Abstract

We study the effect of a DC magnetic field on the phase sensitivity of a double-lambda system coupled by two laser fields, a probe and a pump. It is demonstrated that the gain and the refractive index of the probe can be controlled by either the magnetic field or the relative phase between the two laser fields. More interestingly, when the system reduces to a single-lambda system, turning on the magnetic field transforms the system from a phase-insensitive process to a phase-sensitive one. In the pulsed-probe regime, we observed switching between slow and fast light when the magnetic field or the relative phase was adjusted. Experiments using a coated 87Rb vapor cell produced results in good agreement with our numerical simulation. This work provides a novel and simple means to manipulate phase sensitive electromagnetically-induced-transparency or four-wave mixing, and could be useful for applications in quantum optics, nonlinear optics and magnetometery based on such systems.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, “Generation of two-mode squeezed and entangled light in a single temporal and spatial mode,” Opt. Express17,14444–14457 (2009).
    [CrossRef] [PubMed]
  26. I. Novikova, D. F. Phillips, and R. L. Walsworth, “Slow light with integrated gain and large pulse delay,” Phys. Rev. Lett.99,173604 (2007).
    [CrossRef] [PubMed]
  27. W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
    [CrossRef] [PubMed]
  28. B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
    [CrossRef]
  29. N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A83,063823 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  32. M. Klein, M. Hohensee, D. F. Phillips, and R. L. Walsworth, “Electromagnetically induced transparency in paraffin-coated vapor cells,” Phys. Rev. A83,013826 (2011).
    [CrossRef]
  33. I. Novikova, R. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev.6,333–353 (2012).
    [CrossRef]
  34. Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
    [CrossRef]

2013

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

2012

I. Novikova, R. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev.6,333–353 (2012).
[CrossRef]

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

J. Dimitrijević and D. Arsenović, “Simple analytical expressions for the analysis of the phase-dependent electromagnetically induced transparency in a double-Λ atomic scheme,” Phys. Scr.T149, 014007 (2012).
[CrossRef]

2011

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

D. Jafari, M. Sahrai, H. Motavalli, and M. Mahmoudi, “Phase control of group velocity in a dielectric slab doped with three-level ladder-type atoms,” Phys. Rev. A84,063811 (2011).
[CrossRef]

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A83,063823 (2011).
[CrossRef]

S. Barreiro, P. Valente, H. Failache, and A. Lezama, “Polarization squeezing of light by single passage through an atomic vapor,” Phys. Rev. A84,033851 (2011).
[CrossRef]

M. Klein, M. Hohensee, D. F. Phillips, and R. L. Walsworth, “Electromagnetically induced transparency in paraffin-coated vapor cells,” Phys. Rev. A83,013826 (2011).
[CrossRef]

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

2010

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
[CrossRef]

2009

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, “Generation of two-mode squeezed and entangled light in a single temporal and spatial mode,” Opt. Express17,14444–14457 (2009).
[CrossRef] [PubMed]

2008

2007

I. Novikova, D. F. Phillips, and R. L. Walsworth, “Slow light with integrated gain and large pulse delay,” Phys. Rev. Lett.99,173604 (2007).
[CrossRef] [PubMed]

2005

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77,633–673 (2005).
[CrossRef]

2003

M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys.75,457–472 (2003).
[CrossRef]

2002

A. F. Huss, E. A. Korsunsky, and L. Windholz, “Phase control of electromagnetically induced transparency in a double-Λ system,” J. Mod. Opt.49,141–155 (2002).
[CrossRef]

2001

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: From subluminal to superluminal light propagation,” Phys. Rev. A63,043818 (2001).
[CrossRef]

1999

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A60,4996–5009 (1999).
[CrossRef]

1996

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

1991

D. Kosachiov, B. Matisov, and Yu. Rozhdestvensky, “Coherent population trapping: sensitivity of an atomic system to the relative phase of exciting fields,” Opt. Commun.85,209–212 (1991).
[CrossRef]

K. J. Boiler, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66,2593–2596 (1991).
[CrossRef]

1990

M. S. Shahriar and P. R. Hemmer, “Direct excitation of microwave-spin dressed states using a laser-excited resonance Raman interaction,” Phys. Rev. Lett.65,1865–1868 (1990).
[CrossRef] [PubMed]

1986

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

S. P. Krinitzky and D. T. Pegg, “Coherent irradiation of multilevel atoms in branched and cyclic configurations,” Phys. Rev. A33,403–406 (1986).
[CrossRef] [PubMed]

Arsenovic, D.

J. Dimitrijević and D. Arsenović, “Simple analytical expressions for the analysis of the phase-dependent electromagnetically induced transparency in a double-Λ atomic scheme,” Phys. Scr.T149, 014007 (2012).
[CrossRef]

Asha, K.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

Bai, Y.

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Balabas, M. V.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

Balik, S.

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

Baluschev, S.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

Barnett, S. M.

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

Barreiro, S.

S. Barreiro, P. Valente, H. Failache, and A. Lezama, “Polarization squeezing of light by single passage through an atomic vapor,” Phys. Rev. A84,033851 (2011).
[CrossRef]

Boiler, K. J.

K. J. Boiler, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66,2593–2596 (1991).
[CrossRef]

Bortman-Arbiv, D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: From subluminal to superluminal light propagation,” Phys. Rev. A63,043818 (2001).
[CrossRef]

Buckle, S. J.

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

Budker, D.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Chen, X.

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Corsini, E.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Crescimanno, M.

Dimitrijevic, J.

J. Dimitrijević and D. Arsenović, “Simple analytical expressions for the analysis of the phase-dependent electromagnetically induced transparency in a double-Λ atomic scheme,” Phys. Scr.T149, 014007 (2012).
[CrossRef]

Failache, H.

S. Barreiro, P. Valente, H. Failache, and A. Lezama, “Polarization squeezing of light by single passage through an atomic vapor,” Phys. Rev. A84,033851 (2011).
[CrossRef]

Fan, S.

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Fan, X.

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

Fernholz, T.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77,633–673 (2005).
[CrossRef]

Friedmann, H.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: From subluminal to superluminal light propagation,” Phys. Rev. A63,043818 (2001).
[CrossRef]

Gao, J.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Gao, R.

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

Gorshkov, A. V.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A83,063823 (2011).
[CrossRef]

Guo, H.

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Han, D.

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Hancox, C.

Harris, S. E.

K. J. Boiler, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66,2593–2596 (1991).
[CrossRef]

Havey, M. D.

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

Hemmati, R.

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
[CrossRef]

Hemmer, P. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

M. S. Shahriar and P. R. Hemmer, “Direct excitation of microwave-spin dressed states using a laser-excited resonance Raman interaction,” Phys. Rev. Lett.65,1865–1868 (1990).
[CrossRef] [PubMed]

Higbie, J. M.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Hohensee, M.

Horrom, T.

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

Hovde, D. C.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Hu, X.

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

Huss, A.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

Huss, A. F.

A. F. Huss, E. A. Korsunsky, and L. Windholz, “Phase control of electromagnetically induced transparency in a double-Λ system,” J. Mod. Opt.49,141–155 (2002).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77,633–673 (2005).
[CrossRef]

K. J. Boiler, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66,2593–2596 (1991).
[CrossRef]

Jafari, D.

D. Jafari, M. Sahrai, H. Motavalli, and M. Mahmoudi, “Phase control of group velocity in a dielectric slab doped with three-level ladder-type atoms,” Phys. Rev. A84,063811 (2011).
[CrossRef]

Jensen, K.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, “Generation of two-mode squeezed and entangled light in a single temporal and spatial mode,” Opt. Express17,14444–14457 (2009).
[CrossRef] [PubMed]

Jia, K.

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

Jiang, L.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Jiang, Y.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Kang, Z.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Klein, M.

M. Klein, M. Hohensee, D. F. Phillips, and R. L. Walsworth, “Electromagnetically induced transparency in paraffin-coated vapor cells,” Phys. Rev. A83,013826 (2011).
[CrossRef]

Knigt, P. L.

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

Korsunsky, E.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

Korsunsky, E. A.

A. F. Huss, E. A. Korsunsky, and L. Windholz, “Phase control of electromagnetically induced transparency in a double-Λ system,” J. Mod. Opt.49,141–155 (2002).
[CrossRef]

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A60,4996–5009 (1999).
[CrossRef]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

Kosachiov, D.

D. Kosachiov, B. Matisov, and Yu. Rozhdestvensky, “Coherent population trapping: sensitivity of an atomic system to the relative phase of exciting fields,” Opt. Commun.85,209–212 (1991).
[CrossRef]

Kosachiov, D. V.

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A60,4996–5009 (1999).
[CrossRef]

Kou, J.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Krauter, H.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, “Generation of two-mode squeezed and entangled light in a single temporal and spatial mode,” Opt. Express17,14444–14457 (2009).
[CrossRef] [PubMed]

Krinitzky, S. P.

S. P. Krinitzky and D. T. Pegg, “Coherent irradiation of multilevel atoms in branched and cyclic configurations,” Phys. Rev. A33,403–406 (1986).
[CrossRef] [PubMed]

Lauder, M. A.

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

Leinfellner, N.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

Lezama, A.

S. Barreiro, P. Valente, H. Failache, and A. Lezama, “Polarization squeezing of light by single passage through an atomic vapor,” Phys. Rev. A84,033851 (2011).
[CrossRef]

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

Li, H.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

Liang, Y.

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

Liu, Z.

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

Lukin, M. D.

M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys.75,457–472 (2003).
[CrossRef]

Madsen, L. S.

Mahmoudi, M.

D. Jafari, M. Sahrai, H. Motavalli, and M. Mahmoudi, “Phase control of group velocity in a dielectric slab doped with three-level ladder-type atoms,” Phys. Rev. A84,063811 (2011).
[CrossRef]

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
[CrossRef]

Maichen, W.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

Maleki, A.

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
[CrossRef]

Manukumara, M.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77,633–673 (2005).
[CrossRef]

Matisov, B.

D. Kosachiov, B. Matisov, and Yu. Rozhdestvensky, “Coherent population trapping: sensitivity of an atomic system to the relative phase of exciting fields,” Opt. Commun.85,209–212 (1991).
[CrossRef]

Mazets, I.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

Mikhailov, E. E.

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett.33,1213–1215 (2008).
[CrossRef] [PubMed]

Motavalli, H.

D. Jafari, M. Sahrai, H. Motavalli, and M. Mahmoudi, “Phase control of group velocity in a dielectric slab doped with three-level ladder-type atoms,” Phys. Rev. A84,063811 (2011).
[CrossRef]

Muschik, C.

Narayanan, A.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

Novikova, I.

I. Novikova, R. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev.6,333–353 (2012).
[CrossRef]

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A83,063823 (2011).
[CrossRef]

E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett.33,1213–1215 (2008).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, and R. L. Walsworth, “Slow light with integrated gain and large pulse delay,” Phys. Rev. Lett.99,173604 (2007).
[CrossRef] [PubMed]

Patton, B.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Pegg, D. T.

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

S. P. Krinitzky and D. T. Pegg, “Coherent irradiation of multilevel atoms in branched and cyclic configurations,” Phys. Rev. A33,403–406 (1986).
[CrossRef] [PubMed]

Phillips, D. F.

M. Klein, M. Hohensee, D. F. Phillips, and R. L. Walsworth, “Electromagnetically induced transparency in paraffin-coated vapor cells,” Phys. Rev. A83,013826 (2011).
[CrossRef]

C. Hancox, M. Hohensee, M. Crescimanno, D. F. Phillips, and R. L. Walsworth, “Lineshape asymmetry for joint coherent population trapping and three-photon N resonances,” Opt. Lett.33,1536–1538 (2008).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, and R. L. Walsworth, “Slow light with integrated gain and large pulse delay,” Phys. Rev. Lett.99,173604 (2007).
[CrossRef] [PubMed]

Phillips, N. B.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A83,063823 (2011).
[CrossRef]

Polzik, E. S.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, “Generation of two-mode squeezed and entangled light in a single temporal and spatial mode,” Opt. Express17,14444–14457 (2009).
[CrossRef] [PubMed]

Preethi, T. M.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

Qu, W.

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

Renema, J. J.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

Renzoni, F.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

Roshi, D. A.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

Rostovtsev, Y. V.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

Rozhdestvensky, Yu.

D. Kosachiov, B. Matisov, and Yu. Rozhdestvensky, “Coherent population trapping: sensitivity of an atomic system to the relative phase of exciting fields,” Opt. Commun.85,209–212 (1991).
[CrossRef]

Sahrai, M.

D. Jafari, M. Sahrai, H. Motavalli, and M. Mahmoudi, “Phase control of group velocity in a dielectric slab doped with three-level ladder-type atoms,” Phys. Rev. A84,063811 (2011).
[CrossRef]

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
[CrossRef]

Sautenkov, V. A.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

Scully, M. O.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

Shahriar, M. S.

M. S. Shahriar and P. R. Hemmer, “Direct excitation of microwave-spin dressed states using a laser-excited resonance Raman interaction,” Phys. Rev. Lett.65,1865–1868 (1990).
[CrossRef] [PubMed]

Sun, H.

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Tong, D.

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

Valente, P.

S. Barreiro, P. Valente, H. Failache, and A. Lezama, “Polarization squeezing of light by single passage through an atomic vapor,” Phys. Rev. A84,033851 (2011).
[CrossRef]

Versolato, O. O.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Vijay, J.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

Walsworth, R.

I. Novikova, R. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev.6,333–353 (2012).
[CrossRef]

Walsworth, R. L.

M. Klein, M. Hohensee, D. F. Phillips, and R. L. Walsworth, “Electromagnetically induced transparency in paraffin-coated vapor cells,” Phys. Rev. A83,013826 (2011).
[CrossRef]

C. Hancox, M. Hohensee, M. Crescimanno, D. F. Phillips, and R. L. Walsworth, “Lineshape asymmetry for joint coherent population trapping and three-photon N resonances,” Opt. Lett.33,1536–1538 (2008).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, and R. L. Walsworth, “Slow light with integrated gain and large pulse delay,” Phys. Rev. Lett.99,173604 (2007).
[CrossRef] [PubMed]

Wan, R.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Wang, L.

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

Wasilewski, W.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, “Generation of two-mode squeezed and entangled light in a single temporal and spatial mode,” Opt. Express17,14444–14457 (2009).
[CrossRef] [PubMed]

Welch, G. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

Wilson-Gordon, A. D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: From subluminal to superluminal light propagation,” Phys. Rev. A63,043818 (2001).
[CrossRef]

Windholz, L.

A. F. Huss, E. A. Korsunsky, and L. Windholz, “Phase control of electromagnetically induced transparency in a double-Λ system,” J. Mod. Opt.49,141–155 (2002).
[CrossRef]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

Xiao, M.

Y. Zhang and M. Xiao, Multi-Wave Mixing Processes (Springer, Berlin, 2009).
[CrossRef]

Xiao, Y.

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

I. Novikova, R. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev.6,333–353 (2012).
[CrossRef]

Xu, Z.

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

Zhang, Y.

Y. Zhang and M. Xiao, Multi-Wave Mixing Processes (Springer, Berlin, 2009).
[CrossRef]

Appl. Phys. Lett.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett.101,083502 (2012).
[CrossRef]

Chin. Phys. B

Z. Xu, W. Qu, R. Gao, X. Hu, and Y. Xiao, “Linewidth of electromagnetically induced transparency under motional averaging in a coated vapor cell,” Chin. Phys. B22,033202 (2013).
[CrossRef]

Eur. Phys. J. D

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D56,105–112 (2010).
[CrossRef]

Euro. Phys. Lett.

T. M. Preethi, M. Manukumara, K. Asha, J. Vijay, D. A. Roshi, and A. Narayanan, “Phase-sensitive microwave optical double resonance in an N system,” Euro. Phys. Lett.95,34005 (2011).
[CrossRef]

J. Mod. Opt.

A. F. Huss, E. A. Korsunsky, and L. Windholz, “Phase control of electromagnetically induced transparency in a double-Λ system,” J. Mod. Opt.49,141–155 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Laser Photonics Rev.

I. Novikova, R. Walsworth, and Y. Xiao, “Electromagnetically induced transparency-based slow and stored light in warm atoms,” Laser Photonics Rev.6,333–353 (2012).
[CrossRef]

Opt. Acta

S. J. Buckle, S. M. Barnett, P. L. Knigt, M. A. Lauder, and D. T. Pegg, “Atomic interferometers: Phase-dependence in multilevel atomic transitions,” Opt. Acta33,1129–1140 (1986).
[CrossRef]

Opt. Commun.

D. Kosachiov, B. Matisov, and Yu. Rozhdestvensky, “Coherent population trapping: sensitivity of an atomic system to the relative phase of exciting fields,” Opt. Commun.85,209–212 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

H. Sun, H. Guo, Y. Bai, D. Han, S. Fan, and X. Chen, “Light propagation from subluminal to superluminal in a three-level Lambda-type system,” Phys. Lett. A335,68–75 (2005).
[CrossRef]

Phys. Rev. A

D. Jafari, M. Sahrai, H. Motavalli, and M. Mahmoudi, “Phase control of group velocity in a dielectric slab doped with three-level ladder-type atoms,” Phys. Rev. A84,063811 (2011).
[CrossRef]

J. Kou, R. Wan, Z. Kang, L. Jiang, L. Wang, Y. Jiang, and J. Gao, “Phase-dependent coherent population trapping and optical switching,” Phys. Rev. A84,063807 (2011).
[CrossRef]

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, “Transient coherent population trapping in a closed loop interaction scheme,” Phys. Rev. A53,3444–3448 (1996).
[CrossRef] [PubMed]

E. A. Korsunsky and D. V. Kosachiov, “Phase-dependent nonlinear optics with double-Λ atoms,” Phys. Rev. A60,4996–5009 (1999).
[CrossRef]

X. Fan, Z. Liu, Y. Liang, K. Jia, and D. Tong, “Phase control of probe response in a Doppler-broadened N-type four-level system,” Phys. Rev. A83,043805 (2011).
[CrossRef]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A80,023820 (2009).
[CrossRef]

S. P. Krinitzky and D. T. Pegg, “Coherent irradiation of multilevel atoms in branched and cyclic configurations,” Phys. Rev. A33,403–406 (1986).
[CrossRef] [PubMed]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, “Phase-dependent electromagnetically induced transparency,” Phys. Rev. A59,2302–2305 (1999).
[CrossRef]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: From subluminal to superluminal light propagation,” Phys. Rev. A63,043818 (2001).
[CrossRef]

T. Horrom, S. Balik, A. Lezama, M. D. Havey, and E. E. Mikhailov, “Polarization self-rotation in ultracold atomic 87Rb,” Phys. Rev. A83, 053850 (2011).
[CrossRef]

N. B. Phillips, A. V. Gorshkov, and I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A83,063823 (2011).
[CrossRef]

S. Barreiro, P. Valente, H. Failache, and A. Lezama, “Polarization squeezing of light by single passage through an atomic vapor,” Phys. Rev. A84,033851 (2011).
[CrossRef]

M. Klein, M. Hohensee, D. F. Phillips, and R. L. Walsworth, “Electromagnetically induced transparency in paraffin-coated vapor cells,” Phys. Rev. A83,013826 (2011).
[CrossRef]

Phys. Rev. Lett.

I. Novikova, D. F. Phillips, and R. L. Walsworth, “Slow light with integrated gain and large pulse delay,” Phys. Rev. Lett.99,173604 (2007).
[CrossRef] [PubMed]

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum noise limited and entanglement-assisted magnetometry,” Phys. Rev. Lett.104,133601 (2010).
[CrossRef] [PubMed]

K. J. Boiler, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett.66,2593–2596 (1991).
[CrossRef]

M. S. Shahriar and P. R. Hemmer, “Direct excitation of microwave-spin dressed states using a laser-excited resonance Raman interaction,” Phys. Rev. Lett.65,1865–1868 (1990).
[CrossRef] [PubMed]

Phys. Scr.

J. Dimitrijević and D. Arsenović, “Simple analytical expressions for the analysis of the phase-dependent electromagnetically induced transparency in a double-Λ atomic scheme,” Phys. Scr.T149, 014007 (2012).
[CrossRef]

Rev. Mod. Phys.

M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys.75,457–472 (2003).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77,633–673 (2005).
[CrossRef]

Other

Y. Zhang and M. Xiao, Multi-Wave Mixing Processes (Springer, Berlin, 2009).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Level configurations for a double-lambda system coupled by two orthogonally polarized laser fields resonant with the lower excited state, represented (a) in the circular basis where the two circularly polarized fields are E1 and E2, and (b) in the linear basis where the two linearly polarized fields are Ec and Ep. Here, | X = ( | 3 + | 4 ) / 2, | Y = ( | 3 | 4 ) / 2. Due to the selection rules and Clebsch-Gordan coefficients of Rb, E1 couples |3〉 → |2〉, |1〉 both with Rabi frequency Ω1, and E2 couples |4〉 → |2〉, |1〉 with Rabi frequency Ω2, −Ω2 respectively. Similarly, Ep couples |Y〉 → |2〉, |X〉 → |1〉 both with Rabi frequency Ωp, and Ec couples |X〉 → |2〉, |Y〉 → |1〉 both with Rabi frequency Ωc.

Fig. 2
Fig. 2

Schematics of the experimental setup. AOM: acoustic-optical modulator, PZT: piezoelectric transducer, PBS: polarization beam splitter, PD: photo-detector.

Fig. 3
Fig. 3

Calculated probe transmission (normalized to the input) vs the relative phase between the probe and the pump for different δB in the cold atom regime, where the excited state decay rate Γ/2π = 6 MHz. (a) The black dashed, grey solid and black solid curves are for δB = 0 Hz, 10 Hz and 80 Hz respectively. (b) The black dashed, grey solid and black solid curves are for δB = 0 Hz, −10 Hz and −80 Hz respectively. Simulation parameters: Ωc/2π = 20 kHz, Ωp/2π = 5 kHz, γ1/2π = γ2/2π = 10 Hz, and the optical depth was 0.15. Changes in the optical depth do not affect the main features of the curves as described in the text.

Fig. 4
Fig. 4

(a) Measured output probe transmission vs the relative phase for different δB. The black dashed, black solid and grey solid curves are for δB = 0 Hz, 40 Hz and −40 Hz respectively. Experimental conditions are in section 3. (b) Corresponding theoretical results where the excited state decay rate Γ/2π = 500 MHz. Other simulation parameters: γ1/2π = 25 Hz, γ2/2π = 28 Hz, Ωc/2π = 240 kHz, Ωp/2π = 60 kHz, and the optical depth was 15.

Fig. 5
Fig. 5

Probe transmission vs δB for several relative phases. (a) Measured results, with experimental conditions stated in section 3. (b) Calculated results, with identical simulation parameters as used in Fig. 4(b).

Fig. 6
Fig. 6

Measured slow and fast light results. Probe pulse transmission is normalized to the reference (black solid curve) pulse. The blue dashed curve is the fast light, and the red dashdotted curve is the slow light. (a) δB = −91 Hz. (b) relative phase φ = 0.

Fig. 7
Fig. 7

Calculated spectrum of the real part of (ρ1X +ρ2Y)/Ep vs the probe frequency, with the pump frequency fixed. (a) Relative phase manipulation for δB = −91 Hz. (b) Magnetic field manipulation for the relative phase φ = 0. Simulation parameters are the same as in Fig. 4(b).

Equations (7)

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H ^ = 2 π δ B ( | 3 3 | | 4 4 | ) / 2 + Δ | 1 1 | + Ω 1 | 2 3 | + Ω 2 | 2 4 | + Ω 1 | 1 3 | Ω 2 | 1 4 | + H . c ..
( E 1 E 2 ) = 1 2 ( 1 i 1 i ) ( E c E p )
ρ ^ ˙ = 1 i h ¯ [ H ^ , ρ ^ ] + Γ ^ exc Γ ^ rel
Ω 1 z = i κ ( ρ 23 + ρ 13 )
Ω 2 z = i κ ( ρ 24 ρ 14 )
W p | Ω p ( L ) | 2 = ( | Ω 1 ( L ) | 2 + | Ω 2 ( L ) | 2 2 | Ω 1 ( L ) | | Ω 2 ( L ) | × cos θ ) / 2
v g = c n + ω d n d ω ,

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