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Potentials of long-range cesium Rydberg molecule

Han Xiao-Xuan Zhao Jian-Ming Li Chang-Yong Jia Suo-Tang

Potentials of long-range cesium Rydberg molecule

Han Xiao-Xuan, Zhao Jian-Ming, Li Chang-Yong, Jia Suo-Tang
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  • Rydberg atom, with a large principal quantum number n, has big size, long lifetime, strong long-range interactions, and so on. These properties make Rydberg atoms potential candidate of quantum gate and single-photon source. Rydberg electron can interact with nearby ground-state atom, which is polarized by the Rydberg electron and is bound to the orbit of Rydberg electrons forming Rydberg molecule. As the kinetic energy of the Rydberg electron is very low, only the lowest partial waves will contribute to the molecular potential.#br#In this paper, the low electron-atom scattering with the semi-classical approximation is introduced, and the pseudopotential of interaction between Rydberg electron and ground-state atom is used to describe the long-range Rydberg molecular potential. Molecular potential curves for cesium (nS, n=30-60) are plotted according to the results of numerical computation, from which the outermost potential depth De and the equilibrium distance r0 of long-range cesium Rydberg molecule are deduced. Potential curves of cesium Rydberg molecules are consistent with the distribution curves in radial probability densities of cesium Rydberg electrons. Dependences of De and r0 on the principal quantum number n are investigated, this has an important role for the experimental measurements. The size of a Rydberg molecule depends on the equilibrium distance r0 and is proportional to the square of effective principal quantum number (n-δ )2. The calculated outermost potential depth De of Rydberg molecule becomes smaller with the increase of principal quantum number n. Rydberg molecule is very sensitive to the external field and can be used to measure and monitor weak signals.
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grant Nos. 11274209, 61475090, 61378013, 61378039), and the Shanxi Scholarship Council of China (Grant No. 2014-009).
    [1]

    Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press) p11-47

    [2]

    Boisseau C, Simbotin I, Côté R 2002 Phys. Rev. Lett. 88 133004

    [3]

    Farooqi S M, Tong D, Krishnan S, Stanojevic J, Zhang Y P, Ensher J R, Estrin A S, Boisseau C, Côté R, Eyler E E, Gould P L 2003 Phys. Rev. Lett. 91 183002

    [4]

    Overstreet K R, Schwettmann A, Tallant J, Shaffer J P 2007 Phys. Rev. A 76 011403

    [5]

    Greene C H, Dickinson A S, Sadeghpour H R 2000 Phys. Rev. Lett. 85 2458

    [6]

    Fermi E 1934 Nuovo Cimento 11 157

    [7]

    Vadla C, Horvatic V, Niemax K 2009 Phys. Rev. A 80 052506

    [8]

    Bendkowsky V, Butscher B, Nipper J, Balewski J B, Shaffer J P, Löw R, Pfau T, Li W, Stanojevic J, Pohl T, Rost J M 2010 Phys. Rev. Lett. 105 163201

    [9]

    Butscher B, Bendkowsky V, Nipper J, Balewski J B, Kukota L, Löw R, Pfau T, Li W, Pohl T, Rost J M 2011 J. Phys. B 44 184004

    [10]

    Samboy N, Stanojevic J, Côté R 2011 Phys. Rev. A 83 050501

    [11]

    Butscher B, Nipper J, Balewski J B, Kukota L, Bendkowsky V, Löw R, Pfau T 2010 Nature Phys. 6 970

    [12]

    Li W, Pohl T, Rost J M, Rittenhouse Seth T, Sadeghpour H R, Nipper J, Butscher B, Balewski J B, Bendkowsky V, Löw R, Pfau T 2011 Science 334 1110

    [13]

    Mayle M, Rittenhouse S T, Schmelcher P, Sadeghpour H R 2012 Phys. Rev. A 85 052511

    [14]

    Kurz M, Schmelcher P 2013 Phys. Rev. A 88 022501

    [15]

    Krupp A T, Gaj A, Balewski J B, Ilzhöfer P, Hofferberth S, Löw R, Pfau T, Kurz M, Schmelcher P 2014 Phys. Rev. Lett. 112 143008

    [16]

    Kurz M, Schmelcher P 2014 J. Phys. B 47 165101

    [17]

    Bendkowsky V 2010 Ph. D. Dissertation (Universität Stuttgart)

    [18]

    Blatt J M, Jackson J D 1949 Phys. Rev. 76 18

    [19]

    O'Malley T F, Spruch L, Rosenberg L 1961 J. Math. Phys. 2 491

    [20]

    Omont A 1997 Journal de Physique 38 1343

    [21]

    Bhatti S A, Cromer C L, Cooke W E 1981 Phys. Rev. A 24 161

    [22]

    He X H, Li B W, Zhang C X 1989 Acta Phys. Sin. 38 1717 (in Chinese) [何兴虹, 李白文, 张承修 1989 物理学报 38 1717]

    [23]

    Fabrikant I I 1986 J. Phys. B 19 1527

    [24]

    Bahrim C, Thumm U, Fabrikant I I 2001 J. Phys. B 34 L195

    [25]

    Bahrim C, Thumm U 2000 Phys. Rev. A 61 022722

    [26]

    Bendkowsky V, Butscher B, Nipper J, Shaffer J P, Löw R, Pfau T 2009 Nature 458 1005

    [27]

    Lorenzen C -J, Niemax K 1984 Z. phys. A 315 127

    [28]

    Overstreet K R, Schwettmann A, Tallant J, Booth D, Shaffer J P 2009 Nature Phys. 5 581

  • [1]

    Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press) p11-47

    [2]

    Boisseau C, Simbotin I, Côté R 2002 Phys. Rev. Lett. 88 133004

    [3]

    Farooqi S M, Tong D, Krishnan S, Stanojevic J, Zhang Y P, Ensher J R, Estrin A S, Boisseau C, Côté R, Eyler E E, Gould P L 2003 Phys. Rev. Lett. 91 183002

    [4]

    Overstreet K R, Schwettmann A, Tallant J, Shaffer J P 2007 Phys. Rev. A 76 011403

    [5]

    Greene C H, Dickinson A S, Sadeghpour H R 2000 Phys. Rev. Lett. 85 2458

    [6]

    Fermi E 1934 Nuovo Cimento 11 157

    [7]

    Vadla C, Horvatic V, Niemax K 2009 Phys. Rev. A 80 052506

    [8]

    Bendkowsky V, Butscher B, Nipper J, Balewski J B, Shaffer J P, Löw R, Pfau T, Li W, Stanojevic J, Pohl T, Rost J M 2010 Phys. Rev. Lett. 105 163201

    [9]

    Butscher B, Bendkowsky V, Nipper J, Balewski J B, Kukota L, Löw R, Pfau T, Li W, Pohl T, Rost J M 2011 J. Phys. B 44 184004

    [10]

    Samboy N, Stanojevic J, Côté R 2011 Phys. Rev. A 83 050501

    [11]

    Butscher B, Nipper J, Balewski J B, Kukota L, Bendkowsky V, Löw R, Pfau T 2010 Nature Phys. 6 970

    [12]

    Li W, Pohl T, Rost J M, Rittenhouse Seth T, Sadeghpour H R, Nipper J, Butscher B, Balewski J B, Bendkowsky V, Löw R, Pfau T 2011 Science 334 1110

    [13]

    Mayle M, Rittenhouse S T, Schmelcher P, Sadeghpour H R 2012 Phys. Rev. A 85 052511

    [14]

    Kurz M, Schmelcher P 2013 Phys. Rev. A 88 022501

    [15]

    Krupp A T, Gaj A, Balewski J B, Ilzhöfer P, Hofferberth S, Löw R, Pfau T, Kurz M, Schmelcher P 2014 Phys. Rev. Lett. 112 143008

    [16]

    Kurz M, Schmelcher P 2014 J. Phys. B 47 165101

    [17]

    Bendkowsky V 2010 Ph. D. Dissertation (Universität Stuttgart)

    [18]

    Blatt J M, Jackson J D 1949 Phys. Rev. 76 18

    [19]

    O'Malley T F, Spruch L, Rosenberg L 1961 J. Math. Phys. 2 491

    [20]

    Omont A 1997 Journal de Physique 38 1343

    [21]

    Bhatti S A, Cromer C L, Cooke W E 1981 Phys. Rev. A 24 161

    [22]

    He X H, Li B W, Zhang C X 1989 Acta Phys. Sin. 38 1717 (in Chinese) [何兴虹, 李白文, 张承修 1989 物理学报 38 1717]

    [23]

    Fabrikant I I 1986 J. Phys. B 19 1527

    [24]

    Bahrim C, Thumm U, Fabrikant I I 2001 J. Phys. B 34 L195

    [25]

    Bahrim C, Thumm U 2000 Phys. Rev. A 61 022722

    [26]

    Bendkowsky V, Butscher B, Nipper J, Shaffer J P, Löw R, Pfau T 2009 Nature 458 1005

    [27]

    Lorenzen C -J, Niemax K 1984 Z. phys. A 315 127

    [28]

    Overstreet K R, Schwettmann A, Tallant J, Booth D, Shaffer J P 2009 Nature Phys. 5 581

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  • Received Date:  09 December 2014
  • Accepted Date:  27 February 2015
  • Published Online:  05 July 2015

Potentials of long-range cesium Rydberg molecule

  • 1. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
Fund Project:  Project supported by the National Basic Research Program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grant Nos. 11274209, 61475090, 61378013, 61378039), and the Shanxi Scholarship Council of China (Grant No. 2014-009).

Abstract: Rydberg atom, with a large principal quantum number n, has big size, long lifetime, strong long-range interactions, and so on. These properties make Rydberg atoms potential candidate of quantum gate and single-photon source. Rydberg electron can interact with nearby ground-state atom, which is polarized by the Rydberg electron and is bound to the orbit of Rydberg electrons forming Rydberg molecule. As the kinetic energy of the Rydberg electron is very low, only the lowest partial waves will contribute to the molecular potential.#br#In this paper, the low electron-atom scattering with the semi-classical approximation is introduced, and the pseudopotential of interaction between Rydberg electron and ground-state atom is used to describe the long-range Rydberg molecular potential. Molecular potential curves for cesium (nS, n=30-60) are plotted according to the results of numerical computation, from which the outermost potential depth De and the equilibrium distance r0 of long-range cesium Rydberg molecule are deduced. Potential curves of cesium Rydberg molecules are consistent with the distribution curves in radial probability densities of cesium Rydberg electrons. Dependences of De and r0 on the principal quantum number n are investigated, this has an important role for the experimental measurements. The size of a Rydberg molecule depends on the equilibrium distance r0 and is proportional to the square of effective principal quantum number (n-δ )2. The calculated outermost potential depth De of Rydberg molecule becomes smaller with the increase of principal quantum number n. Rydberg molecule is very sensitive to the external field and can be used to measure and monitor weak signals.

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