Abstract

Resonant nonlinear-optical interference processes in four-level Doppler-broadened media are studied. Specific features of amplification and optical switching of short-wavelength radiation in a strongly-absorbing resonant gas under coherent quantum control with two longer wavelength radiations, are investigated. The major outcomes are illustrated with virtual experiments aimed at inversionless short-wavelength amplification, which also address deficiencies in this regard in recent experiments. With numerical simulations related to the proposed experiment in optically-dense sodium dimer vapor, we show optimal condition for optical switching and the expected gain of the probe radiation, which is above the oscillation threshold.

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References

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  1. [ � ] Thomas F. George, piano, Michael Kaupa, trumpet/fl�gelhorn, "Close Your Eyes" � 1995 Hester Park, http://www.uwsp.edu/admin/chancellor/tgeorge/CDreview.htm
  2. O. Kocharovskaya and P.Mandel, "Basic models of lasing without inversion: General form of amplification condition and problem of self-consistency," ibid., 217-230.
  3. B. G. Levi, "Some benefits of quantum interference become transparent," Physics Today 45, 17-19 (Ma 1992).
    [CrossRef]
  4. P. Mandel, "Lasing without inversion: a useful concept?" Contemp. Phys. 34, 235-246 (1993).
  5. M. O. Scully and M. Fleischhauer, "Laser without inversion," Science 263, 337-338 (1994).
    [CrossRef]
  6. A. K. Popov and S. G. Rautian, "Atomic coherence and interference phenomena in resonant nonlinear optical interactions" (invited paper), in Coherent Phenomena and Amplification without Inversion, A.V. Andreev, O. Kocharovskaya and P. Mandel, eds., Proc. SPIE 2798, 49-61 (1996), http://xxx.lanl.gov/abs/quant-ph/0005114.
    [CrossRef]
  7. A. K. Popov, "Inversionless amplification and laser-induced transparency at discrete transitions and the transitions to continuum" (review), Bull. Russ. Acad. Sci., Phys. 60, 927-945 (1996), http://xxx.lanl.gov/abs/quant-ph/0005108.
    [CrossRef] [PubMed]
  8. S. E. Harris, "Electromagnetically induced transparency," Physics Today 50, 36-42 (Jul 1997).
  9. A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient gas-phase generation of coherent vacuum ultraviolet radiation," Opt. Lett. 24, 625-627 (1999).
  10. S. E. Harris and L. V. Hau, "Nonlinear optics in low light-levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
    [CrossRef]
  11. S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1999.
    [CrossRef]
  12. M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, "Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence," Phys. Rev. Lett. 82, 1847-1850 (1999).
    [CrossRef]
  13. U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, "Continuous parametric amplification in a resonantly driven double-P system," Opt. Commun. 166, 127-132 (1999).
    [CrossRef]
  14. A. K. Popov and S. A. Myslivets, "Resonant four-wave frequency mixing in Doppler-broadened transitions," Quantum Electron. 27 1004-1008 (1997), http://turpion.ioc.ac.ru/.
    [CrossRef]
  15. A. K. Popov, "Interference at quantum transitions: lasing without inversion and resonant four-wave mixing in strong fields at Doppler-broadened transitions," in Nonlinear Optics,Sergei G. Rautian, Igor M. Beterov and Natalia M. Rubtsova, eds., Proc. SPIE 3485, 252-263 (1998), http://xxx.lanl.gov/abs/quant-ph/0005118.
    [CrossRef]
  16. T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovskii, "Nonlinear interference effects in emission, absorption, and generation spectra," JETP 30, 466 (1970) [Translated from Zh. Eksp. Teor. Fiz. 57 850, (1969)], http://xxx.lanl.gov/abs/quant-ph/0005094.
    [CrossRef]
  17. T. Ya. Popova, A. K. Popov, "Effect of resonance radiative processes on the amplification factor," Zhurn.Prikl. Spektrosk., 12, No 6, 989, (1970) [Translated in Engl.: J. Appl. Spectr 12, No 6, 734, (1970), http://xxx.lanl.gov/abs/quant-ph/0005047.
  18. T. Ya. Popova, A. K. Popov, "Shape of the amplification line corresponding to an adjacent transition in a strong field," Izv.Vysh. Uchebn. Zaved., Fizika No 11, 38, (1970) [Translated in Engl.: Soviet Phys. Journ. 13, No 11, 1435, (1970)], http://xxx.lanl.gov/abs/quant-ph/0005049.
  19. A. K. Popov, Introduction in Nonlinear Spectroscopy, Nauka, Novosibirsk, 1983, 274p. (in Russ).
  20. I. M. Beterov, "Investigation on nonlinear resonant interaction of optical fields in three-level gas laser," Cand. Sci. Dissertation, Institute of Semiconductor Physics SD USSR AS, Novosibirsk, Dec. 1970.
  21. A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen and G.Tartakovsky, "Quantum interference and Manle -Rowe relations at resonant four-wave mixing in optically -thick Doppler-broadened Media," JETP Lett. 69, 912-16 (1999), http://ojps.aip.org/jetplo/.
  22. M.O. Scully, "Resolving conumdrums in lasing without inversion via exact solutions to simple models" Quantum Optics 6, 203-215 (1994).

Other (22)

[ � ] Thomas F. George, piano, Michael Kaupa, trumpet/fl�gelhorn, "Close Your Eyes" � 1995 Hester Park, http://www.uwsp.edu/admin/chancellor/tgeorge/CDreview.htm

O. Kocharovskaya and P.Mandel, "Basic models of lasing without inversion: General form of amplification condition and problem of self-consistency," ibid., 217-230.

B. G. Levi, "Some benefits of quantum interference become transparent," Physics Today 45, 17-19 (Ma 1992).
[CrossRef]

P. Mandel, "Lasing without inversion: a useful concept?" Contemp. Phys. 34, 235-246 (1993).

M. O. Scully and M. Fleischhauer, "Laser without inversion," Science 263, 337-338 (1994).
[CrossRef]

A. K. Popov and S. G. Rautian, "Atomic coherence and interference phenomena in resonant nonlinear optical interactions" (invited paper), in Coherent Phenomena and Amplification without Inversion, A.V. Andreev, O. Kocharovskaya and P. Mandel, eds., Proc. SPIE 2798, 49-61 (1996), http://xxx.lanl.gov/abs/quant-ph/0005114.
[CrossRef]

A. K. Popov, "Inversionless amplification and laser-induced transparency at discrete transitions and the transitions to continuum" (review), Bull. Russ. Acad. Sci., Phys. 60, 927-945 (1996), http://xxx.lanl.gov/abs/quant-ph/0005108.
[CrossRef] [PubMed]

S. E. Harris, "Electromagnetically induced transparency," Physics Today 50, 36-42 (Jul 1997).

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient gas-phase generation of coherent vacuum ultraviolet radiation," Opt. Lett. 24, 625-627 (1999).

S. E. Harris and L. V. Hau, "Nonlinear optics in low light-levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1999.
[CrossRef]

M. D. Lukin, A. V. Matsko, M. Fleischhauer, and M. O. Scully, "Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence," Phys. Rev. Lett. 82, 1847-1850 (1999).
[CrossRef]

U. Hinze, L. Meyer, B. N. Chichkov, E. Tiemann, and B. Wellegehausen, "Continuous parametric amplification in a resonantly driven double-P system," Opt. Commun. 166, 127-132 (1999).
[CrossRef]

A. K. Popov and S. A. Myslivets, "Resonant four-wave frequency mixing in Doppler-broadened transitions," Quantum Electron. 27 1004-1008 (1997), http://turpion.ioc.ac.ru/.
[CrossRef]

A. K. Popov, "Interference at quantum transitions: lasing without inversion and resonant four-wave mixing in strong fields at Doppler-broadened transitions," in Nonlinear Optics,Sergei G. Rautian, Igor M. Beterov and Natalia M. Rubtsova, eds., Proc. SPIE 3485, 252-263 (1998), http://xxx.lanl.gov/abs/quant-ph/0005118.
[CrossRef]

T. Ya. Popova, A. K. Popov, S. G. Rautian, and R. I. Sokolovskii, "Nonlinear interference effects in emission, absorption, and generation spectra," JETP 30, 466 (1970) [Translated from Zh. Eksp. Teor. Fiz. 57 850, (1969)], http://xxx.lanl.gov/abs/quant-ph/0005094.
[CrossRef]

T. Ya. Popova, A. K. Popov, "Effect of resonance radiative processes on the amplification factor," Zhurn.Prikl. Spektrosk., 12, No 6, 989, (1970) [Translated in Engl.: J. Appl. Spectr 12, No 6, 734, (1970), http://xxx.lanl.gov/abs/quant-ph/0005047.

T. Ya. Popova, A. K. Popov, "Shape of the amplification line corresponding to an adjacent transition in a strong field," Izv.Vysh. Uchebn. Zaved., Fizika No 11, 38, (1970) [Translated in Engl.: Soviet Phys. Journ. 13, No 11, 1435, (1970)], http://xxx.lanl.gov/abs/quant-ph/0005049.

A. K. Popov, Introduction in Nonlinear Spectroscopy, Nauka, Novosibirsk, 1983, 274p. (in Russ).

I. M. Beterov, "Investigation on nonlinear resonant interaction of optical fields in three-level gas laser," Cand. Sci. Dissertation, Institute of Semiconductor Physics SD USSR AS, Novosibirsk, Dec. 1970.

A. K. Popov, S. A. Myslivets, E. Tiemann, B. Wellegehausen and G.Tartakovsky, "Quantum interference and Manle -Rowe relations at resonant four-wave mixing in optically -thick Doppler-broadened Media," JETP Lett. 69, 912-16 (1999), http://ojps.aip.org/jetplo/.

M.O. Scully, "Resolving conumdrums in lasing without inversion via exact solutions to simple models" Quantum Optics 6, 203-215 (1994).

Supplementary Material (4)

» Media 1: MOV (2021 KB)     
» Media 2: MOV (2032 KB)     
» Media 3: MOV (1542 KB)     
» Media 4: MOV (1500 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Energy levels and coupled fields.

Fig. 2.
Fig. 2.

Intensity-dependent absorption index for the signal radiation, Stokes amplification index for the idle radiation and real and imaginary parts of the FWM cross coupling parameters vs signal frequency resonance detuning. The driving fields are set to the resonance. (a) and (b) — mov1a.mov (2.02MB, audio†) (G 3=20MHz, G 1 varies); (c) — mov1b.mov (2.03MB, audio†) (G 1=60 MHz, G 3 varies). The current magnitude of the variable Rabi frequency runs at the top of the screen. [Media 1]

Fig. 3.
Fig. 3.

Inversionless gain in optically thick Doppler-broadened medium. a and c — mov2b.mov (1.50MB, audio‡)(G 10=60MHz, G 30 varies); b — mov2a.mov (1.54MB, audio‡)(G 30=20 MHz, G 10 varies). The current magnitudes of the variable Rabi frequency are displayed at the top of the screen. [Media 4]

Fig. 4.
Fig. 4.

Optical switch.

Fig. 5.
Fig. 5.

Numerical simulation of the experiment [13] — (a) and (b), and of the proposed experiment towards inversionless gain — (c) and (d).

Equations (4)

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d E 4,2 ( z ) d z = i σ 4,2 E 4,2 + i σ ˜ 4,2 E 1 E 3 E 2,4 * ,
d E 1,3 ( z ) d z = i σ 1,3 E 1,3 + i σ ˜ 1,3 E 4 E 2 E 3,1 * .
I 4 I 40 = exp ( α 4 l 2 ) + ( γ 2 ( 2 β ) 2 ) [ exp ( g 2 L 2 ) exp ( α 4 L 2 ) ] 2 .
η 4 = I 4 I 20 = ( γ 4 2 2 β 2 ) exp ( g 2 L 2 ) exp ( α 4 L 2 ) 2 .

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