Abstract

We measure the electromagnetically induced transparency (EIT) of a single-frequency comb mode interacting with laser-cooled Rb87 atoms. A Λ hyperfine level structure in a D2 transition is used in the configuration of co-propagated probe (frequency comb) and coupling (continuous-wave) laser fields. The signature of EIT in the transmission of a single comb mode as well as the radiation pressure force is experimentally detected. The results are satisfactorily reproduced by the developed theoretical models, where EIT is seen to occur due to coherent accumulation. Our results could find application in quantum computing and communication with optical frequency combs.

© 2019 Optical Society of America

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References

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    [Crossref]

2019 (1)

N. Šantić, D. Buhin, D. Kovačić, I. Krešić, D. Aumiler, and T. Ban, “Cooling of atoms using an optical frequency comb,” Sci. Rep. 9, 2510 (2019).
[Crossref]

2018 (1)

S. K. Lee, N. S. Han, T. H. Yoon, and M. Cho, “Frequency comb single-photon interferometry,” Commun. Phys. 1, 51 (2018).
[Crossref]

2017 (6)

L. Ma, O. Slattery, and X. Tang, “Optical quantum memory based on electromagnetically induced transparency,” J. Opt. 19, 043001 (2017).
[Crossref]

B. Lomsadze and S. T. Cundiff, “Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy,” Science 357, 1389–1391 (2017).
[Crossref]

A. Zhang, V. A. Sautenkov, Y. V. Rostovtsev, and G. R. Welch, “Observation of coherent effects using a mode-locked rubidium laser,” J. Phys. B 50, 035503 (2017).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,” Nat. Commun. 8, 15645 (2017).
[Crossref]

D. A. Long, A. J. Fleisher, D. F. Plusquellic, and J. T. Hodges, “Electromagnetically induced transparency in vacuum and buffer gas potassium cells probed via electro-optic frequency combs,” Opt. Lett. 42, 4430–4433 (2017).
[Crossref]

2016 (1)

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

2015 (2)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
[Crossref]

2014 (2)

J. Roslund, R. M. De Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref]

2012 (1)

O. Pinel, P. Jian, R. M. De Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett. 108, 083601 (2012).
[Crossref]

2011 (1)

E. Ilinova, M. Ahmad, and A. Derevianko, “Doppler cooling with coherent trains of laser pulses and a tunable velocity comb,” Phys. Rev. A 84, 033421 (2011).
[Crossref]

2010 (4)

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
[Crossref]

D. Aumiler, “Coherent population trapping in 87rb atoms induced by the optical frequency comb excitation,” Phys. Rev. A 82, 055402(2010).
[Crossref]

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
[Crossref]

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, and C. Monroe, “Entanglement of atomic qubits using an optical frequency comb,” Phys. Rev. Lett. 104, 140501 (2010).
[Crossref]

2009 (1)

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329 (2009).
[Crossref]

2007 (1)

A. A. Soares and L. E. E. de Araujo, “Coherent accumulation of excitation in the electromagnetically induced transparency of an ultrashort pulse train,” Phys. Rev. A 76, 043818 (2007).
[Crossref]

2006 (3)

T. Ban, D. Aumiler, H. Skenderović, and G. Pichler, “Mapping of the optical frequency comb to the atom-velocity comb,” Phys. Rev. A 73, 043407 (2006).
[Crossref]

Y. Niu and S. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
[Crossref]

G. J. De Valcarcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[Crossref]

2005 (2)

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

V. A. Sautenkov, Y. V. Rostovtsev, C. Y. Ye, G. R. Welch, O. Kocharovskaya, and M. O. Scully, “Electromagnetically induced transparency in rubidium vapor prepared by a comb of short optical pulses,” Phys. Rev. A 71, 063804 (2005).
[Crossref]

2004 (1)

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[Crossref]

2003 (1)

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Coherent accumulation in two-level atoms excited by a train of ultrashort pulses,” Opt. Commun. 215, 69–73 (2003).
[Crossref]

2002 (2)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[Crossref]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref]

2001 (1)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

1997 (1)

S. Hopkins, E. Usadi, H. Chen, and A. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level λ-type systems,” Opt. Commun. 138, 185–192 (1997).
[Crossref]

1995 (1)

D. J. Fulton, R. R. Moseley, S. Shepherd, B. D. Sinclair, and M. H. Dunn, “Effects of Zeeman splitting of electromagnetically-induced transparency,” Opt. Commun. 116, 231–239 (1995).
[Crossref]

1990 (1)

J. Harris, S. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref]

Acioli, L. H.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Coherent accumulation in two-level atoms excited by a train of ultrashort pulses,” Opt. Commun. 215, 69–73 (2003).
[Crossref]

Adler, F.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
[Crossref]

Afzelius, M.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
[Crossref]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329 (2009).
[Crossref]

Ahmad, M.

E. Ilinova, M. Ahmad, and A. Derevianko, “Doppler cooling with coherent trains of laser pulses and a tunable velocity comb,” Phys. Rev. A 84, 033421 (2011).
[Crossref]

Amari, A.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
[Crossref]

Arzani, F.

Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,” Nat. Commun. 8, 15645 (2017).
[Crossref]

Aumiler, D.

N. Šantić, D. Buhin, D. Kovačić, I. Krešić, D. Aumiler, and T. Ban, “Cooling of atoms using an optical frequency comb,” Sci. Rep. 9, 2510 (2019).
[Crossref]

D. Aumiler, “Coherent population trapping in 87rb atoms induced by the optical frequency comb excitation,” Phys. Rev. A 82, 055402(2010).
[Crossref]

T. Ban, D. Aumiler, H. Skenderović, and G. Pichler, “Mapping of the optical frequency comb to the atom-velocity comb,” Phys. Rev. A 73, 043407 (2006).
[Crossref]

Azaña, J.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Ban, T.

N. Šantić, D. Buhin, D. Kovačić, I. Krešić, D. Aumiler, and T. Ban, “Cooling of atoms using an optical frequency comb,” Sci. Rep. 9, 2510 (2019).
[Crossref]

T. Ban, D. Aumiler, H. Skenderović, and G. Pichler, “Mapping of the optical frequency comb to the atom-velocity comb,” Phys. Rev. A 73, 043407 (2006).
[Crossref]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Bosco, C. A. C.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Coherent accumulation in two-level atoms excited by a train of ultrashort pulses,” Opt. Commun. 215, 69–73 (2003).
[Crossref]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Budker, D.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[Crossref]

Buhin, D.

N. Šantić, D. Buhin, D. Kovačić, I. Krešić, D. Aumiler, and T. Ban, “Cooling of atoms using an optical frequency comb,” Sci. Rep. 9, 2510 (2019).
[Crossref]

Cai, Y.

Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,” Nat. Commun. 8, 15645 (2017).
[Crossref]

Campbell, W.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, and C. Monroe, “Entanglement of atomic qubits using an optical frequency comb,” Phys. Rev. Lett. 104, 140501 (2010).
[Crossref]

Caspani, L.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Chalopin, B.

O. Pinel, P. Jian, R. M. De Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett. 108, 083601 (2012).
[Crossref]

Chen, H.

S. Hopkins, E. Usadi, H. Chen, and A. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level λ-type systems,” Opt. Commun. 138, 185–192 (1997).
[Crossref]

Chen, M.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref]

Cho, M.

S. K. Lee, N. S. Han, T. H. Yoon, and M. Cho, “Frequency comb single-photon interferometry,” Commun. Phys. 1, 51 (2018).
[Crossref]

Chu, S. T.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Cino, A.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Cortés, L. R.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Cossel, K. C.

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
[Crossref]

Cundiff, S. T.

B. Lomsadze and S. T. Cundiff, “Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy,” Science 357, 1389–1391 (2017).
[Crossref]

de Araujo, L. E. E.

A. A. Soares and L. E. E. de Araujo, “Coherent accumulation of excitation in the electromagnetically induced transparency of an ultrashort pulse train,” Phys. Rev. A 76, 043818 (2007).
[Crossref]

De Araujo, R. M.

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M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
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D. J. Fulton, R. R. Moseley, S. Shepherd, B. D. Sinclair, and M. H. Dunn, “Effects of Zeeman splitting of electromagnetically-induced transparency,” Opt. Commun. 116, 231–239 (1995).
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L. Ma, O. Slattery, and X. Tang, “Optical quantum memory based on electromagnetically induced transparency,” J. Opt. 19, 043001 (2017).
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A. A. Soares and L. E. E. de Araujo, “Coherent accumulation of excitation in the electromagnetically induced transparency of an ultrashort pulse train,” Phys. Rev. A 76, 043818 (2007).
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F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
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Treps, N.

Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,” Nat. Commun. 8, 15645 (2017).
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Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
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J. Roslund, R. M. De Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

O. Pinel, P. Jian, R. M. De Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett. 108, 083601 (2012).
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G. J. De Valcarcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
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T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
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S. Hopkins, E. Usadi, H. Chen, and A. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level λ-type systems,” Opt. Commun. 138, 185–192 (1997).
[Crossref]

Usmani, I.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
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Vianna, S. S.

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Coherent accumulation in two-level atoms excited by a train of ultrashort pulses,” Opt. Commun. 215, 69–73 (2003).
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D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
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Walther, A.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
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Weis, A.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
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Welch, G. R.

A. Zhang, V. A. Sautenkov, Y. V. Rostovtsev, and G. R. Welch, “Observation of coherent effects using a mode-locked rubidium laser,” J. Phys. B 50, 035503 (2017).
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V. A. Sautenkov, Y. V. Rostovtsev, C. Y. Ye, G. R. Welch, O. Kocharovskaya, and M. O. Scully, “Electromagnetically induced transparency in rubidium vapor prepared by a comb of short optical pulses,” Phys. Rev. A 71, 063804 (2005).
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M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
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C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
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Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,” Nat. Commun. 8, 15645 (2017).
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D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
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V. A. Sautenkov, Y. V. Rostovtsev, C. Y. Ye, G. R. Welch, O. Kocharovskaya, and M. O. Scully, “Electromagnetically induced transparency in rubidium vapor prepared by a comb of short optical pulses,” Phys. Rev. A 71, 063804 (2005).
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A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
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F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
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S. K. Lee, N. S. Han, T. H. Yoon, and M. Cho, “Frequency comb single-photon interferometry,” Commun. Phys. 1, 51 (2018).
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Zhang, A.

A. Zhang, V. A. Sautenkov, Y. V. Rostovtsev, and G. R. Welch, “Observation of coherent effects using a mode-locked rubidium laser,” J. Phys. B 50, 035503 (2017).
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Zhang, Y.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
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Zheng, Z.

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
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Annu. Rev. Anal. Chem. (1)

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
[Crossref]

Commun. Phys. (1)

S. K. Lee, N. S. Han, T. H. Yoon, and M. Cho, “Frequency comb single-photon interferometry,” Commun. Phys. 1, 51 (2018).
[Crossref]

J. Opt. (1)

L. Ma, O. Slattery, and X. Tang, “Optical quantum memory based on electromagnetically induced transparency,” J. Opt. 19, 043001 (2017).
[Crossref]

J. Phys. B (1)

A. Zhang, V. A. Sautenkov, Y. V. Rostovtsev, and G. R. Welch, “Observation of coherent effects using a mode-locked rubidium laser,” J. Phys. B 50, 035503 (2017).
[Crossref]

Nat. Commun. (1)

Y. Cai, J. Roslund, G. Ferrini, F. Arzani, X. Xu, C. Fabre, and N. Treps, “Multimode entanglement in reconfigurable graph states using optical frequency combs,” Nat. Commun. 8, 15645 (2017).
[Crossref]

Nat. Photonics (1)

J. Roslund, R. M. De Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

Nature (3)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Opt. Commun. (3)

S. Hopkins, E. Usadi, H. Chen, and A. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level λ-type systems,” Opt. Commun. 138, 185–192 (1997).
[Crossref]

D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, “Coherent accumulation in two-level atoms excited by a train of ultrashort pulses,” Opt. Commun. 215, 69–73 (2003).
[Crossref]

D. J. Fulton, R. R. Moseley, S. Shepherd, B. D. Sinclair, and M. H. Dunn, “Effects of Zeeman splitting of electromagnetically-induced transparency,” Opt. Commun. 116, 231–239 (1995).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (9)

Z. Zheng, O. Mishina, N. Treps, and C. Fabre, “Atomic quantum memory for multimode frequency combs,” Phys. Rev. A 91, 031802 (2015).
[Crossref]

D. Aumiler, “Coherent population trapping in 87rb atoms induced by the optical frequency comb excitation,” Phys. Rev. A 82, 055402(2010).
[Crossref]

A. A. Soares and L. E. E. de Araujo, “Coherent accumulation of excitation in the electromagnetically induced transparency of an ultrashort pulse train,” Phys. Rev. A 76, 043818 (2007).
[Crossref]

V. A. Sautenkov, Y. V. Rostovtsev, C. Y. Ye, G. R. Welch, O. Kocharovskaya, and M. O. Scully, “Electromagnetically induced transparency in rubidium vapor prepared by a comb of short optical pulses,” Phys. Rev. A 71, 063804 (2005).
[Crossref]

T. Ban, D. Aumiler, H. Skenderović, and G. Pichler, “Mapping of the optical frequency comb to the atom-velocity comb,” Phys. Rev. A 73, 043407 (2006).
[Crossref]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329 (2009).
[Crossref]

Y. Niu and S. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
[Crossref]

G. J. De Valcarcel, G. Patera, N. Treps, and C. Fabre, “Multimode squeezing of frequency combs,” Phys. Rev. A 74, 061801 (2006).
[Crossref]

E. Ilinova, M. Ahmad, and A. Derevianko, “Doppler cooling with coherent trains of laser pulses and a tunable velocity comb,” Phys. Rev. A 84, 033421 (2011).
[Crossref]

Phys. Rev. Lett. (6)

O. Pinel, P. Jian, R. M. De Araujo, J. Feng, B. Chalopin, C. Fabre, and N. Treps, “Generation and characterization of multimode quantum frequency combs,” Phys. Rev. Lett. 108, 083601 (2012).
[Crossref]

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

J. Harris, S. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref]

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, and C. Monroe, “Entanglement of atomic qubits using an optical frequency comb,” Phys. Rev. Lett. 104, 140501 (2010).
[Crossref]

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. De Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503 (2010).
[Crossref]

Rev. Mod. Phys. (3)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153–1201 (2002).
[Crossref]

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

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Sci. Rep. (1)

N. Šantić, D. Buhin, D. Kovačić, I. Krešić, D. Aumiler, and T. Ban, “Cooling of atoms using an optical frequency comb,” Sci. Rep. 9, 2510 (2019).
[Crossref]

Science (3)

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[Crossref]

B. Lomsadze and S. T. Cundiff, “Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy,” Science 357, 1389–1391 (2017).
[Crossref]

Other (2)

H. J. Metcalf and P. V. D. Straten, Laser Cooling and Trapping (Springer, 1999).

D. A. Steck, “Rubidium 87 D line data,” 2001, http://steck.us/alkalidata .

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Figures (5)

Fig. 1.
Fig. 1. Scheme for observing the single FC mode EIT. (a) Energy levels of the Rb87 D2-line. A cw coupling laser is resonant with the F=1F=2 transition, and the nth FC mode detuning Δ is scanned over the F=2F=2 transition. The nth comb mode has here the role of a probe. The other transitions, driven by the (n+3)rd and (n2)nd comb modes, do not contribute significantly to EIT and can be neglected, producing (b) an effective Λ-system. (c) Setup schematics for the radiative force measurements. Radiative force on cold rubidium atoms induced by co-propagated cw (blue) and FC (black) laser beams is determined by measuring the cloud center of mass displacement in the beam propagation direction. (d) Schematics for measuring the transmission of a single comb mode. After passing through the cloud, the cw coupling beam is separated from the FC beam on a polarizing beam splitter (PBS) and blocked from further measurements. Using a PBS the FC beam is co-propagated with a reference (green) cw laser beam stabilized close to the F=2F=2 transition and a beat with the nth FC mode is observed on a spectrum analyzer.
Fig. 2.
Fig. 2. Theoretical prediction of single comb mode EIT. (a) Time dependence of the imaginary part of optical coherence ρ2,3 in a Λ model. The orange and blue curves show the numerical solutions of Eqs. (3) and (4) at Δ=0.5Γ and Δ=0, respectively. The dashed horizontal lines are the analytical steady-state first-order solutions (see text), proportional to the negative absorption coefficient [1]. Steady-state (b) real and (c) imaginary parts of the optical coherence excited by the nth comb mode. The solid orange lines are the numerical solutions in the Λ model via the impulse approximation [30]. The dashed black lines are steady-state analytical calculations in the first order (see text). The red dots are calculated numerically from the six-level model. Parameters: Ec=86.96V/m, Ef=5.03×104V/m, Δc=0, 150 pulses, Tp=200fs, 1/Trep=80.54MHz.
Fig. 3.
Fig. 3. Experimental (top row) and numerical (bottom row) scans of the radiation pressure force against FC detuning Δ, for varying Δc. Purple solid line: total force. Orange dashed line: force due to excitation of F=2. Red dashed line: force due to excitation of F=1. Green dashed line: force due to excitation of F=3. Black dashed line: force due to excitation of F=0. Columns: scans for different coupling beam detunings Δc of (from left to right) 1.2Γ, 0.7Γ, 0.3Γ, and 1.2Γ. The experimentally used powers of 0.3 and 15 mW for the coupling and the FC beams correspond to the numerically used electric fields Ec=70V/m and Ef=5×104V/m to within the measurement uncertainty.
Fig. 4.
Fig. 4. Experimental (top row) and numerical (bottom row) scans of the radiation pressure force against FC detuning Δ, for varying coupling beam powers at Δc=0. The figure layout is the same as in Fig. 3, except that the upper columns now correspond to different coupling beam powers of (from left to right) 1.55 mW, 0.8 mW, 0.25 mW, and 80 μW and the lower columns correspond to different Ec fields of (from left to right) 150 V/m, 110 V/m, 60 V/m, and 35 V/m.
Fig. 5.
Fig. 5. Left: experimental scans of nth comb mode transmission against detuning Δ from the F=2F=2 transition. The blue squares (red circles) correspond to a scan with the coupling laser off (on). The beat signals for the data points marked (a) and (b) are shown in the plot on the right (lines are guides to the eye). To get the data points in the left plot the beat signal is squared and the area under the curve summed. This quantity is then divided by the same quantity for the case when the MOT was turned off.

Equations (7)

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ddtρm,n=in|[H,ρ]|mΓm,nρm,n,
H=Δ|22|+Δc|11|(μ23Ef(t)|32|+μ13Ec|31|+h.c.),
ρ2,2n,τ=ρ2,2ncos2(θ/2)+ρ3,3nsin2(θ/2)+Im(ρ2,3n)sinθ,ρ3,3n,τ=ρ2,2nsin2(θ/2)+ρ3,3ncos2(θ/2)Im(ρ2,3n)sinθ,ρ2,1n,τ=ρ2,1ncos(θ/2)+iρ3,1nsin(θ/2),ρ2,3n,τ=i2(ρ3,3nρ2,2n)sinθ+ρ2,3ncos2(θ/2)+ρ3,2nsin2(θ/2),ρ3,1n,τ=ρ3,1ncos(θ/2)+iρ2,1nsin(θ/2),
ddtρ2,2=Γ2ρ3,3,ddtρ3,3=Γρ3,3+ΩcIm(ρ3,1),ddtρ2,1=i((ΔΔc)ρ2,1+12Ωcρ2,3),ddtρ2,3=Γ2ρ2,3i(Δρ2,3+12Ωcρ2,1),ddtρ3,1=Γ2ρ3,1+i(Δcρ3,1+12Ωc(ρ1,1ρ3,3)),
ρ2,1(1)(t)=eΓ4tiΔt(ρ2,1ncos(θ/2)f+(t)(12sinθ+iρ2,3ncos2(θ/2)+iρ3,2nsin2(θ/2))g(t)),ρ2,3(1)(t)=eΓ4tiΔt(iρ2,1ncos(θ/2)g(t)(i2sinθρ2,3ncos2(θ/2)ρ3,2nsin2(θ/2))f(t)),
f±(t)={cosh(ηt/2)±Γ2ηsinh(ηt/2),Ωc<Γ21±Γ4t,Ωc=Γ2cos(ηt/2)±Γ2ηsin(ηt/2),Ωc>Γ2,
g(t)={Ωcηsinh(ηt/2),Ωc<Γ2Γ4t,Ωc=Γ2Ωcηsin(ηt/2),Ωc>Γ2,

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