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A molecular hydrogen ion HD+, composed of a proton, a deuteron, and an electron, has a rich set of rovibrational transitions that can be theoretically calculated and experimentally measured precisely. Currently, the relative accuracy of the rovibrational transition frequencies of the HD+ molecular ions has reached the order of 10-12. By comparing experimental measurements and theoretical calculations of the HD+ rovibrational spectrum, the precise determination of the proton-electron mass ratio, the testing of QED (quantum electrodynamics) theory, and the exploration of new physics beyond the standard model can be achieved. The HD+ rovibrational spectrum experiment has achieved the highest accuracy in measuring proton-electron mass ratio, with an accuracy of 20 ppt. This article comprehensively introduces the current state of research on HD+ rovibrational spectroscopy, detailing the experimental method of the high-precision rovibrational spectroscopic measurement based on the sympathetic cooling of HD+ ions by laser-cooled Be+ ions. In section 2, the generation and trapping technique of both Be+ and HD+ ions are introduced. Three ion generation methods including electron impact, laser ablation and photoionization are also compared in this section. In section 3, we show the successful control of the kinetic energy of HD+ molecular ions through the sympathetic cooling, and the importance of laser frequency stabilization for sympathetic cooling of HD+ molecular ions. In section 4, two methods for preparing internal states of HD+ molecular ions, optical pumping and resonance enhanced threshold photoionization, are introduced. Both methods show the significant increase of population on the ground rovibrational state. In section 5, we introduce two methods for determining the number changes of HD+ molecular ions: secular excitation and molecular dynamic simulation. Both methods combined with resonance enhanced multiphoton dissociation can detect the rovibrational transitions of HD+ molecular ions. In section 6, the experimental setup and process for the rovibrational spectrum of HD+ molecular ions are given and the up-to-date results are shown. Finally, the paper is concluded with the summary of the techniques used in HD+ rovibrational spectroscopic measurements, the prospects of potential spectroscopic technologies for further improving frequency measurement precision, and the development of spectroscopic methods of different isotopic hydrogen molecular ions.
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Keywords:
- rovibrational spectroscopy /
- HD+ molecular ion /
- sympathetic cooling
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[1] Karr J P, Hilico L, Koelemeij J C, Korobov V 2016 Phys. Rev. A 94 050501
[2] Colbourn E A, Bunker P R 1976 J. Mol. Spectrosc 63 155
[3] Korobov V I, Karr J P 2021 Phys. Rev. A 104 032806
[4] Korobov V I 2022 Phys. Part. Nuclei 53 1
[5] Yan Z C, Zhang J Y 2004 J. Phys. B: At. Mol. Opt. Phys. 37 1055
[6] Ye N, Yan Z C 2014 Phys. Rev. A 90 032516
[7] Aznabayev D T, Bekbaev A K, Korobov V I 2019 Phys. Rev. A 99 012501
[8] Bakalov D, Korobov V I, Schiller S 2006 Phys. Rev. Lett. 97 243001
[9] Haidar M, Korobov V I, Hilico L, Karr J P 2022 Phys. Rev. A 106 042815
[10] Zhong Z X, Zhang P P, Yan Z C, Shi T Y 2012 Phys. Rev. A 86 064502
[11] Zhong Z X, Zhou W P, Mei X S 2018 Phys. Rev. A 98 032502
[12] Korobov V I, Karr J P, Haidar M, Zhong Z X 2020 Phys. Rev. A 102 022804
[13] Wing W H, Ruff G A, Lamb Jr W E, Spezeski J J 1976 Phys. Rev. Lett. 36 1488
[14] Koelemeij J C J, Roth B, Wicht A, Ernsting I, Schiller S 2007 Phys. Rev. Lett. 98 173002
[15] Bressel U, Borodin A, Shen J, Hansen M G, Ernsting I, Schiller S 2012 Phys. Rev. Lett. 108 18 183003
[16] Alighanbari S, Hansen M G, Korobov V I, Schiller S 2018 Nat. Phys. 14 555
[17] Alighanbari S, Giri G S, Constantin F L, Korobov V I, Schiller S 2020 Nature 581 152
[18] Kortunov I V, Alighanbari S, Hansen M G, Giri G, Korobov V I, Schiller S 2021 Nat. Phys. 17 569
[19] Alighanbari S, Kortunov I V, Giri G S, Schiller S 2023 Nat. Phys. 19 1263
[20] Biesheuvel J, Karr J P, Hilico L, Eikema K, Ubachs W, Koelemeij J 2016 Nat. Commun. 7 10385
[21] Patra S, Germann M, Karr J P, Haidar M, Hilico L, Korobov V I, Cozijn F M J, Eikema K S E, Ubachs W, Koelemeij J C J 2020 Science 369 1238
[22] Sturm S, Köhler F, Zatorski J, Wagner A, Harman Z, Werth G, Quint W, Keitel C H, Blaum K 2014 Nature 506 467
[23] Heiße F, Rau S, Köhler-Langes F, Quint W, Werth G, Sturm S, Blaum K 2019 Phys. Rev. A 100 022518
[24] Hori M, Aghai-Khozani H, Sótér A, Barna D, Dax A, Hayano R, Kobayashi T, Murakami Y, Todoroki K, Yamada H, Horváth D, Venturelli L 2016 Science 354 610
[25] Borkowski M, Buchachenko A A, Ciuryo R, Julienne P S, Takahashi Y 2019 Sci. Rep. 9 14807
[26] Germann M, Patra S, Karr J P, Hilico L, Koelemeij J C J 2021 Phys. Rev. Res. 3 L022028
[27] Shi W, Jacobi J, Knopp H, Schippers S, Müller A 2003 Nucl. Instrum. Methods B 205 201
[28] Udrescu S M, Torres D A, Garcia Ruiz R F 2024 Phys. Rev. Res. 6 013128
[29] Leibrandt D R, Clark R J, Labaziewicz J, Antohi P, Bakr W, Brown K R, Chuang I L 2007 Phys. Rev. A 76 055403
[30] Thini F, Romans K L, Acharya B P, de Silva A H N C, Compton K, Foster K, Rischbieter C, Russ O, Sharma S, Dubey S, Fischer D 2020 J. Phys. B: At. Mol. Opt. Phys. 53 095201
[31] Benda J, Mašín Z 2021 Sci. Rep. 11 11686
[32] Hashimoto Y, Matsuoka L, Osaki H, Fukushima Y, Hasegawa S 2006 Jpn. J. Appl. Phys. 45 7108
[33] Li M, Zhang Y, Zhang Q Y, Bai W L, He S G, Peng W C, Tong X 2022 J. Phys. B: At. Mol. Opt. Phys. 55 035002
[34] Wahnschaffe M 2016 Ph.D. Dissertation (Hannover: Gottfried Wilhelm Leibniz University)
[35] Zhang Y, Zhang Q Y, Bai W L, Peng W C, He S G, Tong X 2023 Chinese J. Phys. 84 164
[36] Roth B, Blythe P, Wenz H, Daerr H, Schiller S 2006 Phys. Rev. A 73 042712
[37] Leibfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[38] Blythe P, Roth B, Fröhlich U, Wenz H, Schiller S 2005 Phys. Rev. Lett. 95 183002
[39] Carollo R A, Lane D A, Kleiner E K, Kyaw P A, Teng C C, Ou C Y, Qiao S, Hanneke D 2017 Opt. Express 25 7220
[40] Wellers C, Schenkel M R, Giri G S, Brown K R, Schiller S 2022 Mol. Phys. 120 e2001599
[41] Okada K, Wada M, Nakamura T, Iida R, Ohtani S, Tanaka J-i, Kawakami H, Katayama I 1998 J. Phys. Soc. Jpn. 67 3073
[42] Wu Q, Filzinger M, Shi Y, Wang Z, Zhang J 2021 Rev. Sci. Instrum. 92 063201
[43] Li Z, Li L, Hua X, Tong X 2024 J. Appl. Phys. 135 144402
[44] Li L, Li Z, Hua X, Tong X 2024 J. Phys. D: Appl. Phys. 57 315205
[45] Buica G, Nakajima T 2008 J. Quant. Spectrosc. Radiat. Transfer 109 107
[46] Tang X, Bachau H 1993 J. Phys. B: At. Mol. Opt. Phys. 26 75
[47] Wolf S, Studer D, Wendt K, Schmidt-Kaler F 2018 Appl. Phys. B 124 30
[48] Zhang Y, Zhang Q Y, Bai W L, Ao Z Y, Peng W C, He S G, Tong X 2023 Phys. Rev. A 107 043101
[49] Chandler D W, Thorne L R 1986 J. Chem. Phys. 85 1733
[50] Buck J D, Robie D C, Hickman A P, Bamford D J, Bischel W K 1989 Phys. Rev. A 39 3932
[51] Trimby E, Hirzler H, Fürst H, Safavi-Naini A, Gerritsma R, Lous R S 2022 New J. Phys. 24 035004
[52] Wayne M I, Bergquist J C, Bollinger J J, Wineland D J 1995 Phys. Scr. 1995 106
[53] Larson D J, Bergquist J C, Bollinger J J, Itano W M, Wineland D J 1986 Phys. Rev. Lett. 57 70
[54] Bohman M, Grunhofer V, Smorra C, Wiesinger M, Will C, Borchert M J, Devlin J A, Erlewein S, Fleck M, Gavranovic S, Harrington J, Latacz B, Mooser A, Popper D, Wursten E, Blaum K, Matsuda Y, Ospelkaus C, Quint W, Walz J, Ulmer S, Collaboration B 2021 Nature 596 514
[55] Karl R, Yin Y, Willitsch S 2024 Mol. Phys. 122 2199099
[56] Li M, Zhang Y, Zhang Q Y, Bai W L, He S G, Peng W C, Tong X 2023 Chin. Phys. B 32 036402
[57] Cozijn F M J, Biesheuvel J, Flores A S, Ubachs W, Blume G, Wicht A, Paschke K, Erbert G, Koelemeij J C J 2013 Opt. Lett. 38 13 2370
[58] King S A, Leopold T, Thekkeppatt P, Schmidt P O 2018 Appl. Phys. B 124 214
[59] Ohmae N, Katori H 2019 Rev. Sci. Instrum. 90 063201
[60] Vasilyev S, Nevsky A, Ernsting I, Hansen M, Shen J, Schiller S 2011 Appl. Phys. B 103 27
[61] Lo H Y, Alonso J, Kienzler D, Keitch B C, de Clercq L E, Negnevitsky V, Home J P 2014 Appl. Phys. B 114 17
[62] Schnitzler H, Fröhlich U, Boley T K W, Clemen A E M, Mlynek J, Peters A, Schiller S 2002 Appl. Opt. 41 7000
[63] Wilson A C, Ospelkaus C, VanDevender A P, Mlynek J A, Brown K R, Leibfried D, Wineland D J 2011 Appl. Phys. B 105 741
[64] Ahmadi M, Alves B X R, Baker C J, Bertsche W, Butler E, Capra A, Carruth C, Cesar C L, Charlton M, Cohen S, Collister R, Eriksson S, Evans A, Evetts N, Fajans J, Friesen T, Fujiwara M C, Gill D R, Gutierrez A, Hangst J S, Hardy W N, Hayden M E, Isaac C A, Ishida A, Johnson M A, Jones S A, Jonsell S, Kurchaninov L, Madsen N, Mathers M, Maxwell D, McKenna J T K, Menary S, Michan J M, Momose T, Munich J J, Nolan P, Olchanski K, Olin A, Pusa P, Rasmussen C Ø, Robicheaux F, Sacramento R L, Sameed M, Sarid E, Silveira D M, Stracka S, Stutter G, So C, Tharp T D, Thompson J E, Thompson R I, van der Werf D P, Wurtele J S 2017 Nature 541 506
[65] Kraus B, Dawel F, Hannig S, Kramer J, Nauk C, Schmidt P O 2022 Opt. Express 30 44992
[66] Cook E C, Vira A D, Patterson C, Livernois E, Williams W D 2018 Phys. Rev. Lett. 121 053001
[67] Drever R W P, Hall J L, Kowalski F V, Hough J, Ford G M, Munley A J, Ward H 1983 Appl. Phys. B 31 97
[68] Bai W L, Peng W C, Zhang Q Y, Wang C, Ao Z Y, Tong X 2024 Chinese J. Phys. 89 1500
[69] Hirota A, Igosawa R, Kimura N, Kuma S, Chartkunchand K C, Mishra P M, Lindley M, Yamaguchi T, Nakano Y, Azuma T 2020 Phys. Rev. A 102 023119
[70] Windberger A, Schwarz M, Versolato O O, Baumann T, Bekker H, Schmöger L, Hansen A K, Gingell A D, Klosowski L, Kristensen S, Schmidt P O, Ullrich J, Drewsen M, López-Urrutia J R C 2013 10th International Workshop on Non-Neutral Plasmas Greifswald, GERMANY, Aug 27-30 p250-256
[71] Pagano G, Hess P W, Kaplan H B, Tan W L, Richerme P, Becker P, Kyprianidis A, Zhang J, Birckelbaw E, Hernandez M R, Wu Y, Monroe C 2019 Quantum Sci. Technol 4 014004
[72] Kas M, Liévin J, Vaeck N, Loreau J 2020 31st International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC) Deauville, FRANCE, Jul 23-30
[73] Dörfler A D, Yurtsever E, Villarreal P, González-Lezana T, Gianturco F A, Willitsch S 2020 Phys. Rev. A 101 012706
[74] Schmidt J, Louvradoux T, Heinrich J, Sillitoe N, Simpson M, Karr J P, Hilico L 2020 Phys. Rev. Appl. 14 024053
[75] Tong X, Winney A H, Willitsch S 2010 Phys. Rev. Lett. 105 143001
[76] Lien C Y, Seck C M, Lin Y W, Nguyen J H V, Tabor D A, Odom B C 2014 Nat. Commun. 5 4783
[77] Schneider T, Roth B, Duncker H, Ernsting I, Schiller S 2010 Nat. Phys. 6 275
[78] Wu H, Mills M, West E, Heaven M C, Hudson E R 2021 Phys. Rev. A 104 063103
[79] Kilaj A, Käser S, Wang J, Straňák P, Schwilk M, Xu L, von Lilienfeld O A, Küpper J, Meuwly M, Willitsch S 2023 Phys. Chem. Chem. Phys 25 13933
[80] Calvin A, Eierman S, Peng Z, Brzeczek M, Satterthwaite L, Patterson D 2023 Nature 621 295
[81] Moreno J, Schmid F, Weitenberg J, Karshenboim S G, Hänsch T W, Udem T, Ozawa A 2023 Eur. Phys. J. D 77 1
[82] Okada K, Ichikawa M, Wada M, Schuessler H A 2015 Phys. Rev. Appl. 4 054009
[83] Germann M, Tong X, Willitsch S 2014 Nat. Phys. 10 820
[84] Tran V Q, Karr J P, Douillet A, Koelemeij J C J, Hilico L 2013 Phys. Rev. A 88 033421
[85] Karr J P 2014 J. Mol. Spectrosc 300 37
[86] Schiller S, Bakalov D, Korobov V I 2014 Phys. Rev. Lett. 113 023004
[87] Koelemeij J C J, Roth B, Schiller S 2007 Phys. Rev. A 76 023413
[88] Schmidt P O, Rosenband T, Langer C, Itano W M, Bergquist J C, Wineland D J 2005 Science 309 749
[89] Myers E G 2018 Phys. Rev. A 98 010101
[90] Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001
[91] Danev P, Bakalov D, Korobov V I, Schiller S 2021 Phys. Rev. A 103 012805
[92] Schenkel M, Alighanbari S, Schiller S 2024 Nat. Phys. 20 383
[93] Zammit M C, Charlton M, Jonsell S, Colgan J, Savage J S, Fursa D V, Kadyrov A S, Bray I, Forrey R C, Fontes C J, Leiding J A, Kilcrease D P, Hakel P, Timmermans E 2019 Phys. Rev. A 100 042709
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