Abstract

We report our observations on probe transmission, four-wave mixing (FWM), and fluorescence signals with dressing effect in two V-type three-level as well as in two two-level atomic systems. According to the phenomena observed in such systems, we find that the dressing effect at the same energy level can be affected by hyperfine structure and at different energy levels by transition dipole moment. We also find that both the x- and y-directional spatial splittings of probe beam and FWM signals are affected greatly by the dressing effect, which can also control the spatial shift and focusing of FWM signal. Studies on such controllable beam splitting can be very useful in understanding spatial pattern formation and applications of spatial signal processing.

© 2013 Optical Society of America

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2012

2010

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

2009

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

2008

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

2007

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef]

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[CrossRef]

2002

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

2001

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64, 013412 (2001).
[CrossRef]

1999

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A. 60, 3225–3228 (1999).
[CrossRef]

1998

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

B. Lu, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. 23, 804–806 (1998).
[CrossRef]

1997

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1995

1992

Agrawal, G. P.

Anderson, B.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Arimondo, E.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[CrossRef]

Boyd, R. W.

Boyer, V.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[CrossRef]

Brown, A. W.

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Burkett, W. H.

Chen, H. X.

Cronin-Golomb, M.

Denz, C.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Donoghue, J.

Du, S. W.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef]

Fleischhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A. 60, 3225–3228 (1999).
[CrossRef]

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Hemmer, P. R.

Jia, S. Q.

Katz, D. P.

Kauranen, M.

Khadka, U.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

Kocharovskaya, O.

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

Krolikowski, W.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Kumar, P.

Lett, P. D.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[CrossRef]

Li, C. B.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Li, N.

Li, P. Y.

Li, P. Z.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

Li, Y. H.

Lu, B.

Lu, K. Q.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Lukin, M. D.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A. 60, 3225–3228 (1999).
[CrossRef]

Luther-Davies, B.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Maki, J. J.

Marino, A. M.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

Matsko, A. B.

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

McCormick, C. F.

C. F. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[CrossRef]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[CrossRef]

Nie, Z. Q.

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

Rickey, E. G.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Rostovtsev, Y. V.

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

Rubin, M. H.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef]

Saffman, M.

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Scully, M. O.

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A. 60, 3225–3228 (1999).
[CrossRef]

Shahriar, M. S.

Song, J. P.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Stentz, A. J.

Wang, H.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

Wang, Z. G.

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Welch, G. R.

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

Wen, F.

Wen, J. M.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef]

Xiao, M.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

B. Lu, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. 23, 804–806 (1998).
[CrossRef]

Yan, M.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Yang, Y. M.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

Yelin, S. F.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A. 60, 3225–3228 (1999).
[CrossRef]

Yin, G. Y.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef]

Yuan, C. Z.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

Zhang, Y.

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

Zhang, Y. P.

N. Li, Z. Y. Zhao, H. X. Chen, P. Y. Li, Y. H. Li, Y. Zhao, G. Z. Zhou, S. Q. Jia, and Y. P. Zhang, “Observation of dressed odd-order multi-wave mixing in five-level atomic medium,” Opt. Express 20, 1912–1929 (2012).
[CrossRef]

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler–Townes splitting in high-order nonlinear processes,” Opt. Lett. 35, 3420–3422 (2010).
[CrossRef]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

Zhao, Y.

Zhao, Z. Y.

Zheng, H. B.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82, 053837 (2010).
[CrossRef]

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave-mixing processes,” Appl. Phys. Lett. 95, 041103 (2009).
[CrossRef]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A. 77, 063829 (2008).
[CrossRef]

Zhou, G. Z.

Zhu, Y. F.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Zibrov, A. S.

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef]

Appl. Phys. Lett.

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91, 061113 (2007).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

(a), (b) Two energy-level system diagram between |0 and |2 or between |0 and |1, corresponding to wavelengths of 589.0 and 589.6 nm, respectively. (c), (d) V-type energy-level system diagrams, one dye laser beams wavelength is 589.0 nm, the other is 589.6 nm. (e) The scheme of the experiment device. HR, high reflective mirror; BS, beam splitter (50%); L, convex lens (f=50mm); PMT, photomultiplier tube. (f) The spatial alignments of the incident beams.

Fig. 2.
Fig. 2.

(a), (c), (e) Measured evolution of the probe transmission, FWM signals and fluorescence signals versus Δ2 in two-level (|0|2) systems, for Δ1=139.98, 100.6, 74.6, 28.2, 0, 30.6, 78, 100.1, 141.43GHz, from (1) to (9), respectively. The dotted lines in (a) and (c) represents the shift trace of the characteristic regions in the spectrum. (b), (d), (f) Theoretical plots corresponds to (a), (c), and (e), respectively. (g) The dressed-state pictures of the DFWM signal. |G+ and |G: two dressed states caused by the field E2(E2).

Fig. 3.
Fig. 3.

(a), (b) Measured probe transmission and FWM signals versus Δ2 at Δ1=105.7GHz in two-level (|0|2) system when (1) no beam blocked, (2) E2 blocked, (3) E2 blocked, (4) E2 and E2 both blocked, and (5) E1 blocked, respectively. (c) Measured fluorescence signal versus Δ2 at Δ1=105.7GHz when (c1) no beam blocked, (c2) E3 blocked, (c3) E2 blocked, (c4) E2 blocked, (c5) E2 and E2 both blocked, (c6) E3, E2, and E2 all blocked, (c7) E1 blocked, (c8) E1 blocked, (c9) E1 and E2 both blocked, (c10) E1 and E1 both blocked, (c11) E3, E1, and E1 all blocked, (c12) E1, E1, E2, and E2 all blocked, (c13) E1, E1, E3, E2, and E2 all blocked. (d) The theoretical results corresponding to (c). (e), (f) are the experimental images corresponding to (a) and (b), respectively. (g) The calculated Kerr nonlinear refractive indices of E1, E1 (solid curves) and E2, E2 (dashed curves) versus Δ2. The condition is same as that of (a).

Fig. 4.
Fig. 4.

(a) Measured evolution of the probe transmission signals, (b) FWM signals, and (c) fluorescence signals versus Δ2 with (1) Δ1=81.43GHz, (2) Δ1=40.07GHz, (3) Δ1=19.24GHz, (4) Δ1=0, (5) Δ1=59.84GHz, (6) Δ1=80.68GHz, (7) Δ1=99.39GHz, (8) Δ1=100.29GHz, (9) Δ1=121.35GHz in two-level (|0|2) systems, respectively. (d), (e) Measured images of probe transmission and DFWM signals corresponding to (a) and (b), respectively. (f1)–(f7) The calculated Kerr nonlinear refractive indices of E1, E1 (solid curves) and E2, E2 (dashed curves) versus Δ2. The condition is same as that of (a). (f8) The calculated Kerr nonlinear refractive indices of E1 and E1 versus Δ1.

Fig. 5.
Fig. 5.

(a), (b) Measured evolution of the probe transmission and the FWM signals versus Δ2 at different Δ1 increased from Δ1=230GHz to Δ1=120GHz by a step size of 40 GHz from the left to right, respectively. (a1), (b1) the probe transmissions are obtained in two-level (|0|2) system. (a2), (b2) the FWM signals are obtained in two-level (|0|1) system. (c) The energy-level system diagrams, in which the COM in two-level is marked out as the horizontal dashed line and labeled as COM.

Fig. 6.
Fig. 6.

(a), (c), (e) Measured evolution of the probe transmission, the DFWM, and fluorescence signals versus Δ2 with (a1) Δ1=135.97GHz, (a2) Δ1=89.6GHz, (a3) Δ1=45.6GHz, (a4) Δ1=0, (a5) Δ1=30.6GHz, (a6) Δ1=68.2GHz, (a7) Δ1=95.4GHz, respectively, in V-type energy-level system as shown in Fig. 1(d). (b), (d), (f) The theoretical results corresponds to (a), (c), and (e). (g) The dressed-state pictures for the suppression and enhancement of the DFWM signal. |G+ and |G: two dressed states caused by the field E2(E2).

Fig. 7.
Fig. 7.

(a), (c), (e) Measured evolution of the probe transmission, the DFWM signals, and fluorescence signals versus Δ2 with (a1) Δ1=134.5GHz, (a2) Δ1=97.7GHz, (a3) Δ1=69.6GHz, (a4) Δ1=32.2GHz, (a5) Δ1=0, (a6) Δ1=28.5GHz, (a7) Δ1=80.2GHz, (a8) Δ1=120.1GHz, respectively, in V-type energy-level system as shown in Fig. 1(c). (b), (d), (f) Theoretical results correspond to (a), (c), and (e). (g1)–(g5) The dressed-state pictures of the suppression and enhancement of the DFWM signal. |G+ and |G: two dressed states caused by the field E2(E2).

Fig. 8.
Fig. 8.

(a), (c), (e) Measured evolution of the probe transmission, the two coexisting DFWM signals, and fluorescence signals versus Δ2 with (a1) Δ1=136.9GHz, (a2) Δ1=99.3GHz, (a3) Δ1=73.1GHz, (a4) Δ1=35.2GHz, (a5) Δ1=0GHz, (a6) Δ1=32.6GHz, (a7) Δ1=79.4GHz, (a8) Δ1=99.1GHz, (a9) Δ1=128.4GHz, respectively, first in two-level (|0|2) system and then in three-level system as shown in Fig. 1(d). (b), (d), (f) Theoretical results correspond to (a), (c), and (e). (g1)–(g3) and (g4)–(g6) Atomic levels diagrams, in which the COM in two-level and three-level types are marked out as the horizontal dashed lines and labeled as COM, respectively.

Fig. 9.
Fig. 9.

(a), (b), (c) Measured evolution of the probe transmission, the two coexisting DFWM signals, and fluorescence signals versus Δ2 with (a1) Δ1=338.5GHz, (a2) Δ1=292.6GHz, (a3) Δ1=255.6GHz, (a4) Δ1=218.2GHz, (a5) Δ1=177.3GHz, (a6) Δ1=136.4GHz, (a7) Δ1=98.5GHz, (a8) Δ1=46.2GHz, (a9) Δ1=0, (a10) Δ1=32.5GHz, (a11) Δ1=75.3GHz, (a12) Δ1=114.6GHz, (a13) Δ1=150.3GHz, (a14) Δ1=191.6GHz, (a15) Δ1=238.2GHz, (a16) Δ1=275.1GHz, (a17) Δ1=311.8GHz, respectively. (d1)–(d4) Atomic levels diagrams, in which the COM in four different energy level types are marked out as the horizontal dashed lines and labeled as COM, respectively The signals in (a)–(c) are distributed according to the distribution of the energy levels in (d).

Equations (42)

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u3Zi2u32k3=ik3n0(n2S1|u3|2+2n2X1|u1|2+2n2X2|u1|2+2n2X3|u2|2+2n2X4|u2|2)u3,
uF1Zi2uF12kF1=ikF1n0(n2S2|uF1|2+2n2X5|u1|2+2n2X6|u1|2+2n2X7|u2|2+2n2X8|u2|2)uF1,
n2X2i|G1|2GpΓ00[d1+|G1|2Γ11+|G2|2d3]2,
n2X4i|G1|2Gpd3[Γ10+iΔ1+|G1|2Γ11+|G2|2d3]2,
n2X6i|G1|2GFΓ00[d1+|G1|2Γ11+|G2|2d3]2,
n2X8i|G1|2GFd3[d1+|G1|2Γ11+|G2|2d3]2.
ρ22(2)=G12(d1+|G1|2Γ00+|G2|2d3)(Γ22+|G2|2d2+|G1|2d1),
ρ22(2)=G1G2(d2+|G2|2Γ00+|G1|2d4)(d8+|G1|2d2+|G2|2d6),
ρ22(2)=G1G2(d1+|G1|2Γ00+|G2|2d3)(d7+|G2|2d1+|G1|2d5),
ρ22(2)=G22(d2+|G2|2Γ00+|G1|2d4)(Γ22+|G2|2d2+|G1|2d1),
ρ22(4)=G12G22Γ00(d2+|G1|2d4+|G2|2Γ00)(d1+|G1|2Γ00+|G2|2d3)×1[Γ22+|G1|2(1d1+1d9)+|G2|2(1d2+1d10)],
ρ22(4)=G12G22d4(d2+|G1|2d4+|G2|2Γ00)(d2+|G1|2d4+|G2|2Γ00)×1[Γ22+|G1|2(1d1+1d9)+|G2|2(1d2+1d10)],
ρ22(4)=G12G22Γ00(d1+|G2|2d3+|G1|2Γ00)(d2+|G1|2d4+|G2|2Γ00)×1[Γ22+|G1|2(1d1+1d9)+|G2|2(1d2+1d10)],
ρ22(4)=G12G22d3(d1+|G2|2d3+|G1|2Γ00)(d1+|G2|2d3+|G1|2Γ00)×1[Γ22+|G1|2(1d1+1d9)+|G2|2(1d2+1d10)],
DFWM(F1)ρ00(0)ω1*ρ20(1)ω1*ρ00(2)ω3ρ20(3),XFWM(F3)ρ00(0)ω2ρ20(1)ω1*ρ00(2)ω3ρ20(3),
ρF1(3)=iG3G1(G1)*(Γ00+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10)×1(d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ22+|G2|2d7)2,
ρF3(3)=iG3G2(G1)*(d4+|G2|2d9+|G1|2d2)(d2+|G2|2Γ22+|G2|2Γ00+|G1|2d8)2,
ρ20(1)=iG3d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ00+|G1|2Γ22+|G1|2Γ22+|G2|2d7,
ρ11(2)=G12(d1+|G1|2Γ00+|G2|2d3)(Γ22+|G2|2d2+|G1|2d1),
ρ11(2)=G1G2(d2+|G2|2Γ00+|G1|2d4)(d8+|G1|2d2+|G2|2d6),
ρ11(2)=G1G2(d1+|G1|2Γ00+|G2|2d3)(d7+|G2|2d1+|G1|2d5),
ρ11(2)=G22(d2+|G2|2Γ00+|G1|2d4)(Γ22+|G2|2d2+|G1|2d1),
ρ11(4)=G12G22Γ00(d2+|G1|2d4+|G2|2Γ00)(d1+|G1|2Γ00+|G2|2d3)×1(Γ11+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10),
ρ11(4)=G12G22d4(d2+|G1|2d4+|G2|2Γ00)(d2+|G1|2d4+|G2|2Γ00)×1(Γ11+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10),
ρ11(4)=G12G22Γ00(d1+|G2|2d3+|G1|2Γ00)(d2+|G1|2d4+|G2|2Γ00)×1(Γ11+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10),
ρ11(4)=G12G22d3(d1+|G2|2d3+|G1|2Γ00)(d1+|G2|2d3+|G1|2Γ00)×1(Γ11+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10),
DFWM(F1)ρ00(0)ω1*ρ10(1)ω1*ρ00(2)ω3ρ10(3),XFWM(F3)ρ00(0)ω2ρ10(1)ω1*ρ00(2)ω3ρ10(3),
ρF1(3)=iG3G1(G1)*(Γ00+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10)×1(d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ11+|G2|2d7)2,
ρF3(3)=iG3G2(G1)*(d4+|G2|2d9+|G1|2d2)(d2+|G2|2Γ11+|G2|2Γ00+|G1|2d8)2,
ρ10(1)=iG3d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ00+|G1|2Γ11+|G2|2d7.
ρ11(2)=G22(d1+|G1|2Γ00)(Γ00+|G2|2d2),
ρ22(2)=G12(d2+|G2|2Γ00)(Γ00+|G1|2d1),
ρ11(4)=G12G22Γ00(Γ11+|G1|2d1+|G1|2d9)(d1+|G1|2Γ00)(d2+|G2|2Γ00),
ρ22(4)=G12G22Γ00(Γ11+|G2|2d2+|G1|2d9)(d1+|G1|2Γ00)(d2+|G2|2Γ00).
ρF1(3)=iG3G1(G1)*(Γ00+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10)×1(d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ11+|G2|2d11)2,
ρ20(1)=iG3d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ00+|G2|2d11.
ρ11(2)=G12(d1+|G1|2Γ00)(Γ00+|G2|2d2),
ρ22(2)=G22(d2+|G2|2Γ00)(Γ00+|G1|2d1),
ρ11(4)=G12G22Γ00(Γ11+|G1|2d1+|G1|2d9)(d1+|G1|2Γ00)(d2+|G2|2Γ00),
ρ22(4)=G12G22Γ00(Γ22+|G2|2d2+|G2|2d9)(d1+|G1|2Γ00)(d2+|G2|2Γ00).
ρF1(3)=iG3G1(G1)*(Γ00+|G1|2d1+|G1|2d9+|G2|2d2+|G2|2d10)×1(d1+|G1|2Γ00+|G2|2/d2+|G1|2Γ11+|G2|2d12)2,
ρ10(1)=iG3d1+|G2|2Γ00+|G2|2/d2+|G1|2Γ00+|G1|2Γ11+|G2|2d12.

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