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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17059–17064
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All-optical switching in an N-type four-level atom-cavity system

Jiteng Sheng, Xihua Yang, Utsab Khadka, and Min Xiao  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17059-17064 (2011)
http://dx.doi.org/10.1364/OE.19.017059


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Abstract

We report an experimental observation of all-optical switching in an N-type atom-cavity system with a rubidium atomic vapor cell inside an optical ring cavity. Both absorptive and dispersive switching can be realized on dark- or bright-polariton peaks by a weak switching laser beam (with the extinction ratio better than 20:1). The switching mechanism can be explained as the combination of quantum interference and intracavity dispersion properties.

© 2011 OSA

1. Introduction

All-optical switching, where controlling light with light can be realized in an optical nonlinear material, is an essential element in optical communication and information networks, and has been extensively studied in recent years [1

1. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).

13

13. X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity-atom system,” Phys. Rev. A 82(3), 033808 (2010). [CrossRef]

]. Utilizing the properties of electromagnetically induced transparency (EIT) [14

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

], in which linear susceptibility vanishes and nonlinearity is greatly enhanced resulting from quantum interference, absorptive all-optical switching can be realized at low light levels in an N-type atomic system [2

2. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]

], which was experimentally demonstrated in cold atoms [3

3. M. Yan, E. G. Rickey, and Y. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A 64(4), 041801(R) (2001). [CrossRef]

5

5. Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30(23), 3207–3209 (2005). [CrossRef] [PubMed]

] and hot atomic vapor [6

6. W. Jiang, Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, “Optical pumping-assisted electromagnetically induced transparency,” Phys. Rev. A 73(5), 053804 (2006). [CrossRef]

-7

7. M. G. Bason, A. K. Mohapatra, K. J. Weatherill, and C. S. Adams, “Narrow absorptive resonances in a four-level atomic system,” J. Phys. B 42(7), 075503 (2009). [CrossRef]

] in free space. Large Kerr-nonlinearity (cross-phase modulation) has also been expected in such N-type atomic system [15

15. H. Schmidt and A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996). [CrossRef] [PubMed]

17

17. H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83(4), 041804(R) (2011). [CrossRef]

]. A variety of other types of all-optical switching have been realized based on enhanced Kerr nonlinearity [8

8. H. Wang, D. Goorskey, and M. Xiao, “Controlling the cavity field with enhanced Kerr nonlinearity in three-level atoms,” Phys. Rev. A 65(5), 051802(R) (2002). [CrossRef]

], optical bistability [9

9. A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical Bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003). [CrossRef]

], electromagnetically induced absorption (EIA) grating [10

10. A. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30(7), 699–701 (2005). [CrossRef] [PubMed]

], parametric instability [11

11. A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005). [CrossRef] [PubMed]

], and phase-controlled interference [12

12. H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73(1), 011802(R) (2006). [CrossRef]

]. Recently, an experimental observation of all-optical switching in a system consisting of cold three-level atoms and an optical cavity was reported [13

13. X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity-atom system,” Phys. Rev. A 82(3), 033808 (2010). [CrossRef]

].

Here, we present our experimental observation of all-optical switching in an N-type four-level atom-cavity system. The major advantages of the current system include: (1) both absorptive switching and dispersive switching can be realized on either dark- or bright-polariton peaks by a switching laser (on or off); (2) the extinction ratio can be greatly improved at a relatively low switching laser power with an optical cavity; (3) the switching laser power in this N-type four-level system can be much lower than in a Λ-type three-level structure [8

8. H. Wang, D. Goorskey, and M. Xiao, “Controlling the cavity field with enhanced Kerr nonlinearity in three-level atoms,” Phys. Rev. A 65(5), 051802(R) (2002). [CrossRef]

], which used the self-phase modulation; (4) large atomic density can be obtained by heating the vapor cell, and the non-Doppler-free effect of this scheme is actually small by using the counter-propagating beam configuration [18

18. C. Y. Ye, A. S. Zibrov, Y. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A 65(4), 043805 (2002). [CrossRef]

].

2. Experiment and result

The experimental setup is shown in Fig. 1(a)
Fig. 1 (Color online) (a) Experimental setup. PBS1 & PBS2: polarization beam splitters; M1-M3: cavity mirrors; APD: avalanche photodiode detector; and PZT: piezoelectric transducer. (b) Four-level atomic system in 87Rb and the corresponding laser coupling scheme. (c) Atomic energy levels in the dressed-state picture with both coupling and switching lasers on resonance.
. A three-mirror optical ring cavity consists of an input mirror M1 and an output mirror M2 with 3% and 1.4% transmissivities, respectively, and a third mirror M3 with reflectivity larger than 99.5%, mounted on a piezoelectric transducer (PZT) for cavity frequency scanning and locking. The ring cavity length is 37 cm. The rubidium vapor cell, without buffer gas, is 5 cm long with Brewster windows, and is wrapped in μ-metal sheet for magnetic field shielding and in heat tape for heating. Four energy levels in the D lines of 87Rb atoms are used for the N-type four-level system [2

2. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]

], as shown in Fig. 1(b). The coupling (ωc) and switching (ωs) laser beams are injected separately through two polarization beam splitters (PBS 1 and PBS 2) and counter-propagate through the vapor cell. The probe (ωp) beam is injected into the cavity via the input mirror M1 and circulates in the cavity as the cavity field, and the output is detected by an avalanche photodiode detector (APD). The coupling beam co-propagates with the cavity field, and is about 2 degrees misaligned to avoid its circulation in the cavity. The switching beam is carefully aligned to obtain good overlaps with other beams in the vapor cell by monitoring the absorption. The frequency detunings for the probe, coupling, and switching lasers are defined to be Δp = ωp – ω13, Δc = ωc – ω23, and Δs = ωs – ω24, respectively. The radii of the coupling, switching, and probe laser beams are estimated to be 400 μm, 400 μm and 100 μm at the center of the atomic cell, respectively. The temperature of the rubidium cell keeps about 74°C during the experiment. The optical depth (OD) of the probe laser beam is estimated to be about 40 under the current experimental conditions. The empty cavity finesse is about 100. When the atomic cell and PBS are included, the cavity finesse decreases to about 48. An additional frequency-stabilized diode laser is used to lock the optical ring cavity (not shown in Fig. 1(a)), and the cavity frequency detuning is defined to be Δθ = ωcav – ω13. Figure 1(c) is the dressed-state picture when both coupling and switching lasers are on resonance, i.e., Δc = Δs = 0.

The cavity transmission spectra with and without the switching laser beam are measured when the probe laser frequency is scanning. The probe beam power and the coupling beam power are fixed at 0.5 mW and 13.5 mW, respectively. The cavity detuning is fixed at zero, and the coupling and switching lasers are locked on the saturated absorption spectrum with Δc = Δs = 0, which are shown in Fig. 2
Fig. 2 Measured cavity transmission spectra versus the probe laser detuning. (a) The switching laser is off. (b) The switching laser is on with Ps = 0.7 mW and Δs = 0. (c) The switching laser is on with Ps = 3.3 mW and Δs = 0. Other experimental parameters are T = 74 °C, Pp = 0.5 mW, Pc = 13.5 mW, Δc = 0, and Δθ = 0. The cavity transmission is normalized to the central peak height when the switching laser power is zero.
. In Fig. 2(a), one can observe one central peak (the dark polariton) and two side peaks (the bright polaritons) in the typical three-level Λ-type EIT atom-cavity system without the switching laser beam [19

19. H. Wu, J. Gea-Banacloche, and M. Xiao, “Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium,” Phys. Rev. Lett. 100(17), 173602 (2008). [CrossRef] [PubMed]

]. When the switching laser is applied, the central peak height will reduce (EIT destroyed) because of the two-photon absorption [2

2. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]

]. With the increase of switching laser power, the central peak height decreases further until it disappears (totally absorbed), as shown in Fig. 3
Fig. 3 Measured central peak heights in the cavity transmission spectra as a function of switching laser power. The central peak heights are normalized to the highest peak when the switching laser power is zero. Other experimental parameters are the same as in Fig. 2.
. The situation in Fig. 2(b) corresponds to the data point in Fig. 3 when the switching laser power is about 0.7 mW, where the central peak is totally absorbed. By further increasing the switching laser power, two additional peaks (close to the center) appear, as shown in Fig. 2(c), and at the same time the two side peaks (bright polaritons) move further away from the center. The frequency positions (Δp) of the two side peaks depend on the density of the atomic sample (temperature), the coupling laser power, and the switching laser power. When the switching laser power is zero, the positions of the two side peaks are given by ±g2N+Ωc2/4 [19

19. H. Wu, J. Gea-Banacloche, and M. Xiao, “Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium,” Phys. Rev. Lett. 100(17), 173602 (2008). [CrossRef] [PubMed]

], where g is the atom-cavity coupling strength, N is the number of atoms in the cavity mode, and Ωc is the Rabi frequency of the coupling field. When the switching laser power is not zero, the separation between the two side peaks becomes larger, which can be qualitatively understood by considering the change of the refractive property besides the absorption due to the switching beam. As shown in Figs. 2(a) and (b), the right side peak moves outward slightly because the switching laser power is relatively weak, while the left side peak shape is modified due to the more complicated energy level structure, which is not discussed here.

Figure 4
Fig. 4 All-optical switching of the cavity transmission controlled by the switching laser. (a) The switching laser power as a function of time. (b)-(d) The cavity transmissions as a function of time, with the probe laser frequency fixed at (b) Δp ≈0, (c) Δp ≈220 MHz, and (d) Δp ≈50 MHz, respectively. The cavity transmission is normalized to the central peak height when the switching laser power is zero. Other experimental parameters are the same as in Fig. 2.
shows the absorptive and dispersive switching of the cw probe laser controlled by a pulsed switching laser, with the coupling laser always on. When the switching laser is turned on and off by an AOM, the switching between different cavity transmission intensities can be made at three different probe frequency positions, marked as I, II, and III, respectively, in Figs. 2(a) and (c). Figure 4(a) is the switching laser power modulated by a square waveform. Figures 4 (b)-(d) show the cavity transmissions as a function of time when the probe frequency is locked onto a Fabry-Perot cavity at Δp ≈0, Δp ≈220 MHz, and Δp ≈50 MHz, corresponding to positions I, II, and III in Figs. 2(a) and (c), respectively. Notice that the switching patterns in Figs. 4(b) and (c) are out of phase to the one in Fig. 4(d), i.e., when the switching laser is on, the powers shown in Figs. 4(b) and (c) (peaks I and II) are also on, while the power shown in Fig. 4(d) (peak III) is off. In order to obtain a stable on-state power shown in Fig. 4(b), we used a relatively strong coupling beam (13.5 mW) to get large linewidth of the central peak. In order to reach a good extinction ratio for switching, we also used a relatively strong switching beam (3.3 mW) to observe the obvious shift of the side peaks, as shown in Fig. 4(c) and to observe two additional peaks around the center frequency, as shown in Fig. 4(d). However, a weak switching beam (0.7 mW) can be used if one needs to make an absorptive switching at the central peak. All the three switchings have the switching speed in the order of 1 µs (limited by the AOM used in the experiment) and the extinction ratio can reach 20:1 in the current experiment.

3. Discussion

The physical mechanism of such switching can be well understood by combining the quantum interference and intracavity dispersion properties. In Fig. 2(a), the central peak is usually referred to as the dark-polariton peak and the two side peaks are the bright-polariton peaks, which can be well explained in cavity-QED theory [19

19. H. Wu, J. Gea-Banacloche, and M. Xiao, “Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium,” Phys. Rev. Lett. 100(17), 173602 (2008). [CrossRef] [PubMed]

], or by considering the intracavity dispersion properties [20

20. J. Sheng, H. Wu, M. Mumba, J. Gea-Banacloche, and M. Xiao, “Understanding cavity resonances with intracavity dispersion properties,” Phys. Rev. A 83(2), 023829 (2011). [CrossRef]

]. At the weak switching laser power limit, with increasing the switching laser power, the absorption at the center line increases, the dispersion around the center gradually changes from normal to anomalous. Also, the two anomalous dispersion regions at the two sides resulting from the dressed-states | + > and |-> move away from the center, which leads to the changes of the side peak positions. As shown in Fig. 2(b), the central peak is totally absorbed, leaving the two side peaks moving slightly away from the center. By further increasing the switching laser power, the separations between the dressed-states | + > and |0>, and |0> and |-> become even larger. By analyzing the free-space absorption and dispersion behaviors, we find there are two absorption reduced windows around the center due to the destructive interference, and the dispersion can be understood as the superposition of three dispersive curves [21

21. T. Y. Abi-Salloum, B. Henry, J. Davis, and F. Narducci, “Resonances and excitation pathways in four-level N-scheme atomic systems,” Phys. Rev. A 82(1), 013834 (2010). [CrossRef]

]. By using the detuning-line method [20

20. J. Sheng, H. Wu, M. Mumba, J. Gea-Banacloche, and M. Xiao, “Understanding cavity resonances with intracavity dispersion properties,” Phys. Rev. A 83(2), 023829 (2011). [CrossRef]

], we also find the cavity round-trip phase is close to zero at the positions where the absorption reduces near the center, thus, we can easily find two additional peaks appearing around the center, as shown in Fig. 2(c). Increasing the switching laser power even further, the two peaks around the center, as well as the two side peaks, move further outward. The asymmetry of the two side peaks at high switching laser power results from the hyperfine structure of the D lines.

This N-type four-level atom-cavity system is the extension of the lambda-type three-level EIT atom-cavity system by adding a third (switching) laser beam between one of the ground states to the fourth (excited) level, and the transition between this fourth level (|4>) and the other ground state (|1>) is forbidden. Therefore, this system has most of the properties as in the three-level EIT system. However, this four-level scheme can be more promising for applications, since it has more flexibility with experimental controls of the parameters, larger enhanced nonlinearities, and both absorption and dispersion properties of the intracavity medium can be dramatically modified. These properties can be useful in studying optical bistability and multistability, as well as in controlled all-optical switching. Here, we have only investigated the dependence of switching behavior on the laser power in this system, other interesting phenomena can also be observed when other experimental parameters are modified, such as switching detuning (Δs) and, cavity detuning (Δθ), etc.

4. Conclusion

In summary, we have experimentally demonstrated an all-optical switching in an N-type atom-cavity system. In this system, three different types of all-optical switching can be achieved by simply choosing different probe frequencies, which can be useful for multi-channel communication applications. All these three switching processes are quite stable, and by using the optical cavity, high extinction ratio with a relatively small switching laser power can be realized, which can lead to the realization of logic gates at the single-photon level.

Acknowledgments

We acknowledge the funding support from the National Science Foundation.

References and links

1.

H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).

2.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]

3.

M. Yan, E. G. Rickey, and Y. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A 64(4), 041801(R) (2001). [CrossRef]

4.

D. A. Braje, V. Balić, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68(4), 041801(R) (2003). [CrossRef]

5.

Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, and I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30(23), 3207–3209 (2005). [CrossRef] [PubMed]

6.

W. Jiang, Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, “Optical pumping-assisted electromagnetically induced transparency,” Phys. Rev. A 73(5), 053804 (2006). [CrossRef]

7.

M. G. Bason, A. K. Mohapatra, K. J. Weatherill, and C. S. Adams, “Narrow absorptive resonances in a four-level atomic system,” J. Phys. B 42(7), 075503 (2009). [CrossRef]

8.

H. Wang, D. Goorskey, and M. Xiao, “Controlling the cavity field with enhanced Kerr nonlinearity in three-level atoms,” Phys. Rev. A 65(5), 051802(R) (2002). [CrossRef]

9.

A. Brown, A. Joshi, and M. Xiao, “Controlled steady-state switching in optical Bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003). [CrossRef]

10.

A. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30(7), 699–701 (2005). [CrossRef] [PubMed]

11.

A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005). [CrossRef] [PubMed]

12.

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73(1), 011802(R) (2006). [CrossRef]

13.

X. Wei, J. Zhang, and Y. Zhu, “All-optical switching in a coupled cavity-atom system,” Phys. Rev. A 82(3), 033808 (2010). [CrossRef]

14.

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

15.

H. Schmidt and A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996). [CrossRef] [PubMed]

16.

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91(9), 093601 (2003). [CrossRef] [PubMed]

17.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83(4), 041804(R) (2011). [CrossRef]

18.

C. Y. Ye, A. S. Zibrov, Y. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A 65(4), 043805 (2002). [CrossRef]

19.

H. Wu, J. Gea-Banacloche, and M. Xiao, “Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium,” Phys. Rev. Lett. 100(17), 173602 (2008). [CrossRef] [PubMed]

20.

J. Sheng, H. Wu, M. Mumba, J. Gea-Banacloche, and M. Xiao, “Understanding cavity resonances with intracavity dispersion properties,” Phys. Rev. A 83(2), 023829 (2011). [CrossRef]

21.

T. Y. Abi-Salloum, B. Henry, J. Davis, and F. Narducci, “Resonances and excitation pathways in four-level N-scheme atomic systems,” Phys. Rev. A 82(1), 013834 (2010). [CrossRef]

OCIS Codes
(190.4180) Nonlinear optics : Multiphoton processes
(230.1150) Optical devices : All-optical devices
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Quantum Optics

History
Original Manuscript: July 1, 2011
Revised Manuscript: July 22, 2011
Manuscript Accepted: July 22, 2011
Published: August 16, 2011

Citation
Jiteng Sheng, Xihua Yang, Utsab Khadka, and Min Xiao, "All-optical switching in an N-type four-level atom-cavity system," Opt. Express 19, 17059-17064 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17059


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References

  1. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).
  2. S. E. Harris, Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81(17), 3611–3614 (1998). [CrossRef]
  3. M. Yan, E. G. Rickey, Y. Zhu, “Observation of absorptive photon switching by quantum interference,” Phys. Rev. A 64(4), 041801(R) (2001). [CrossRef]
  4. D. A. Braje, V. Balić, G. Y. Yin, S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68(4), 041801(R) (2003). [CrossRef]
  5. Y.-F. Chen, Z.-H. Tsai, Y.-C. Liu, I. A. Yu, “Low-light-level photon switching by quantum interference,” Opt. Lett. 30(23), 3207–3209 (2005). [CrossRef] [PubMed]
  6. W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Optical pumping-assisted electromagnetically induced transparency,” Phys. Rev. A 73(5), 053804 (2006). [CrossRef]
  7. M. G. Bason, A. K. Mohapatra, K. J. Weatherill, C. S. Adams, “Narrow absorptive resonances in a four-level atomic system,” J. Phys. B 42(7), 075503 (2009). [CrossRef]
  8. H. Wang, D. Goorskey, M. Xiao, “Controlling the cavity field with enhanced Kerr nonlinearity in three-level atoms,” Phys. Rev. A 65(5), 051802(R) (2002). [CrossRef]
  9. A. Brown, A. Joshi, M. Xiao, “Controlled steady-state switching in optical Bistability,” Appl. Phys. Lett. 83(7), 1301–1303 (2003). [CrossRef]
  10. A. Brown, M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30(7), 699–701 (2005). [CrossRef] [PubMed]
  11. A. M. C. Dawes, L. Illing, S. M. Clark, D. J. Gauthier, “All-optical switching in rubidium vapor,” Science 308(5722), 672–674 (2005). [CrossRef] [PubMed]
  12. H. Kang, G. Hernandez, J. Zhang, Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73(1), 011802(R) (2006). [CrossRef]
  13. X. Wei, J. Zhang, Y. Zhu, “All-optical switching in a coupled cavity-atom system,” Phys. Rev. A 82(3), 033808 (2010). [CrossRef]
  14. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]
  15. H. Schmidt, A. Imamogdlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21(23), 1936–1938 (1996). [CrossRef] [PubMed]
  16. H. Kang, Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91(9), 093601 (2003). [CrossRef] [PubMed]
  17. H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. Yu, Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83(4), 041804(R) (2011). [CrossRef]
  18. C. Y. Ye, A. S. Zibrov, Y. V. Rostovtsev, M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A 65(4), 043805 (2002). [CrossRef]
  19. H. Wu, J. Gea-Banacloche, M. Xiao, “Observation of intracavity electromagnetically induced transparency and polariton resonances in a Doppler-broadened medium,” Phys. Rev. Lett. 100(17), 173602 (2008). [CrossRef] [PubMed]
  20. J. Sheng, H. Wu, M. Mumba, J. Gea-Banacloche, M. Xiao, “Understanding cavity resonances with intracavity dispersion properties,” Phys. Rev. A 83(2), 023829 (2011). [CrossRef]
  21. T. Y. Abi-Salloum, B. Henry, J. Davis, F. Narducci, “Resonances and excitation pathways in four-level N-scheme atomic systems,” Phys. Rev. A 82(1), 013834 (2010). [CrossRef]

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