Abstract

We show that the giant Kerr nonlinearity in the regime of electromagnetically induced transparency in vapor can give rise to the formation of Thirring-type spatial solitons, which are supported solely by cross-phase modulation that couples the two copropagating light beams.

© 2005 Optical Society of America

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2005 (1)

I. Friedler, G. Kurizki, and D. Petrosyan, Phys. Rev. A 71, 023803 (2005).
[CrossRef]

2004 (1)

I. Friedler, G. Kurizki, and D. Petrosyan, Europhys. Lett. 68, 625 (2004).
[CrossRef]

2003 (3)

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

T. Hong, Phys. Rev. Lett. 90, 183901 (2003).
[CrossRef]

J. R. Salgueiro, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 28, 1457 (2003).
[CrossRef] [PubMed]

2002 (4)

M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65, 022314 (2002).
[CrossRef]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2031 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[CrossRef]

2001 (3)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, 041801(R) (2001).
[CrossRef]

2000 (3)

Z. Chen, M. Acks, E. Ostrovskaya, and Y. Kivshar, Opt. Lett. 25, 417 (2000).
[CrossRef]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

M. Lukin and A. Imamo?lu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

1999 (1)

S. Harris and L. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

1998 (2)

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

1997 (2)

1996 (1)

1993 (1)

1976 (1)

A. V. Mikhailov, JETP Lett. 23, 320 (1976).

1958 (1)

W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
[CrossRef]

Acks, M.

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Carmon, T.

Chen, Z.

Christodoulides, D. N.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Cohen, O.

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Dykstra, R.

Fleischer, J. W.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65, 022314 (2002).
[CrossRef]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

Friedler, I.

I. Friedler, G. Kurizki, and D. Petrosyan, Phys. Rev. A 71, 023803 (2005).
[CrossRef]

I. Friedler, G. Kurizki, and D. Petrosyan, Europhys. Lett. 68, 625 (2004).
[CrossRef]

Giordmaine, J. A.

Harris, S.

S. Harris and L. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Harris, S. E.

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Hau, L.

S. Harris and L. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Hong, T.

T. Hong, Phys. Rev. Lett. 90, 183901 (2003).
[CrossRef]

Imamoglu, A.

Kang, H.

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

Kurizki, G.

I. Friedler, G. Kurizki, and D. Petrosyan, Phys. Rev. A 71, 023803 (2005).
[CrossRef]

I. Friedler, G. Kurizki, and D. Petrosyan, Europhys. Lett. 68, 625 (2004).
[CrossRef]

Lan, S.

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Lukin, M.

M. Lukin and A. Imamo?lu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

Lukin, M. D.

M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65, 022314 (2002).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

Luther-Davies, B.

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Mikhailov, A. V.

A. V. Mikhailov, JETP Lett. 23, 320 (1976).

Mitchell, D. J.

Mitchell, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Odoulov, S.

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2031 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Ostrovskaya, E.

Petrosyan, D.

I. Friedler, G. Kurizki, and D. Petrosyan, Phys. Rev. A 71, 023803 (2005).
[CrossRef]

I. Friedler, G. Kurizki, and D. Petrosyan, Europhys. Lett. 68, 625 (2004).
[CrossRef]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Rickey, E. G.

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, 041801(R) (2001).
[CrossRef]

Salgueiro, J. R.

Schmidt, H.

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), Chap. 7.
[CrossRef]

Segev, M.

O. Cohen, S. Lan, T. Carmon, J. A. Giordmaine, and M. Segev, Opt. Lett. 27, 2013 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2031 (2002).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Seror, C.

Snyder, A. W.

Sukhorukov, A. A.

Thirring, W.

W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
[CrossRef]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

Vaupel, M.

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

Yan, M.

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, 041801(R) (2001).
[CrossRef]

Zhu, Y.

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, 041801(R) (2001).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), Chap. 7.
[CrossRef]

Ann. Phys. (N.Y.) (1)

W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
[CrossRef]

Europhys. Lett. (1)

I. Friedler, G. Kurizki, and D. Petrosyan, Europhys. Lett. 68, 625 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

A. V. Mikhailov, JETP Lett. 23, 320 (1976).

Nature (1)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Opt. Lett. (6)

Phys. Rev. A (3)

M. Fleischhauer and M. D. Lukin, Phys. Rev. A 65, 022314 (2002).
[CrossRef]

I. Friedler, G. Kurizki, and D. Petrosyan, Phys. Rev. A 71, 023803 (2005).
[CrossRef]

M. Yan, E. G. Rickey, and Y. Zhu, Phys. Rev. A 64, 041801(R) (2001).
[CrossRef]

Phys. Rev. Lett. (9)

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

S. Harris and L. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

H. Kang and Y. Zhu, Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

T. Hong, Phys. Rev. Lett. 90, 183901 (2003).
[CrossRef]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

M. Lukin and A. Imamo?lu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611 (1998).
[CrossRef]

Phys. Today (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Other (2)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), Chap. 7.
[CrossRef]

In the Thirring model dispersion and/or diffraction result only from linear coupling between two modes.

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Figures (3)

Fig. 1
Fig. 1

Atomic level scheme involving two species of atoms A and B, both subject to EIT conditions. The fields E 1 , E 2 interact via Kerr-nonlinear XPM. For the case in which E 1 , 2 are cw fields, atoms A and Ω d ( A ) can be ignored, as they are unnecessary.

Fig. 2
Fig. 2

Fundamental-mode Thirring-type solitons. (a)–(c) Soliton profiles for different ratios between the peak amplitudes. (d) Soliton existence curve: FWHM of each field versus the peak amplitude E 2 ( 0 ) at a fixed peak amplitude E 1 ( 0 ) = 1 . Points a–c correspond to the solitons of (a)–(c), respectively.

Fig. 3
Fig. 3

(a) Composite Thirring-type soliton solutions with beam E 1 in the fundamental (ground-state) mode and beam E 2 in the dipole (first asymmetric) mode. The amplitude ratio is 1 (equal intensities). (b) Same as (a) for amplitude ratio 2. (c) Propagation of the solution shown in (a): beam E 1 (upper) and beam E 2 (lower) without (left) the nonlinearity for one diffraction length and with (right) the nonlinearity for 10 diffraction lengths. During nonlinear propagation the composite entity splits into two fundamental Thirring-type solitons diverging away from one another. (d) Propagation of the solution shown in (b) in the presence of initial noise. Both components fuse into a single fundamental Thirring-type soliton.

Equations (4)

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2 i k 1 z E 1 + 2 E 1 = k 1 2 η E 2 2 E 1 ,
2 i k 2 z E 2 + 2 E 2 = k 2 2 η E 1 2 E 2 ,
2 E 1 + i ζ E 1 + σ E 2 2 E 1 = 0 ,
a 2 2 E 2 + i a ζ E 2 + σ E 1 2 E 2 = 0 ,

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