## Perturbation analysis of Raman echo

JOSA B, Vol. 15, Issue 6, pp. 1780-1790 (1998)

http://dx.doi.org/10.1364/JOSAB.15.001780

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### Abstract

A time-dependent perturbational approach is used to study the Raman echo generated by an inhomogeneous ensemble of three-level atomic systems in the Λ configuration. The sixth-order perturbative solution for coherence between the two lower states contains eight echo terms that are visualized with double Feynman diagrams. The echo is interpreted as a response of the ensemble to six short single-frequency optical pulses whose timing satisfies a special condition. Nonperturbative numerical simulation confirms the predictions of the perturbation analysis about the main characteristics of the echo. When the excitation pulses vary adiabatically with respect to fast optical coherence decay the echo amplitude depends on interference of the eight terms. A computational scheme developed for the higher-order perturbative analysis is also discussed.

© 1998 Optical Society of America

**OCIS Codes**

(190.5650) Nonlinear optics : Raman effect

(300.6240) Spectroscopy : Spectroscopy, coherent transient

(300.6450) Spectroscopy : Spectroscopy, Raman

**Citation**

Heiki Sõnajalg and Myung K. Kim, "Perturbation analysis of Raman echo," J. Opt. Soc. Am. B **15**, 1780-1790 (1998)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-15-6-1780

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### References

- S. R. Hartmann, “Photon, spin, and Raman echoes,” IEEE J. Quantum Electron. 4, 802–807 (1968).
- P. Hu, S. Geschwind, and T. M. Jedju, “Spin-flip Raman echo in n-type CdS,” Phys. Rev. Lett. 37, 1357–1360 (1976).
- K. P. Leung, T. W. Mossberg, and S. R. Hartmann, “Observation and density dependence of the Raman echo in atomic thallium vapor,” Opt. Commun. 43, 145–150 (1982).
- M. Tanigawa, Y. Fukuda, T. Kohmoto, K. Sakuno, and T. Hashi, “Sublevel echoes selectively excited by light-pulse trains: synchronized-quantum-beat echoes,” Opt. Lett. 8, 620–622 (1983).
- T. Mishina, M. Tanigawa, Y. Fukuda, and T. Hashi, “Synchronized quantum beat echoes in Cs vapor with diode lasers,” Opt. Commun. 62, 166–170 (1987).
- S. Burschka and J. Mlynek, “Optically induced spin transients in the ground state of atomic sodium,” Opt. Commun. 66, 59–64 (1988).
- M. Rosatzin, D. Suter, and J. Mlynek, “Light-shift-induced spin echoes in a J=1/2 atomic ground state,” Phys. Rev. A 42, 1839–1841 (1990).
- P. R. Hemmer, K. Z. Cheng, J. Kierstead, M. S. Shahriar, and M. K. Kim, “Time-domain optical data storage by use of Raman coherent population trapping,” Opt. Lett. 19, 296–298 (1994).
- B. S. Ham, M. S. Shahriar, M. K. Kim, and P. R. Hemmer, “Frequency-selective time-domain optical data storage by electromagnetically induced transparency in a rare-earth-doped solid,” Opt. Lett. 22, 1849–1851 (1997).
- E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
- I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
- T. W. Mossberg, R. Kachru, S. R. Hartmann, and A. M. Flusberg, “Echoes in gaseous media: a generalized theory of rephasing phenomena,” Phys. Rev. A 20, 1976–1996 (1979).
- T. W. Mossberg and S. R. Hartmann, “Diagrammatic representation of photon echoes and other laser-induced ordering processes in gases,” Phys. Rev. A 23, 1271–1280 (1981).
- R. P. Feynman, F. L. Vernon, Jr., and R. W. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. Appl. Phys. 28, 49–52 (1957).
- M. Takatsuji, “Theory of coherent two-photon resonance,” Phys. Rev. A 11, 619–624 (1975).
- D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixing and pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
- S. Aoki, “Double-quantum photon echo in an adiabatic-vector-model approximation,” Phys. Rev. A 14, 2258–2263 (1976).
- H. R. Gray, R. M. Whitley, and C. R. Stroud, Jr., “Coherent trapping of atomic populations,” Opt. Lett. 3, 218–220 (1978).
- M. S. Shahriar and P. R. Hemmer, “Direct excitation of microwave-spin dressed states using a laser-excited resonance Raman interaction,” Phys. Rev. Lett. 65, 1865–1868 (1990).
- M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55, 2272–2282 (1997).
- P. R. Hemmer and M. G. Prentiss, “Coupled-pendulum model of the stimulated resonance Raman effect,” J. Opt. Soc. Am. B 5, 1613–1623 (1988).
- A. Yariv, “The application of time evolution operators and Feynman diagrams to nonlinear optics,” IEEE J. Quantum Electron. 13, 943–950 (1977).
- T. K. Yee and T. K. Gustafson, “Diagrammatic analysis of the density operator for nonlinear calculations: pulsed and cw responses,” Phys. Rev. A 18, 1597–1617 (1978).
- A. Yariv, Quantum Electronics (Wiley, New York, 1989), Chaps. 3 and 16.
- Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984), Chaps. 2 and 21.
- M. Mitsunaga and R. G. Brewer, “Generalized perturbation theory of coherent optical emission,” Phys. Rev. A 32, 1605–1613 (1985).
- P. R. Hemmer, M. S. Shahriar, B. S. Ham, M. K. Kim, and Yu. Rozhdestvensky, “Optical spectral holeburning with Raman coherent population trapping,” Mol. Cryst. Liq. Cryst. 291, 287–294 (1996).

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