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For a one-dimensional optical lattice clock built in the horizontal direction, when the stability and uncertainty of the system reach the order of 10–18 or more, the clock frequency shift caused by the quantum tunneling effect becomes not negligible. In the shallow optical lattice, the quantum tunneling effect will cause the clock transition spectrum to be significantly broadened. So, in this paper the quantum tunneling phenomenon in the shallow optical lattice is studied, laying a foundation for the evaluation of uncertainty of 87Sr atomic optical lattice clock system. In this experiment, on the platform of one-dimensional 87Sr atomic optical lattice clock, the narrow-linewidth 1S0(
$ \left|g \right\rangle $ )→3P0($ \left|e \right\rangle $ ) transition (that is, the clock transition) is excited by an ultra-stable and ultra-narrow linewidth 698 nm laser, and the distribution of strontium atoms in a specific quantum state is prepared. In the deep optical lattice, after the cold 87Sr atoms in preparation reach a$ \left|e,{n}_{z}=1 \right\rangle $ state, the lattice depth of the optical lattice is adiabatically reduced. Then, the carrier-sideband resolved clock transition spectral line is detected in the shallow optical lattice. The obvious splitting of the carrier spectral line is observed from the clock transition spectral line, which indicates that the strontium atom has an obvious quantum tunneling phenomenon between the adjacent lattice sites of the optical lattice. In addition, when the lattice potential lattice depth is reduced, owing to the incommensurability of lattice light wavelength (813 nm) and clock laser wavelength (698 nm), the tunneling of atoms between adjacent lattice points will lead to spin-orbit coupling effect. Owing to the exceptionally long lifetime (120(3) s) of 3P0 state, it can not only suppress the decoherence, but also reduce the atomic loss rate caused by spontaneous emission. This has a natural advantage for studying the spin-orbit coupling of fermions. Therefore, the understanding of quantum tunneling mechanism in optical lattice is not only conducive to improving the uncertainty of the 87Sr atomic optical lattice clock, but also lays the foundation for observing the spin-orbit coupling effect of fermions on this platform.-
Keywords:
- optical lattice /
- clock transition spectrum /
- quantum state /
- tunneling phenomenon
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[19] Kolkowitz S, Bromley S L, Bothwell T, Wall M L, Ye J 2017 Nature 542 66
Google Scholar
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Google Scholar
[21] Van Hove L 1953 Phys. Rev. 89 1189
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Lu X T, Li T, Kong D H, Wang Y B, Chang H 2019 Acta Phys. Sin. 68 233401
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-
图 1 隧穿速率J随
$ {U}_{z}/{E}_{r} $ 的变化关系Figure 1. Variation of tunneling rate J with
$ {U}_{z}/{E}_{r} $ .
图 2 实验装置简图. 其中HR为高反镜, CL为凸透镜, GP为格兰-泰勒棱镜, PBS为偏振分光棱镜, PMF为保偏光纤, FNC为相位噪声抑制系统, AOM为声光调制器, PMT为光电倍增管, ULE为超稳光学参考腔, DAQ为数据采集卡, VVA为压控衰减器, AFG为信号源, MS为微波开关
Figure 2. Experimental setup. HR, high-reflection mirror; CL, convex lens; GP, Gran Taylor prism; PBS, polarization splitting prism; PMF, polarization maintaining fiber; FNC, phase noise cancellation system; AOM, acoustic-optic modulator; PMT, photomultiplier tube; ULE, ultra-stable optical reference cavity; DAQ, data acquisition card; VVA, voltage variable attenuator; AFG, signal source; MS, microwave switch.
图 3 载波-边带可分辨的钟跃迁谱线
Figure 3. Carrier-sideband resolved clock transition spectra.
图 4 (a)锶原子能级图; (b)态制备及激发态钟跃迁谱线探测时序图
Figure 4. (a) Simplified level scheme of strontium; (b) state preparation and excited state transition spectrum detection clock sequence diagram.
图 5 载波-边带可分辨钟跃迁谱线 (a)原子初态在
$ \left|e, {n}_{z}=0 \right\rangle $ 态; (b) 原子初态在$ \left|e, {n}_{z}=1 \right\rangle $ Figure 5. Carrier-sideband resolved clock transition spectra with: (a)Atoms in
$ \left|e, {n}_{z}=0 \right\rangle $ ; (b) atoms in$ \left|e, {n}_{z}=1 \right\rangle $ .
图 6 在浅晶格中, 原子初态在
$ \left|e, {n}_{z}=1 \right\rangle $ 态的 (a)载波-边带可分辨钟跃迁谱线; (b)钟跃迁载波谱线.Figure 6. In shallow lattice, the atoms in
$ \left|e, {n}_{z}=1 \right\rangle $ state: (a) carrier-sideband resolved clock transition spectra; (b) carrier clock transition spectrum. -
[1] Bloom B J, Nicholson T L, Williams J R, Campbell S L, Bishof M, Zhang X, Zhang W, Bromley S L, Ye J 2014 Nature 506 71
Google Scholar
[2] Oelker E, R. Huston B, Kennedy C J, Sonderhouse L, Bothwell T, Goban A, Kedar D, Sanner C, Robinson J M, Marti G E, Legero T, Giunta M, Holzwarth R, Riehle R, Sterr U, Ye J 2019 Nat. Photon. 13 714
Google Scholar
[3] Huntemann N, Sanner C, Lipphardt B, Tamm C, Peik E 2016 Phys. Rev. Lett. 116 063001
Google Scholar
[4] Brewer S M, Chen J S, Hankin A M 2019 Phys. Rev. Lett. 123 033201
Google Scholar
[5] McGrew W F, Zhang X, Fasano R J, Schäffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, Yoon T H, Ludlow A D 2018 Nature 564 87
Google Scholar
[6] Hinkley N, Sherman J A, Phillips N B, Schioppo M, Lemke N D, Beloy K, Pizzocaro M, Oates C W, Ludlow A D 2013 Science 341 1215
Google Scholar
[7] Ushijima I, Takamoto M, Das M, Ohkubo T, Katori H 2015 Nat. Photon. 9 185
Google Scholar
[8] Campbell S L, Hutson R B, Marti G E, Goban A, Oppong N D, Mcally R L, Sonderhouse L, Robinson J M, Zhang W, Bloom B J, Ye J 2017 Science 358 90
Google Scholar
[9] Safronova M S, Budker D, DeMille D, Kimball D F J, Derevianko A, Clark C W 2018 Rev. Mod. Phys. 90 025008
Google Scholar
[10] Huntemann N, Lipphardt B, Tamm C, Gerginov V, Weyers S, Peik E 2014 Phys. Rev. Lett. 113 210802
Google Scholar
[11] Chou C W, Hume D B, Rosenband T, Wineland D J 2010 Science 329 1630
Google Scholar
[12] Kolkowitz S, Pikovski I, Langellier N, Lukin M D, Ye J 2016 Phys. Rev. D 94 124043
Google Scholar
[13] Sanner C, Huntemann N, Lange R, Tamm C, Peik E, Safronova M S, Porsev S G 2019 Nature 567 204
Google Scholar
[14] Roberts B M, Blewitt G, Dailey C, Murphy M, Pospelov M, Rollings A, Sherman J, Williams W, Derevianko A 2017 Nat. Commun. 8 1195
Google Scholar
[15] H Lignier, C Sias, D Ciampini, Y Singh, A Zenesini, O Morsch 2007 Phys. Rev. Lett. 99 220403
Google Scholar
[16] Grossmann F, Dittrich T, Jung P, Hänggi P 1991 Phys. Rev. Lett. 67 516
Google Scholar
[17] Lemonde P, Wolf P 2005 Phys. Rev. A 72 033409
Google Scholar
[18] Beloy K, Bodine M I, Bothwell T, Brewer S M, Zhang X 2021 Nature 591 564
Google Scholar
[19] Kolkowitz S, Bromley S L, Bothwell T, Wall M L, Ye J 2017 Nature 542 66
Google Scholar
[20] Bromley S L, Kolkowitz S, Bothwell T, Kedar D, Safavi-Naini A, Wall M L, Salomon C, Rey A M, Ye J 2018 Nat. Phys. 14 399
Google Scholar
[21] Van Hove L 1953 Phys. Rev. 89 1189
Google Scholar
[22] Kim P, Odom T W, Huang J L, Lieber C M 1999 Phys. Rev. Lett. 82 1225
Google Scholar
[23] Zwerger W 2003 J. Opt. B.:Quantum Semiclass. Opt. 5 S9
Google Scholar
[24] Wall M L, Koller A P, Li S, Zhang X, Cooper N R, Ye J 2016 Phys. Rev. Lett. 116 035301
Google Scholar
[25] 卢晓同, 李婷, 孔德欢, 王叶兵, 常宏 2019 68 233401
Google Scholar
Lu X T, Li T, Kong D H, Wang Y B, Chang H 2019 Acta Phys. Sin. 68 233401
Google Scholar
[26] Lu X T, Yin M J, Li T, Wang Y B, Chang H 2020 Appl. Sci. 10 1440
Google Scholar
[27] Wang Y B, Yin M J, Ren J, Xu Q F, Lu B Q, Han J X, Guo Y, Chang H 2018 Chin. Phys. B 27 023701
Google Scholar
[28] Blatt S, Thomsen J W, CaMpbell G K, Ludlow A D, Swallows M D, Martin M J 2009 Phys. Rev. A 80 3590
[29] Yin M J, Wang T, Lu X T, Li T, Xia J J, Zhang X F, Chang H 2022 Phys. Rev. Lett. 128 073603
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