Abstract

We perform Zeeman spectroscopy on a Rydberg electromagnetically induced transparency (EIT) system in a room-temperature Cs vapor cell, in magnetic fields up to 50 Gauss. The magnetic interactions of the |6S1/2 Fg = 4> ground, |6P3/2 Fe = 5> intermediate, and |33S1/2> Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the Paschen-Back regimes, respectively. We explain the dependence of Rydberg EIT spectra on the magnetic field and polarization. The asymmetry of the EIT spectra, which is caused by the quadratic Zeeman effect of the intermediate state, becomes paramount in magnetic fields ≥40 Gauss. We investigate the interplay between Rydberg EIT, which reduces photon scattering, and optical pumping, which relies on photon scattering. We employ a quantum Monte Carlo wave-function approach to quantitatively model the spectra and their asymmetry behavior. Simulated spectra are in good agreement with the experimental data.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (2)

A. E. Mironov, J. D. Hewitt, and J. G. Eden, “Spin polarization of Rb and Cs np 2P3/2 (n=5, 6) atoms by circularly polarized photoexcitation of a transient diatomic molecule,” Phys. Rev. Lett. 118(11), 113201 (2017).
[Crossref] [PubMed]

L. Ma, D. A. Anderson, and G. Raithel, “Paschen-Back effect and Rydberg-state diamagnetism in vapor-cell electromagnetically induced transparency,” Phys. Rev. A 95(6), 061804 (2017).

2016 (4)

S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
[Crossref]

F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
[Crossref]

Y. C. Jiao, X. X. Han, Z. W. Yang, J. K. Li, G. Raithel, J. M. Zhao, and S. T. Jia, “Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields,” Phys. Rev. A (Coll. Park) 94(2), 023832 (2016).
[Crossref]

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

2014 (1)

M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, “Universal nonequilibrium properties of dissipative Rydberg gases,” Phys. Rev. Lett. 113(21), 210401 (2014).
[Crossref] [PubMed]

2013 (4)

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[Crossref] [PubMed]

J. A. Sedlacek, A. Schwettmann, H. Kübler, and J. P. Shaffer, “Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell,” Phys. Rev. Lett. 111(6), 063001 (2013).
[Crossref] [PubMed]

Z. S. He, J. H. Tsai, Y. Y. Chang, C. C. Liao, and C. C. Tsai, “Ladder-type electromagnetically induced transparency with optical pumping effect,” Phys. Rev. A 87(3), 033402 (2013).
[Crossref]

H. Saßmannshausen, F. Merkt, and J. Deiglmayr, “High-resolution spectroscopy of Rydberg states in an ultracold cesium gas,” Phys. Rev. A 87(3), 032519 (2013).
[Crossref]

2012 (3)

J. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012).
[Crossref]

Y. O. Dudin and A. Kuzmich, “Strongly interacting Rydberg excitations of a cold atomic gas,” Science 336(6083), 887–889 (2012).
[Crossref] [PubMed]

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
[Crossref] [PubMed]

2011 (1)

H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S1/2–5P3/2–5D3/2 transition of 87Rb atoms,” J. Phys. At. Mol. Opt. Phys. 44(5), 055004 (2011).
[Crossref]

2010 (1)

S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, “Dynamical phase transitions and instabilities in open atomic many-body systems,” Phys. Rev. Lett. 105(1), 015702 (2010).
[Crossref] [PubMed]

2009 (2)

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009).
[Crossref]

V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458(7241), 1005–1008 (2009).
[Crossref] [PubMed]

2008 (1)

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4(11), 890–894 (2008).
[Crossref]

2007 (1)

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

2004 (1)

D. Staack, Y. Raitses, and N. J. Fisch, “Shielded electrostatic probe for nonperturbing plasma measurements in hall thrusters,” Rev. Sci. Instrum. 75(2), 393–399 (2004).
[Crossref]

2002 (1)

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65(2), 023806 (2002).
[Crossref]

2000 (1)

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85(10), 2208–2211 (2000).
[Crossref] [PubMed]

1997 (1)

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

1995 (2)

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems,” Phys. Rev. A 52(3), 2302–2311 (1995).
[Crossref] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666 (1995).
[Crossref] [PubMed]

1993 (1)

1992 (1)

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68(5), 580–583 (1992).
[Crossref] [PubMed]

1978 (1)

M. L. Zimmerman, J. C. Castro, and D. Kleppner, “Diamagnetic structure of Na Rydberg states,” Phys. Rev. Lett. 40(16), 1083–1086 (1978).
[Crossref]

1972 (1)

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
[Crossref]

Adams, C. S.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[Crossref] [PubMed]

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4(11), 890–894 (2008).
[Crossref]

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

Anderson, D. A.

L. Ma, D. A. Anderson, and G. Raithel, “Paschen-Back effect and Rydberg-state diamagnetism in vapor-cell electromagnetically induced transparency,” Phys. Rev. A 95(6), 061804 (2017).

Auzinsh, M.

S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
[Crossref]

Bao, S. X.

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

Bason, M. G.

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4(11), 890–894 (2008).
[Crossref]

Bendkowsky, V.

V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458(7241), 1005–1008 (2009).
[Crossref] [PubMed]

Böttcher, F.

F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
[Crossref]

Budker, D.

S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
[Crossref]

Butscher, B.

V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458(7241), 1005–1008 (2009).
[Crossref] [PubMed]

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4(11), 890–894 (2008).
[Crossref]

Carr, C.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[Crossref] [PubMed]

Castin, Y.

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10(3), 524–538 (1993).
[Crossref]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68(5), 580–583 (1992).
[Crossref] [PubMed]

Castro, J. C.

M. L. Zimmerman, J. C. Castro, and D. Kleppner, “Diamagnetic structure of Na Rydberg states,” Phys. Rev. Lett. 40(16), 1083–1086 (1978).
[Crossref]

Chang, Y. Y.

Z. S. He, J. H. Tsai, Y. Y. Chang, C. C. Liao, and C. C. Tsai, “Ladder-type electromagnetically induced transparency with optical pumping effect,” Phys. Rev. A 87(3), 033402 (2013).
[Crossref]

Cirac, J. I.

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85(10), 2208–2211 (2000).
[Crossref] [PubMed]

Côté, R.

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85(10), 2208–2211 (2000).
[Crossref] [PubMed]

Dalibard, J.

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10(3), 524–538 (1993).
[Crossref]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68(5), 580–583 (1992).
[Crossref] [PubMed]

Deiglmayr, J.

H. Saßmannshausen, F. Merkt, and J. Deiglmayr, “High-resolution spectroscopy of Rydberg states in an ultracold cesium gas,” Phys. Rev. A 87(3), 032519 (2013).
[Crossref]

Diehl, S.

M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, “Universal nonequilibrium properties of dissipative Rydberg gases,” Phys. Rev. Lett. 113(21), 210401 (2014).
[Crossref] [PubMed]

S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, “Dynamical phase transitions and instabilities in open atomic many-body systems,” Phys. Rev. Lett. 105(1), 015702 (2010).
[Crossref] [PubMed]

Dudin, Y. O.

Y. O. Dudin and A. Kuzmich, “Strongly interacting Rydberg excitations of a cold atomic gas,” Science 336(6083), 887–889 (2012).
[Crossref] [PubMed]

Dunn, M. H.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems,” Phys. Rev. A 52(3), 2302–2311 (1995).
[Crossref] [PubMed]

Eden, J. G.

A. E. Mironov, J. D. Hewitt, and J. G. Eden, “Spin polarization of Rb and Cs np 2P3/2 (n=5, 6) atoms by circularly polarized photoexcitation of a transient diatomic molecule,” Phys. Rev. Lett. 118(11), 113201 (2017).
[Crossref] [PubMed]

Fazio, R.

S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, “Dynamical phase transitions and instabilities in open atomic many-body systems,” Phys. Rev. Lett. 105(1), 015702 (2010).
[Crossref] [PubMed]

Firstenberg, O.

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
[Crossref] [PubMed]

Fisch, N. J.

D. Staack, Y. Raitses, and N. J. Fisch, “Shielded electrostatic probe for nonperturbing plasma measurements in hall thrusters,” Rev. Sci. Instrum. 75(2), 393–399 (2004).
[Crossref]

Fulton, D. J.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems,” Phys. Rev. A 52(3), 2302–2311 (1995).
[Crossref] [PubMed]

Gaj, A.

F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
[Crossref]

Garrahan, J. P.

M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, “Universal nonequilibrium properties of dissipative Rydberg gases,” Phys. Rev. Lett. 113(21), 210401 (2014).
[Crossref] [PubMed]

Gea-Banacloche, J.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666 (1995).
[Crossref] [PubMed]

Gorshkov, A. V.

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
[Crossref] [PubMed]

Han, X. X.

Y. C. Jiao, X. X. Han, Z. W. Yang, J. K. Li, G. Raithel, J. M. Zhao, and S. T. Jia, “Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields,” Phys. Rev. A (Coll. Park) 94(2), 023832 (2016).
[Crossref]

Happer, W.

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F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
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M. L. Zimmerman, J. C. Castro, and D. Kleppner, “Diamagnetic structure of Na Rydberg states,” Phys. Rev. Lett. 40(16), 1083–1086 (1978).
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J. A. Sedlacek, A. Schwettmann, H. Kübler, and J. P. Shaffer, “Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell,” Phys. Rev. Lett. 111(6), 063001 (2013).
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Y. C. Jiao, X. X. Han, Z. W. Yang, J. K. Li, G. Raithel, J. M. Zhao, and S. T. Jia, “Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields,” Phys. Rev. A (Coll. Park) 94(2), 023832 (2016).
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M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666 (1995).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
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Liao, C. C.

Z. S. He, J. H. Tsai, Y. Y. Chang, C. C. Liao, and C. C. Tsai, “Ladder-type electromagnetically induced transparency with optical pumping effect,” Phys. Rev. A 87(3), 033402 (2013).
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F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
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F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
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J. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
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L. Ma, D. A. Anderson, and G. Raithel, “Paschen-Back effect and Rydberg-state diamagnetism in vapor-cell electromagnetically induced transparency,” Phys. Rev. A 95(6), 061804 (2017).

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M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, “Universal nonequilibrium properties of dissipative Rydberg gases,” Phys. Rev. Lett. 113(21), 210401 (2014).
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H. Saßmannshausen, F. Merkt, and J. Deiglmayr, “High-resolution spectroscopy of Rydberg states in an ultracold cesium gas,” Phys. Rev. A 87(3), 032519 (2013).
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S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, “Dynamical phase transitions and instabilities in open atomic many-body systems,” Phys. Rev. Lett. 105(1), 015702 (2010).
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A. E. Mironov, J. D. Hewitt, and J. G. Eden, “Spin polarization of Rb and Cs np 2P3/2 (n=5, 6) atoms by circularly polarized photoexcitation of a transient diatomic molecule,” Phys. Rev. Lett. 118(11), 113201 (2017).
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A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4(11), 890–894 (2008).
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A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
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D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems,” Phys. Rev. A 52(3), 2302–2311 (1995).
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V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458(7241), 1005–1008 (2009).
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H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S1/2–5P3/2–5D3/2 transition of 87Rb atoms,” J. Phys. At. Mol. Opt. Phys. 44(5), 055004 (2011).
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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
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F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
[Crossref]

J. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012).
[Crossref]

V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458(7241), 1005–1008 (2009).
[Crossref] [PubMed]

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T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
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S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
[Crossref]

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L. Ma, D. A. Anderson, and G. Raithel, “Paschen-Back effect and Rydberg-state diamagnetism in vapor-cell electromagnetically induced transparency,” Phys. Rev. A 95(6), 061804 (2017).

Y. C. Jiao, X. X. Han, Z. W. Yang, J. K. Li, G. Raithel, J. M. Zhao, and S. T. Jia, “Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields,” Phys. Rev. A (Coll. Park) 94(2), 023832 (2016).
[Crossref]

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D. Staack, Y. Raitses, and N. J. Fisch, “Shielded electrostatic probe for nonperturbing plasma measurements in hall thrusters,” Rev. Sci. Instrum. 75(2), 393–399 (2004).
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Raizen, M.

S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
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C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
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S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
[Crossref]

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D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85(10), 2208–2211 (2000).
[Crossref] [PubMed]

Saffman, M.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009).
[Crossref]

Saßmannshausen, H.

H. Saßmannshausen, F. Merkt, and J. Deiglmayr, “High-resolution spectroscopy of Rydberg states in an ultracold cesium gas,” Phys. Rev. A 87(3), 032519 (2013).
[Crossref]

Schlagmüller, M.

F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
[Crossref]

Schwettmann, A.

J. A. Sedlacek, A. Schwettmann, H. Kübler, and J. P. Shaffer, “Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell,” Phys. Rev. Lett. 111(6), 063001 (2013).
[Crossref] [PubMed]

J. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012).
[Crossref]

Sedlacek, J.

J. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012).
[Crossref]

Sedlacek, J. A.

J. A. Sedlacek, A. Schwettmann, H. Kübler, and J. P. Shaffer, “Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell,” Phys. Rev. Lett. 111(6), 063001 (2013).
[Crossref] [PubMed]

Shaffer, J. P.

J. A. Sedlacek, A. Schwettmann, H. Kübler, and J. P. Shaffer, “Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell,” Phys. Rev. Lett. 111(6), 063001 (2013).
[Crossref] [PubMed]

J. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, “Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012).
[Crossref]

V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458(7241), 1005–1008 (2009).
[Crossref] [PubMed]

Shepherd, S.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems,” Phys. Rev. A 52(3), 2302–2311 (1995).
[Crossref] [PubMed]

Sinclair, B. D.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically induced transparency: A comparison of V, Λ, and cascade systems,” Phys. Rev. A 52(3), 2302–2311 (1995).
[Crossref] [PubMed]

Staack, D.

D. Staack, Y. Raitses, and N. J. Fisch, “Shielded electrostatic probe for nonperturbing plasma measurements in hall thrusters,” Rev. Sci. Instrum. 75(2), 393–399 (2004).
[Crossref]

Szymanski, K.

S. M. Rochester, K. Szymański, M. Raizen, S. Pustelny, M. Auzinsh, and D. Budker, “Efficient polarization of high-angular-momentum systems,” Phys. Rev. A 94(4), 043416 (2016).
[Crossref]

Tomadin, A.

S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, “Dynamical phase transitions and instabilities in open atomic many-body systems,” Phys. Rev. Lett. 105(1), 015702 (2010).
[Crossref] [PubMed]

Tsai, C. C.

Z. S. He, J. H. Tsai, Y. Y. Chang, C. C. Liao, and C. C. Tsai, “Ladder-type electromagnetically induced transparency with optical pumping effect,” Phys. Rev. A 87(3), 033402 (2013).
[Crossref]

Tsai, J. H.

Z. S. He, J. H. Tsai, Y. Y. Chang, C. C. Liao, and C. C. Tsai, “Ladder-type electromagnetically induced transparency with optical pumping effect,” Phys. Rev. A 87(3), 033402 (2013).
[Crossref]

Urban, E.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009).
[Crossref]

Vuletic, V.

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488(7409), 57–60 (2012).
[Crossref] [PubMed]

Wade, C. G.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[Crossref] [PubMed]

Walker, T. G.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009).
[Crossref]

Weatherill, K. J.

C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, “Nonequilibrium phase transition in a dilute Rydberg ensemble,” Phys. Rev. Lett. 111(11), 113901 (2013).
[Crossref] [PubMed]

A. K. Mohapatra, M. G. Bason, B. Butscher, K. J. Weatherill, and C. S. Adams, “A giant electro-optic effect using polarizable dark states,” Nat. Phys. 4(11), 890–894 (2008).
[Crossref]

Westphal, K. M.

F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hofferberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93(3), 032512 (2016).
[Crossref]

Xiao, L. T.

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

Xiao, M.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666 (1995).
[Crossref] [PubMed]

Yang, Z. W.

Y. C. Jiao, X. X. Han, Z. W. Yang, J. K. Li, G. Raithel, J. M. Zhao, and S. T. Jia, “Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields,” Phys. Rev. A (Coll. Park) 94(2), 023832 (2016).
[Crossref]

Yavuz, D. D.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009).
[Crossref]

Ye, C. Y.

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65(2), 023806 (2002).
[Crossref]

Zhang, H.

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

Zhang, L. J.

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

Zhao, J. M.

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

Y. C. Jiao, X. X. Han, Z. W. Yang, J. K. Li, G. Raithel, J. M. Zhao, and S. T. Jia, “Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields,” Phys. Rev. A (Coll. Park) 94(2), 023832 (2016).
[Crossref]

Zhou, J.

S. X. Bao, H. Zhang, J. Zhou, L. J. Zhang, J. M. Zhao, L. T. Xiao, and S. T. Jia, “Polarization spectra of Zeeman sublevels in Rydberg electromagnetically induced transparency,” Phys. Rev. A 94(4), 043822 (2016).
[Crossref]

Zibrov, A. S.

C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A 65(2), 023806 (2002).
[Crossref]

Zimmerman, M. L.

M. L. Zimmerman, J. C. Castro, and D. Kleppner, “Diamagnetic structure of Na Rydberg states,” Phys. Rev. Lett. 40(16), 1083–1086 (1978).
[Crossref]

Zoller, P.

S. Diehl, A. Tomadin, A. Micheli, R. Fazio, and P. Zoller, “Dynamical phase transitions and instabilities in open atomic many-body systems,” Phys. Rev. Lett. 105(1), 015702 (2010).
[Crossref] [PubMed]

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85(10), 2208–2211 (2000).
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Figures (5)

Fig. 1
Fig. 1 (a) Energy-level scheme of cesium Rydberg EIT without (left) and with (right) magnetic field. The 852-nm probe laser is resonant with the field-free transition 6S1/2 Fg = 4 → 6P3/2 Fe = 5, and the 510-nm coupling laser scans through the 6P3/2 Fe = 5 → 33S1/2 Rydberg-state transition. The coupling detuning relative to the field-free transition 6P3/2 Fe = 5 → 33S1/2 is denoted Δc. The right side of the energy level scheme shows the Zeeman sublevels of the |g>, |e> and |r> states when a magnetic field on the order of ten Gauss is applied (main separations not to scale). The level ladders that lead to strong signals in the EIT spectra measured with linearly polarized fields (laser electric fields pointing along x) are labeled A, B, C, D and A′, B′, C′ (line thickness increases with line strength). The numbers show Rabi frequencies Ω/2π in MHz, for our experimental conditions. The stronger coupling transitions (solid green lines, Type I) approximately maintain the electron spin, while in the weaker ones (dashed green lines, Type II) the spin mostly flips. (b) Schematic of the experimental setup. The probe and coupling beams are counter-propagating and focused into the center of the cell, which is contained in a cylindrical solenoid and multi-layer magnetic shield. The indicated coordinates define magnetic-field and polarization directions. Half-wave plates (λ/2), Glan-Taylor polarizers (GTP) and quarter-wave plates (λ/4) are used for polarization control.
Fig. 2
Fig. 2 Measurements (left axes, black solid lines) and simulations (right axes, red dashed lines) of Rydberg EIT spectra with magnetic fields of 5 Gauss (a) and 40 Gauss (b). The probe and coupling beams are both linearly polarized in x-direction (transverse to the magnetic field). The experimental data show an increase in transmission above its coupling-laser-free value. EIT on the various three-level ladder systems identified in Fig. 1(a) results in several peaks. The QMCWF simulations show the number of photons scattered by a typical atom sample in the cell (note the number of scattered photons is plotted in descending direction). EIT corresponds with a reduction in photon scattering. With increasing magnetic field, the Rydberg EIT line splits into two approximately symmetric main peaks A′ and A. Asymmetric satellite lines, labeled B′, C′ and B, C, D, appear outside of the interval between A′ and A. The peak labels correspond to the transition labels in Fig. 1(a).
Fig. 3
Fig. 3 (a) Experimental (symbols) and calculated (solid lines) frequency shifts of main peaks A′ (black squares) and A (red circles), and of the blue-shifted satellite peaks B (blue up triangles), C (pink down triangles) and D (green stars). The dashed lines show line shifts calculated under the assumption of no quadratic Zeeman effect. (b) Line intervals divided by magnetic field for the A′-A interval (black squares), and for the average separations between adjacent lines pairs, A-B, B-C and C-D (red circles), as a function of magnetic field. Symbols show experimental data, solid lines show calculated values that take quadratic Zeeman shifts into account.
Fig. 4
Fig. 4 Left: simulated photon scattering rate vs coupling detuning and atom velocity for 40 Gauss magnetic field in x-polarized coupling and probe fields with respective radial Rabi frequencies ΩC,r/(2π) = 8 MHz and ΩP,r/(2π) = 2 MHz, on a linear gray scale ranging from 0 (white) to 2.8 × 106 s−1 (black) per atom. The labels of the features visible in the plot correspond with the labels Fig. 1. Middle and right (zoom-in): simulated expectation values for the ground-state < mI + mJ >, obtained from the same simulation as on the left, on color scales given by the color bars. Regions of strong photon scattering correspond with fairly efficient optical pumping into the aligned states, |mF,g = ± 4>. In the regions of large photon scattering the Zeeman shifts of the probe cycling transitions, |mF,g = ± 4> → |mF,e = ± 5>, are compensated by the Doppler effect at v≈48 m/s. The numbers indicated on the figures show the approximate values of <mI + mJ> on the main EIT resonances, A and A′, and close to them. It is seen that the EIT-induced reduction in probe photon scattering is accompanied by a reduction in optical-pumping efficiency. The plots also show a significant asymmetry between positive and negative v, and between positive and negative ΔC.
Fig. 5
Fig. 5 Experimental (top) and calculated (bottom) Rydberg EIT spectra in 852 σ +/ 510 σ and 852 σ -/ 510 σ + polarized probe and coupling fields. The magnetic fields are 5 Gauss (a) and 40 Gauss (b). The EIT spectra in (a) are approximately symmetric about ΔC = 0, while they are highly asymmetric in shape and background absorption in Fig. 5(b). The asymmetry is due to the quadratic Zeeman effect of the intermediate 6P3/2 level. The line labels and types are explained in Fig. 1 and in the text.

Tables (1)

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Table 1 Sketch of the total Hamiltonian of our ladder-type system.

Equations (6)

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H ^ 0 =( Δ P + k P υ+ i 2 Γ e )|ee|( Δ P + Δ C +( k P k C )υ+ i 2 Γ r )|rr|,
H ^ hfs = A hfs I ^ J ^ 2 + B hfs [ 3 ( I ^ J ^ ) 2 +(3 2 /2)( I ^ J ^ )I(I+1)J(J+1) ] 2I(2I1)J(2J1) ,
H ^ B = μ B ( g J J ^ z + g I I ^ z )B,
H ^ i = E i ε i d ^ i /2
Δ g = μ B B gF,g m F,g Δ e = μ B B gF,e m F,e Δ r = μ B B( g J,r m J + g I m I )+ A hfs,r m I m J
υ= λ P 2π ( Δ P + Δ g Δ e ) Δ C = Δ r + Δ e ( λ P λ C 1 )( Δ P + Δ g ) λ P λ C = Δ r +0.67 Δ e 1.67( Δ P + Δ g )

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