Abstract

This paper describes a novel atom-cavity interaction induced by periodically poled atom-cavity coupling constant which leads to multiple narrow photoemission bands for an initially inverted two-level atom under the strong coupling condition. The emission bandpass narrowing has a close analogy with the folded Šolc filter in the context of quasi-phase matching by periodic poling. We present a closed form solution of the emission probability at the end of interaction and deduce the multiple phase matching condition for this system which is programmable by the interaction time. The Bloch sphere analysis provides a clear understanding of the underlying atomic dynamics associated with the multiple resonances in the semiclassical limit. Furthermore, we show that this interaction can be applied to generation of nonclassical fields with sub-Poisson photon statistics.

© 2009 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  2. P. A. Franken, and J. F. Ward, "Optical harmonics and nonlinear phenomena," Rev. Mod. Phys. 35, 23-39 (1963).
    [CrossRef]
  3. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
    [CrossRef]
  4. M. Houé and P. D. Townsend, "An introduction to methods of periodic poling for second-harmonic generation," J. Phys. D 28, 1747-1763 (1995).
    [CrossRef]
  5. I. Šolc, "Birefringent chain filters," J. Opt. Soc. Am. 55, 621-625 (1965).
    [CrossRef]
  6. P. Yeh, "Electromagnetic propagation in birefringent layered media," J. Opt. Soc. Am. 69, 742-756 (1979).
    [CrossRef]
  7. D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
    [CrossRef] [PubMed]
  8. K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
    [CrossRef] [PubMed]
  9. G. Rempe, F. Schmidt-Kaler, and H. Walther, "Observation of sub-Poissonian photon statistics in a micromaser," Phys. Rev. Lett. 64, 2783-2786 (1990).
    [CrossRef] [PubMed]
  10. W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
    [CrossRef] [PubMed]
  11. P. Yeh, A. Yariv and, C.-S. Hong, "Electromagnetic propagation in periodic stratified media. I. General theory," J. Opt. Soc. Am. 67, 423-437 (1977).
    [CrossRef]
  12. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic Press, San Diego, 1995).
  13. R. P. Feynman, F. L. Vernon, Jr. and R. W. Helwarth, "Geometric representation of the Schrödinger equation for solving maser equations," J. Appl. Phys. 28, 49-52 (1957).
    [CrossRef]
  14. H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
    [CrossRef]
  15. R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
    [CrossRef] [PubMed]
  16. J. H. Eberly and V. D. Popov, "Phase-dependent pump-probe line-shape formulas," Phys. Rev. A 37, 2012-2016 (1988).
    [CrossRef] [PubMed]
  17. T. W. Mossberg and M. Lewenstein, "Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field," Phys. Rev. A 39, 163-170 (1989).
    [CrossRef] [PubMed]

2009 (1)

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

2006 (1)

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

1995 (1)

M. Houé and P. D. Townsend, "An introduction to methods of periodic poling for second-harmonic generation," J. Phys. D 28, 1747-1763 (1995).
[CrossRef]

1994 (1)

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

1990 (1)

G. Rempe, F. Schmidt-Kaler, and H. Walther, "Observation of sub-Poissonian photon statistics in a micromaser," Phys. Rev. Lett. 64, 2783-2786 (1990).
[CrossRef] [PubMed]

1989 (1)

T. W. Mossberg and M. Lewenstein, "Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field," Phys. Rev. A 39, 163-170 (1989).
[CrossRef] [PubMed]

1988 (1)

J. H. Eberly and V. D. Popov, "Phase-dependent pump-probe line-shape formulas," Phys. Rev. A 37, 2012-2016 (1988).
[CrossRef] [PubMed]

1985 (2)

R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
[CrossRef] [PubMed]

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

1979 (1)

1977 (1)

1965 (1)

1963 (1)

P. A. Franken, and J. F. Ward, "Optical harmonics and nonlinear phenomena," Rev. Mod. Phys. 35, 23-39 (1963).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

1957 (1)

R. P. Feynman, F. L. Vernon, Jr. and R. W. Helwarth, "Geometric representation of the Schrödinger equation for solving maser equations," J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

An, K.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Borghs, G.

R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
[CrossRef] [PubMed]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Childs, J. J.

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Choi, W.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

Dasari, R. R.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

De Bisschop, P.

R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
[CrossRef] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Eberly, J. H.

J. H. Eberly and V. D. Popov, "Phase-dependent pump-probe line-shape formulas," Phys. Rev. A 37, 2012-2016 (1988).
[CrossRef] [PubMed]

Fang-Yen, C.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Feld, M. S.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

Feynman, R. P.

R. P. Feynman, F. L. Vernon, Jr. and R. W. Helwarth, "Geometric representation of the Schrödinger equation for solving maser equations," J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

Franken, P. A.

P. A. Franken, and J. F. Ward, "Optical harmonics and nonlinear phenomena," Rev. Mod. Phys. 35, 23-39 (1963).
[CrossRef]

Helwarth, R. W.

R. P. Feynman, F. L. Vernon, Jr. and R. W. Helwarth, "Geometric representation of the Schrödinger equation for solving maser equations," J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

Hong, C.-S.

Hong, H.-G.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

Houé, M.

M. Houé and P. D. Townsend, "An introduction to methods of periodic poling for second-harmonic generation," J. Phys. D 28, 1747-1763 (1995).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Lee, J.-H.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

Lee, M.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

Lewenstein, M.

T. W. Mossberg and M. Lewenstein, "Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field," Phys. Rev. A 39, 163-170 (1989).
[CrossRef] [PubMed]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Meschede, D.

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

Mossberg, T. W.

T. W. Mossberg and M. Lewenstein, "Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field," Phys. Rev. A 39, 163-170 (1989).
[CrossRef] [PubMed]

Müller, G.

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Popov, V. D.

J. H. Eberly and V. D. Popov, "Phase-dependent pump-probe line-shape formulas," Phys. Rev. A 37, 2012-2016 (1988).
[CrossRef] [PubMed]

Rempe, G.

G. Rempe, F. Schmidt-Kaler, and H. Walther, "Observation of sub-Poissonian photon statistics in a micromaser," Phys. Rev. Lett. 64, 2783-2786 (1990).
[CrossRef] [PubMed]

Schmidt-Kaler, F.

G. Rempe, F. Schmidt-Kaler, and H. Walther, "Observation of sub-Poissonian photon statistics in a micromaser," Phys. Rev. Lett. 64, 2783-2786 (1990).
[CrossRef] [PubMed]

Seo, W.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

Silverans, R. E.

R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
[CrossRef] [PubMed]

Šolc, I.

Song, Y.

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

Townsend, P. D.

M. Houé and P. D. Townsend, "An introduction to methods of periodic poling for second-harmonic generation," J. Phys. D 28, 1747-1763 (1995).
[CrossRef]

Van Hove, M.

R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
[CrossRef] [PubMed]

Vernon, F. L.

R. P. Feynman, F. L. Vernon, Jr. and R. W. Helwarth, "Geometric representation of the Schrödinger equation for solving maser equations," J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

Walther, H.

G. Rempe, F. Schmidt-Kaler, and H. Walther, "Observation of sub-Poissonian photon statistics in a micromaser," Phys. Rev. Lett. 64, 2783-2786 (1990).
[CrossRef] [PubMed]

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

Ward, J. F.

P. A. Franken, and J. F. Ward, "Optical harmonics and nonlinear phenomena," Rev. Mod. Phys. 35, 23-39 (1963).
[CrossRef]

Yariv, A.

Yeh, P.

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation: tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

J. Appl. Phys. (1)

R. P. Feynman, F. L. Vernon, Jr. and R. W. Helwarth, "Geometric representation of the Schrödinger equation for solving maser equations," J. Appl. Phys. 28, 49-52 (1957).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Phys. D (1)

M. Houé and P. D. Townsend, "An introduction to methods of periodic poling for second-harmonic generation," J. Phys. D 28, 1747-1763 (1995).
[CrossRef]

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Phys. Rev. A (3)

H.-G. Hong, W. Seo, M. Lee, Y. Song, W. Choi, C. Fang-Yen, R. R. Dasari, M. S. Feld, J.-H. Lee, and K. An, "Effects of coupled bichromatic atom-cavity interaction in the cavity-QED microlaser," Phys. Rev. A 79, 033816 (2009).
[CrossRef]

J. H. Eberly and V. D. Popov, "Phase-dependent pump-probe line-shape formulas," Phys. Rev. A 37, 2012-2016 (1988).
[CrossRef] [PubMed]

T. W. Mossberg and M. Lewenstein, "Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field," Phys. Rev. A 39, 163-170 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

R. E. Silverans, G. Borghs, P. De Bisschop, and M. Van Hove, "Phase effects in bichromatic field interactions with a two-level atom," Phys. Rev. Lett. 55, 1070-1073 (1985).
[CrossRef] [PubMed]

D. Meschede, H. Walther, and G. Müller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985).
[CrossRef] [PubMed]

K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: a laser with one atom in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994).
[CrossRef] [PubMed]

G. Rempe, F. Schmidt-Kaler, and H. Walther, "Observation of sub-Poissonian photon statistics in a micromaser," Phys. Rev. Lett. 64, 2783-2786 (1990).
[CrossRef] [PubMed]

W. Choi, J.-H. Lee, K. An, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Observation of sub-Poisson photon statistics in the cavity-QED microlaser," Phys. Rev. Lett. 96, 093603 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

P. A. Franken, and J. F. Ward, "Optical harmonics and nonlinear phenomena," Rev. Mod. Phys. 35, 23-39 (1963).
[CrossRef]

Other (1)

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic Press, San Diego, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

Periodically poled atom-cavity coupling constant shown as a function of time.

Fig. 2.
Fig. 2.

Density plot of emission probability in δ -η plane. From (a) to (h) N increases from 1 to 8. The dashed lines (called branch lines) indicate the maximum visibility of Rabi oscillation and designated by the index p in the text. We can also recognize the semicircular patterns (called branch circles), which are designated by q. Quasi-phase matching is accomplished at the intersections of the branch lines and the branch circles.

Fig. 3.
Fig. 3.

(a) Emission probability near ϕ=π (q=1) semicircular branch for N=5. The red crosses indicate the points for the complete emission of a photon. The corresponding trajectories of the Bloch vector are shown for (b) p=3, (c) p=2 and (d) p=1. The red curves represent the evolution under +g0 while the blue curves are under -g0 as in the same color convention of Fig. 1.

Fig. 4.
Fig. 4.

Evolution of the Bloch vector in x-z plane assuming ϕ=π. The filled circles are the location of the Bloch vector after each τ and Ω ± are torque vectors associated with ±g0, respectively.

Fig. 5.
Fig. 5.

(a) For given phase matching order p=1 (or θ=π/2N), the passband of the atomic Šolc filter, our atom-cavity system, is shown as a function of ϕ(η,δ). (b) For given number of poling N=8, the passband for different phase matching order p are shown.

Fig. 6.
Fig. 6.

Mandel Q factor for η0=0.24 and D cav=0.0038 as N is varied from 1 (a) to 8 (h). Only the negative part is shown for simplicity.

Fig. 7.
Fig. 7.

The same as Fig. 6 except that the interaction time is averaged over a Gaussian velocity distribution with a full width at half maximum to be 20% of its most probable velocity.

Tables (1)

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Table 1. Emission probabilities after the entire interaction time Nτ.

Equations (39)

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HI(m)=h̅ n g (σ+eiΔt+σeiΔt) ,
g(t)=(1)m+1 g0 for (m1) τ<t<mτ ,
c˙e(t)=ing(t)eiΔtcg (t) ,
c˙g(t)=ing(t)eiΔtce (t) ,
[ce(m)cg(m)]=U(m) [ce(m1)cg(m1)] ,
(U(m))11=(cosϕ2iδϕsinϕ2)eiδ2=(U(m))22*
(U(m))12=(1)miηϕsinϕ2ei(m12)δ=(U(m))21*
T(k)=U(2k) U(2k1)
(T(k))11=(12δ2ϕ2sin2ϕ2iδϕsinϕ)eiδ=(T(k))22*
(T(k))12=2ηδϕ2sin2ϕ2eiδe2ikδ=(T(k))21* .
[ce(N)cg(N)]=k=1N2T(k)[ce(0)cg(0)]
[ce(N)cg(N)]=U(N) k=1(N1)2T(k) [ce(0)cg(0)] .
𝒯11=12δ2ϕ2sin2ϕ2iδϕsinϕ=𝒯22*
𝒯12 = 2 ηδϕ2 sin2 ϕ2 = 𝒯21* .
[ABCD]N = [Asinsin(N1)ξsinξBsinNξsinξCsinNξsinξDsinNξsin(N1)sinξ]
[ce(0)cg(0)]=[10]
[cg(N)]2 = [(𝓣k)21]2
= 4η2δ2ϕ4 (sinkξsinξ)2 sin4 ϕ2
cg(N)2=(U(N)j=1kT(j))212
= η2ϕ2 sin2 ϕ2 [(14δ2ϕsin2ϕ2)sinkξsinξsin(k1)ξsinξ]2 ,
cosξ=12δ2ϕ2sin2ϕ2.
sinkξsinξ=[(k1)cosk1ξ(k3)cosk3ξsin2ξ+(k5)cosk5ξsin4ξ+]
R.=R×Ω
[cosθ(1)m+1sinθ(1)msinθcosθ][1001][cosθ(1)msinθ(1)m+1sinθcosθ]
= [cos2θ(1)m+1sin2θ(1)m+1sin2θcos2θ]
[cos4θsin4θsin4θcos4θ]
[cos2Nθsin2Nθsin2Nθcos2Nθ] .
[cos2Nθsin2Nθsin2Nθcos2Nθ] .
[01] [(1)N+1sin2Nθcos2Nθ] .
θ=(p12N)π,
δoptπ=± (2q1)cos[(p12N)π],
{θ=tan1(ηδ)ϕ=η2+δ2
Q PemnDcavPemn
g(t)=l=𝒢(l)ei2πlt
𝒢(l) = 1 g (t)ei2πltdt.
ce,g(t)=l=𝒞e,g(l)ei2πlt.
𝒞e,g(l)=Nη2πlk=̅𝒢(lk±s)2g0𝒞g,e(k),
T(k)=[aebei(2k1)θb*ei(2k1)θa*e]
k=1NT(k)=[f(a,b)eiNθg(a,b)eiNθg*(a,b)eiNθf*(a,b)eiNθ]

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