Abstract

We present an experimental study of the coherence properties of amplified slow light by four-wave mixing (FWM) in a three-level electromagnetically induced transparency (EIT) system driven by one additional pump field. High energy gain (up to 19) is obtained with a weak pump field (a few mW/cm2) using optically dense cold atomic gases. A large fraction of the amplified light is found to be phase incoherent to the input signal field. The dependence of the incoherent fraction on pump field intensity and detuning and the control field intensity is systematically studied. With the classical input pulses, our results support a recent theoretical study by Lauk et al. [Phys. Rev. A 88, 013823 (2013)], showing that the noise resulting from the atomic dipole fluctuations associated with spontaneous decay is significant in the high gain regime. This effect has to be taken into consideration in EIT-based applications in the presence of FWM.

© 2014 Optical Society of America

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2013

N. Lauk, C. O’Brien, and M. Fleischhauer, Phys. Rev. A 88, 013823 (2013).
[CrossRef]

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

2011

N. B. Philips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

2009

J. Okuma, N. Hayashi, A. Fujisawa, and M. Mitsunaga, Opt. Lett. 34, 1654 (2009).
[CrossRef]

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

N. B. Philips, A. V. Gorshkov, and I. Novikova, J. Mod. Opt. 56, 1916 (2009).
[CrossRef]

2008

2007

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

2005

R. S. Tucker, P.-C. Ku, and C. J. Chang-Hasnain, J. Lightwave Technol. 23, 4046 (2005).
[CrossRef]

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

2004

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

2000

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

1999

M. Y. Lanzerotti, R. W. Schirmer, A. L. Gaeta, and G. S. Agarwal, Phys. Rev. A, 60, 4980 (1999).
[CrossRef]

1998

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

1995

1987

1985

M. D. Reid and D. F. Walls, Phys. Rev. A, 31, 1622 (1985).
[CrossRef]

Agarwal, G. S.

M. Y. Lanzerotti, R. W. Schirmer, A. L. Gaeta, and G. S. Agarwal, Phys. Rev. A, 60, 4980 (1999).
[CrossRef]

Arimondo, E.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Balic, V.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

Boyer, V.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Braje, D. A.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

Chang-Hasnain, C. J.

Chen, Y.-C.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, Opt. Express 16, 3753 (2008).
[CrossRef]

Chen, Y.-F.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Chen, Y.-H.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Chou, H.-C.

Cronin-Golomb, M.

Donoghue, J.

Du, S.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Dwivedi, P. P.

Eilam, A.

Embrey, C. S.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

Fleischhauer, M.

N. Lauk, C. O’Brien, and M. Fleischhauer, Phys. Rev. A 88, 013823 (2013).
[CrossRef]

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

Friedmann, H.

Fujisawa, A.

Gaeta, A. L.

M. Y. Lanzerotti, R. W. Schirmer, A. L. Gaeta, and G. S. Agarwal, Phys. Rev. A, 60, 4980 (1999).
[CrossRef]

Goda, S.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

Gorshkov, A. V.

N. B. Philips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

N. B. Philips, A. V. Gorshkov, and I. Novikova, J. Mod. Opt. 56, 1916 (2009).
[CrossRef]

Harris, S. E.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

Hayashi, N.

Hemmer, P. R.

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Hemmer, R. P.

Howell, J. C.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

Hsai, Z.-H.

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Katz, D. P.

Ku, P.-C.

Kumar, P.

Lanzerotti, M. Y.

M. Y. Lanzerotti, R. W. Schirmer, A. L. Gaeta, and G. S. Agarwal, Phys. Rev. A, 60, 4980 (1999).
[CrossRef]

Lauk, N.

N. Lauk, C. O’Brien, and M. Fleischhauer, Phys. Rev. A 88, 013823 (2013).
[CrossRef]

Lee, M.-J.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Lett, P. D.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Lin, Y.-W.

Liu, Y.-C.

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Löffler, M.

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Lukin, M. D.

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

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Maeda, M. W.

Marino, A. M.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

McCormick, C. F.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Mitsunaga, M.

Novikova, I.

N. B. Philips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

N. B. Philips, A. V. Gorshkov, and I. Novikova, J. Mod. Opt. 56, 1916 (2009).
[CrossRef]

O’Brien, C.

N. Lauk, C. O’Brien, and M. Fleischhauer, Phys. Rev. A 88, 013823 (2013).
[CrossRef]

Okuma, J.

Petrov, P. G.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

Philips, N. B.

N. B. Philips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

N. B. Philips, A. V. Gorshkov, and I. Novikova, J. Mod. Opt. 56, 1916 (2009).
[CrossRef]

Reid, M. D.

M. D. Reid and D. F. Walls, Phys. Rev. A, 31, 1622 (1985).
[CrossRef]

Schirmer, R. W.

M. Y. Lanzerotti, R. W. Schirmer, A. L. Gaeta, and G. S. Agarwal, Phys. Rev. A, 60, 4980 (1999).
[CrossRef]

Scully, M. O.

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Shahrlar, M. S.

Shapiro, J. H.

Tucker, R. S.

Turnbull, M. T.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

Vudyasetu, P. K.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

Walls, D. F.

M. D. Reid and D. F. Walls, Phys. Rev. A, 31, 1622 (1985).
[CrossRef]

Wang, I.-C.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Wang, S.-H.

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Wilson-Gordon, A. D.

Yin, G. Y.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

Yu, I. A.

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, Opt. Express 16, 3753 (2008).
[CrossRef]

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

N. B. Philips, A. V. Gorshkov, and I. Novikova, J. Mod. Opt. 56, 1916 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. Y. Lanzerotti, R. W. Schirmer, A. L. Gaeta, and G. S. Agarwal, Phys. Rev. A, 60, 4980 (1999).
[CrossRef]

N. Lauk, C. O’Brien, and M. Fleischhauer, Phys. Rev. A 88, 013823 (2013).
[CrossRef]

Y.-F. Chen, Y.-C. Liu, Z.-H. Hsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

N. B. Philips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, and V. Boyer, Phys. Rev. A 88, 033845 (2013).
[CrossRef]

M. D. Reid and D. F. Walls, Phys. Rev. A, 31, 1622 (1985).
[CrossRef]

Phys. Rev. Lett.

M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef]

See supplementary material of Y.-H. Chen, M.-J. Lee, I.-C. Wang, S. Du, Y.-F. Chen, Y.-C. Chen, and I. A. Yu, Phys. Rev. Lett. 110, 083601 (2013).
[CrossRef]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Relevant energy levels for Cs133 atoms and laser excitations. (b) Schematic experimental setup. BS, beam splitter; M, mirror; L, lens; AOM, acousto-optic modulator; FC, fiber coupler; P, polarizer; λ/4, quarter waveplate; PMT, photomultiplier tube.

Fig. 2.
Fig. 2.

(a) Representative power data. The blue trace is the input signal pulse. The black trace is a slow light pulse without FWM. The green trace is the amplified signal pulse and is shifted vertically for clarity. The inset shows the idler pulse. (b) The corresponding beatnotes for the same conditions as in (a). The inset shows part of the beatnote of the amplified signal pulse around its peak. The parameters {D, Ω, γ, Ω, Δ/2π} are {102, 0.60Γ, 0.001Γ, 0.68Γ, 49 MHz}, respectively.

Fig. 3.
Fig. 3.

(a) Energy gain versus signal detuning. The parameters {D, Ω, γ, Ω, Δ/2π} are {95, 0.73Γ, 0.001Γ, 0.60Γ, 49 MHz}, respectively. (b) Energy gain versus turn-on time of the pump pulse. Time zero is the time when the signal peak enters the medium. The parameters {D, Ω, γ, Δ/2π} are {127, 0.85Γ, 0.001Γ, 49 MHz}, respectively. The red circles and blue squares indicate data with Ω of 1.08 and 0.76Γ, respectively.

Fig. 4.
Fig. 4.

(a), (c), and (e) Total energy gain (red circle) and the coherent part energy gain (blue square) of the signal pulse versus the pump power, pump detuning, and control power, respectively. (b), (d), and (f) The fraction of the incoherent part energy corresponding to the data in (a), (c), and (e). The parameters {D, Ω, γ, Δ/2π} for (a) and (b) are {153, 0.79Γ, 0.001Γ, 49 MHz}, respectively. Ω is 0.41Γ for a pump power of 0.5 mW. The parameters {D, Ω, γ, Ω} for (c) and (d) are {102, 0.60Γ, 0.001Γ, 0.68Γ}, respectively. The parameters {D, γ, Ω, Δ/2π} for (e) and (f) are {22, 0.001Γ, 0.71Γ, 49 MHz}, respectively. Ω is 0.55Γ for a control power of 0.16 mW.

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