[c3] V. Perinova and A. Luks, Phys. Rev. A 41, 414 (1990).

[c4] L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon Press, New York, 1976), 3rd ed.

[c5] P. D. Drummond and D. F. Walls, J. Phys. A 13, 725 (1980).

[c6] R. J. Glauber, Phys. Rev. 131, 2766 (1963).

[c7] W. Louisell, Quantum Statistical Properties of Radiation (John Wiley and Sons, New York, 1973).

[c8] C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (John Wiley and Sons, New York, 1992).

[c9] G. Gabrielse, H. Dehmelt, and W. Kells, Phys. Rev. Lett. 54, 537 (1985).

[c10] G. Gabrielse and H. Dehmelt, Phys. Rev. Lett. 55, 67 (1985).

[c11] R. J. Glauber, in Quantum Optics and Electronics, Les Houches 1964, C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.

[c12] G. J. Milburn, Phys. Rev. A 33, 674 (1986).

[c13] D. Enzer, Ph.D. thesis, Harvard University, 1996.

[c14] M. Mallalieu and C. R. Stroud, Jr., Phys. Rev. A 49, 2329 (1994).

[c15] H. Dehmelt, F. Palmer, and R. Mittleman, Proc. Natl. Acad. Sci. U.S.A. 89, 5203 (1992).

[c16] C. Tseng and G. Gabrielse, Appl. Phys. B 60, 95 (1995).

[c17] D. Enzer and G. Gabrielse (to be published).

[c18] S. Peil and G. Gabrielse (unpublished).

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Dressed Coherent States of the Anharmonic Oscillator

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